Daily Papers

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

Large, general-purpose robotic policies trained on diverse demonstration datasets have been shown to be remarkably effective both for controlling a variety of robots in a range of different scenes, and for acquiring broad repertoires of manipulation skills. However, the data that such policies are trained on is generally of mixed quality -- not only are human-collected demonstrations unlikely to perform the task perfectly, but the larger the dataset is, the harder it is to curate only the highest quality examples. It also remains unclear how optimal data from one embodiment is for training on another embodiment. In this paper, we present a general and broadly applicable approach that enhances the performance of such generalist robot policies at deployment time by re-ranking their actions according to a value function learned via offline RL. This approach, which we call Value-Guided Policy Steering (V-GPS), is compatible with a wide range of different generalist policies, without needing to fine-tune or even access the weights of the policy. We show that the same value function can improve the performance of five different state-of-the-art policies with different architectures, even though they were trained on distinct datasets, attaining consistent performance improvement on multiple robotic platforms across a total of 12 tasks. Code and videos can be found at: https://nakamotoo.github.io/V-GPS

We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings. Experiments benchmark our method against other Bayesian optimization baselines on functional optimization tasks involving partial differential equations of physical systems, demonstrating better sample efficiency and significant performance gains.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

Despite recent progress made by large language models in code generation, they still struggle with programs that meet complex requirements. Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program. Yet, planning deep-inside requirements in advance can be challenging, and the tests need to be accurate to accomplish self-improvement. To this end, we propose FunCoder, a code generation framework incorporating the divide-and-conquer strategy with functional consensus. Specifically, FunCoder recursively branches off sub-functions as smaller goals during code generation, represented by a tree hierarchy. These sub-functions are then composited to attain more complex objectives. Additionally, we designate functions via a consensus formed by identifying similarities in program behavior, mitigating error propagation. FunCoder outperforms state-of-the-art methods by +9.8% on average in HumanEval, MBPP, xCodeEval and MATH with GPT-3.5 and GPT-4. Moreover, our method demonstrates superiority on smaller models: With FunCoder, StableCode-3b surpasses GPT-3.5 by +18.6% and achieves 97.7% of GPT-4's performance on HumanEval. Further analysis reveals that our proposed dynamic function decomposition is capable of handling complex requirements, and the functional consensus prevails over self-testing in correctness evaluation.

Mobile devices continuously interact with cellular base stations, generating massive volumes of signaling records that provide broad coverage for understanding human mobility. However, such records offer only coarse location cues (e.g., serving-cell identifiers) and therefore limit their direct use in applications that require high-precision GPS trajectories. This paper studies the Sig2GPS problem: reconstructing GPS trajectories from cellular signaling. Inspired by domain experts often lay the signaling trace on the map and sketch the corresponding GPS route, unlike conventional solutions that rely on complex multi-stage engineering pipelines or regress coordinates, Sig2GPS is reframed as an image-to-video generation task that directly operates in the map-visual domain: signaling traces are rendered on a map, and a video generation model is trained to draw a continuous GPS path. To support this paradigm, a paired signaling-to-trajectory video dataset is constructed to fine-tune an open-source video model, and a trajectory-aware reinforcement learning-based optimization method is introduced to improve generation fidelity via rewards. Experiments on large-scale real-world datasets show substantial improvements over strong engineered and learning-based baselines, while additional results on next GPS prediction indicate scalability and cross-city transferability. Overall, these results suggest that map-visual video generation provides a practical interface for trajectory data mining by enabling direct generation and refinement of continuous paths under map constraints.

We propose a unified framework to study policy evaluation (PE) and the associated temporal difference (TD) methods for reinforcement learning in continuous time and space. We show that PE is equivalent to maintaining the martingale condition of a process. From this perspective, we find that the mean--square TD error approximates the quadratic variation of the martingale and thus is not a suitable objective for PE. We present two methods to use the martingale characterization for designing PE algorithms. The first one minimizes a "martingale loss function", whose solution is proved to be the best approximation of the true value function in the mean--square sense. This method interprets the classical gradient Monte-Carlo algorithm. The second method is based on a system of equations called the "martingale orthogonality conditions" with test functions. Solving these equations in different ways recovers various classical TD algorithms, such as TD(lambda), LSTD, and GTD. Different choices of test functions determine in what sense the resulting solutions approximate the true value function. Moreover, we prove that any convergent time-discretized algorithm converges to its continuous-time counterpart as the mesh size goes to zero, and we provide the convergence rate. We demonstrate the theoretical results and corresponding algorithms with numerical experiments and applications.

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

Computing a Gaussian process (GP) posterior has a computational cost cubical in the number of historical points. A reformulation of the same GP posterior highlights that this complexity mainly depends on how many unique historical points are considered. This can have important implication in active learning settings, where the set of historical points is constructed sequentially by the learner. We show that sequential black-box optimization based on GPs (GP-Opt) can be made efficient by sticking to a candidate solution for multiple evaluation steps and switch only when necessary. Limiting the number of switches also limits the number of unique points in the history of the GP. Thus, the efficient GP reformulation can be used to exactly and cheaply compute the posteriors required to run the GP-Opt algorithms. This approach is especially useful in real-world applications of GP-Opt with high switch costs (e.g. switching chemicals in wet labs, data/model loading in hyperparameter optimization). As examples of this meta-approach, we modify two well-established GP-Opt algorithms, GP-UCB and GP-EI, to switch candidates as infrequently as possible adapting rules from batched GP-Opt. These versions preserve all the theoretical no-regret guarantees while improving practical aspects of the algorithms such as runtime, memory complexity, and the ability of batching candidates and evaluating them in parallel.

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

The vast majority of Reinforcement Learning methods is largely impacted by the computation effort and data requirements needed to obtain effective estimates of action-value functions, which in turn determine the quality of the overall performance and the sample-efficiency of the learning procedure. Typically, action-value functions are estimated through an iterative scheme that alternates the application of an empirical approximation of the Bellman operator and a subsequent projection step onto a considered function space. It has been observed that this scheme can be potentially generalized to carry out multiple iterations of the Bellman operator at once, benefiting the underlying learning algorithm. However, till now, it has been challenging to effectively implement this idea, especially in high-dimensional problems. In this paper, we introduce iterated Q-Network (i-QN), a novel principled approach that enables multiple consecutive Bellman updates by learning a tailored sequence of action-value functions where each serves as the target for the next. We show that i-QN is theoretically grounded and that it can be seamlessly used in value-based and actor-critic methods. We empirically demonstrate the advantages of i-QN in Atari 2600 games and MuJoCo continuous control problems.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

The next Point-of-Interest (POI) recommendation task aims to predict users' next destinations based on their historical movement data and plays a key role in location-based services and personalized applications. Accurate next POI recommendation depends on effectively modeling geographic information and POI transition relations, which are crucial for capturing spatial dependencies and user movement patterns. While Large Language Models (LLMs) exhibit strong capabilities in semantic understanding and contextual reasoning, applying them to spatial tasks like next POI recommendation remains challenging. First, the infrequent nature of specific GPS coordinates makes it difficult for LLMs to model precise spatial contexts. Second, the lack of knowledge about POI transitions limits their ability to capture potential POI-POI relationships. To address these issues, we propose GA-LLM (Geography-Aware Large Language Model), a novel framework that enhances LLMs with two specialized components. The Geographic Coordinate Injection Module (GCIM) transforms GPS coordinates into spatial representations using hierarchical and Fourier-based positional encoding, enabling the model to understand geographic features from multiple perspectives. The POI Alignment Module (PAM) incorporates POI transition relations into the LLM's semantic space, allowing it to infer global POI relationships and generalize to unseen POIs. Experiments on three real-world datasets demonstrate the state-of-the-art performance of GA-LLM.

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at https://github.com/sail-sg/autofd .

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

In this paper we propose two algorithms in the tabular setting and an algorithm for the function approximation setting for the Stochastic Shortest Path (SSP) problem. SSP problems form an important class of problems in Reinforcement Learning (RL), as other types of cost-criteria in RL can be formulated in the setting of SSP. We show asymptotic almost-sure convergence for all our algorithms. We observe superior performance of our tabular algorithms compared to other well-known convergent RL algorithms. We further observe reliable performance of our function approximation algorithm compared to other algorithms in the function approximation setting.

In this paper we propose a highly efficient and very accurate deep learning method for estimating the propagation pathloss from a point x (transmitter location) to any point y on a planar domain. For applications such as user-cell site association and device-to-device link scheduling, an accurate knowledge of the pathloss function for all pairs of transmitter-receiver locations is very important. Commonly used statistical models approximate the pathloss as a decaying function of the distance between transmitter and receiver. However, in realistic propagation environments characterized by the presence of buildings, street canyons, and objects at different heights, such radial-symmetric functions yield very misleading results. In this paper we show that properly designed and trained deep neural networks are able to learn how to estimate the pathloss function, given an urban environment, in a very accurate and computationally efficient manner. Our proposed method, termed RadioUNet, learns from a physical simulation dataset, and generates pathloss estimations that are very close to the simulations, but are much faster to compute for real-time applications. Moreover, we propose methods for transferring what was learned from simulations to real-life. Numerical results show that our method significantly outperforms previously proposed methods.

We present a general convergent class of reinforcement learning algorithms that is founded on two distinct principles: (1) mapping value estimates to a different space using arbitrary functions from a broad class, and (2) linearly decomposing the reward signal into multiple channels. The first principle enables incorporating specific properties into the value estimator that can enhance learning. The second principle, on the other hand, allows for the value function to be represented as a composition of multiple utility functions. This can be leveraged for various purposes, e.g. dealing with highly varying reward scales, incorporating a priori knowledge about the sources of reward, and ensemble learning. Combining the two principles yields a general blueprint for instantiating convergent algorithms by orchestrating diverse mapping functions over multiple reward channels. This blueprint generalizes and subsumes algorithms such as Q-Learning, Log Q-Learning, and Q-Decomposition. In addition, our convergence proof for this general class relaxes certain required assumptions in some of these algorithms. Based on our theory, we discuss several interesting configurations as special cases. Finally, to illustrate the potential of the design space that our theory opens up, we instantiate a particular algorithm and evaluate its performance on the Atari suite.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Accurate localization using visual information is a critical yet challenging task, especially in urban environments where nearby buildings and construction sites significantly degrade GNSS (Global Navigation Satellite System) signal quality. This issue underscores the importance of visual localization techniques in scenarios where GNSS signals are unreliable. This paper proposes U-ViLAR, a novel uncertainty-aware visual localization framework designed to address these challenges while enabling adaptive localization using high-definition (HD) maps or navigation maps. Specifically, our method first extracts features from the input visual data and maps them into Bird's-Eye-View (BEV) space to enhance spatial consistency with the map input. Subsequently, we introduce: a) Perceptual Uncertainty-guided Association, which mitigates errors caused by perception uncertainty, and b) Localization Uncertainty-guided Registration, which reduces errors introduced by localization uncertainty. By effectively balancing the coarse-grained large-scale localization capability of association with the fine-grained precise localization capability of registration, our approach achieves robust and accurate localization. Experimental results demonstrate that our method achieves state-of-the-art performance across multiple localization tasks. Furthermore, our model has undergone rigorous testing on large-scale autonomous driving fleets and has demonstrated stable performance in various challenging urban scenarios.

Large Language Models (LLMs) are increasingly deployed in applications that interact with the physical world, such as navigation, robotics, or mapping, making robust geospatial reasoning a critical capability. Despite that, LLMs' ability to reason about GPS coordinates and real-world geography remains underexplored. We introduce GPSBench, a dataset of 57,800 samples across 17 tasks for evaluating geospatial reasoning in LLMs, spanning geometric coordinate operations (e.g., distance and bearing computation) and reasoning that integrates coordinates with world knowledge. Focusing on intrinsic model capabilities rather than tool use, we evaluate 14 state-of-the-art LLMs and find that GPS reasoning remains challenging, with substantial variation across tasks: models are generally more reliable at real-world geographic reasoning than at geometric computations. Geographic knowledge degrades hierarchically, with strong country-level performance but weak city-level localization, while robustness to coordinate noise suggests genuine coordinate understanding rather than memorization. We further show that GPS-coordinate augmentation can improve in downstream geospatial tasks, and that finetuning induces trade-offs between gains in geometric computation and degradation in world knowledge. Our dataset and reproducible code are available at https://github.com/joey234/gpsbench

Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, largescale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers the potential to overcome this limitation by embedding data into exponentially large Hilbert spaces, capturing complex correlations that remain inaccessible to classical computing approaches. In this paper, we propose a Distributed Quantum Gaussian Process (DQGP) method in a multiagent setting to enhance modeling capabilities and scalability. To address the challenging non-Euclidean optimization problem, we develop a Distributed consensus Riemannian Alternating Direction Method of Multipliers (DR-ADMM) algorithm that aggregates local agent models into a global model. We evaluate the efficacy of our method through numerical experiments conducted on a quantum simulator in classical hardware. We use real-world, non-stationary elevation datasets of NASA's Shuttle Radar Topography Mission and synthetic datasets generated by Quantum Gaussian Processes. Beyond modeling advantages, our framework highlights potential computational speedups that quantum hardware may provide, particularly in Gaussian processes and distributed optimization.

While multitask representation learning has become a popular approach in reinforcement learning (RL) to boost the sample efficiency, the theoretical understanding of why and how it works is still limited. Most previous analytical works could only assume that the representation function is already known to the agent or from linear function class, since analyzing general function class representation encounters non-trivial technical obstacles such as generalization guarantee, formulation of confidence bound in abstract function space, etc. However, linear-case analysis heavily relies on the particularity of linear function class, while real-world practice usually adopts general non-linear representation functions like neural networks. This significantly reduces its applicability. In this work, we extend the analysis to general function class representations. Specifically, we consider an agent playing M contextual bandits (or MDPs) concurrently and extracting a shared representation function phi from a specific function class Phi using our proposed Generalized Functional Upper Confidence Bound algorithm (GFUCB). We theoretically validate the benefit of multitask representation learning within general function class for bandits and linear MDP for the first time. Lastly, we conduct experiments to demonstrate the effectiveness of our algorithm with neural net representation.

In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of Hukuhara difference between sets, in order to compensate the lack of "inverse" operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. While proving the well-posedness of a class of set-valued BSDEs, we shall also address some fundamental issues regarding generalized Aumann-Itô integrals, especially when it is connected to the martingale representation theorem. In particular, we propose some necessary extensions of the integral that can be used to represent set-valued martingales with non-singleton initial values. This extension turns out to be essential for the study of set-valued BSDEs.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods, a simply fast-computed function resembling the "complete" test function for the physical model. Also we adopt a simplified model of an eclipsing binary at a circular orbit assuming spherical components with an uniform brightness distribution. This model resembles more advanced models in a sense of correlated parameter estimates due to a similar topology of the test function. Such a model may be applied to detached Algol-type systems, where the tidal distortion of components is negligible.

Large language models (LLMs) have recently shown tremendous promise in serving as the backbone to agentic systems, as demonstrated by their performance in multi-faceted, challenging benchmarks like SWE-Bench and Agent-Bench. However, to realize the true potential of LLMs as autonomous agents, they must learn to identify, call, and interact with external tools and application program interfaces (APIs) to complete complex tasks. These tasks together are termed function calling. Endowing LLMs with function calling abilities leads to a myriad of advantages, such as access to current and domain-specific information in databases and knowledge sources, and the ability to outsource tasks that can be reliably performed by tools, e.g., a Python interpreter or calculator. While there has been significant progress in function calling with LLMs, there is still a dearth of open models that perform on par with proprietary LLMs like GPT, Claude, and Gemini. Therefore, in this work, we introduce the GRANITE-20B-FUNCTIONCALLING model under an Apache 2.0 license. The model is trained using a multi-task training approach on seven fundamental tasks encompassed in function calling, those being Nested Function Calling, Function Chaining, Parallel Functions, Function Name Detection, Parameter-Value Pair Detection, Next-Best Function, and Response Generation. We present a comprehensive evaluation on multiple out-of-domain datasets comparing GRANITE-20B-FUNCTIONCALLING to more than 15 other best proprietary and open models. GRANITE-20B-FUNCTIONCALLING provides the best performance among all open models on the Berkeley Function Calling Leaderboard and fourth overall. As a result of the diverse tasks and datasets used for training our model, we show that GRANITE-20B-FUNCTIONCALLING has better generalizability on multiple tasks in seven different evaluation datasets.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

In this paper, we study the localization problem in dense urban settings. In such environments, Global Navigation Satellite Systems fail to provide good accuracy due to low likelihood of line-of-sight (LOS) links between the receiver (Rx) to be located and the satellites, due to the presence of obstacles like the buildings. Thus, one has to resort to other technologies, which can reliably operate under non-line-of-sight (NLOS) conditions. Recently, we proposed a Received Signal Strength (RSS) fingerprint and convolutional neural network-based algorithm, LocUNet, and demonstrated its state-of-the-art localization performance with respect to the widely adopted k-nearest neighbors (kNN) algorithm, and to state-of-the-art time of arrival (ToA) ranging-based methods. In the current work, we first recognize LocUNet's ability to learn the underlying prior distribution of the Rx position or Rx and transmitter (Tx) association preferences from the training data, and attribute its high performance to these. Conversely, we demonstrate that classical methods based on probabilistic approach, can greatly benefit from an appropriate incorporation of such prior information. Our studies also numerically prove LocUNet's close to optimal performance in many settings, by comparing it with the theoretically optimal formulations.

Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation has been extensively studied with optimal results achieved under certain assumptions, many works shift their interest to offline RL with non-linear function approximation. However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees. In this paper, we propose an oracle-efficient algorithm, dubbed Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI), for offline RL with non-linear function approximation. Our algorithmic design comprises three innovative components: (1) a variance-based weighted regression scheme that can be applied to a wide range of function classes, (2) a subroutine for variance estimation, and (3) a planning phase that utilizes a pessimistic value iteration approach. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation. Our work extends the previous instance-dependent results within simpler function classes, such as linear and differentiable function to a more general framework.

Autonomous driving has garnered significant attention for its potential to improve safety, traffic efficiency, and user convenience. However, the dynamic and complex nature of interactive driving poses significant challenges, including the need to navigate non-linear road geometries, handle dynamic obstacles, and meet stringent safety and comfort requirements. Traditional approaches, such as artificial potential fields (APF), often fall short in addressing these complexities independently, necessitating the development of integrated and adaptive frameworks. This paper presents a novel approach to autonomous vehicle navigation that integrates artificial potential fields, Frenet coordinates, and improved particle swarm optimization (IPSO). A dynamic risk field, adapted from traditional APF, is proposed to ensure interactive safety by quantifying risks and dynamically adjusting lane-changing intentions based on surrounding vehicle behavior. Frenet coordinates are utilized to simplify trajectory planning on non-straight roads, while an enhanced quintic polynomial trajectory generator ensures smooth and comfortable path transitions. Additionally, an IPSO algorithm optimizes trajectory selection in real time, balancing safety and user comfort within a feasible input range. The proposed framework is validated through extensive simulations and real-world scenarios, demonstrating its ability to navigate complex traffic environments, maintain safety margins, and generate smooth, dynamically feasible trajectories.

Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when the order v is large, and GPU-specific implementations are limited. We address the precision limitations of current numerical implementations while dramatically improving the runtime. We propose two novel algorithms for computing the logarithm of modified Bessel functions of the first and second kinds by computing intermediate values on a logarithmic scale. Our algorithms are robust and never have issues with underflows or overflows while having relative errors on the order of machine precision, even for inputs where existing libraries fail. In C++/CUDA, our algorithms have median and maximum speedups of 45x and 6150x for GPU and 17x and 3403x for CPU, respectively, over the ranges of inputs and third-party libraries tested. Compared to SciPy, the algorithms have median and maximum speedups of 77x and 300x for GPU and 35x and 98x for CPU, respectively, over the tested inputs. The ability to robustly compute a solution and the low relative errors allow us to fit von Mises-Fisher, vMF, distributions to high-dimensional neural network features. This is, e.g., relevant for uncertainty quantification in metric learning. We obtain image feature data by processing CIFAR10 training images with the convolutional layers of a pre-trained ResNet50. We successfully fit vMF distributions to 2048-, 8192-, and 32768-dimensional image feature data using our algorithms. Our approach provides fast and accurate results while existing implementations in SciPy and mpmath fail to fit successfully. Our approach is readily implementable on GPUs, and we provide a fast open-source implementation alongside this paper.

Value-based methods constitute a fundamental methodology in planning and deep reinforcement learning (RL). In this paper, we propose to exploit the underlying structures of the state-action value function, i.e., Q function, for both planning and deep RL. In particular, if the underlying system dynamics lead to some global structures of the Q function, one should be capable of inferring the function better by leveraging such structures. Specifically, we investigate the low-rank structure, which widely exists for big data matrices. We verify empirically the existence of low-rank Q functions in the context of control and deep RL tasks. As our key contribution, by leveraging Matrix Estimation (ME) techniques, we propose a general framework to exploit the underlying low-rank structure in Q functions. This leads to a more efficient planning procedure for classical control, and additionally, a simple scheme that can be applied to any value-based RL techniques to consistently achieve better performance on "low-rank" tasks. Extensive experiments on control tasks and Atari games confirm the efficacy of our approach. Code is available at https://github.com/YyzHarry/SV-RL.

We study how to improve large foundation vision-language-action (VLA) systems through online reinforcement learning (RL) in real-world settings. Central to this process is the value function, which provides learning signals to guide VLA learning from experience. In practice, the value function is estimated from trajectory fragments collected from different data sources, including historical policies and intermittent human interventions. Estimating the value function of current behavior quality from the mixture data is inherently an off-policy evaluation problem. However, prior work often adopts conservative on-policy estimation for stability, which avoids direct evaluation of the current high-capacity policy and limits learning effectiveness. In this paper, we propose ALOE, an action-level off-policy evaluation framework for VLA post-training. ALOE applies chunking-based temporal-difference bootstrapping to evaluate individual action sequences instead of predicting final task outcomes. This design improves effective credit assignment to critical action chunks under sparse rewards and supports stable policy improvement. We evaluate our method on three real-world manipulation tasks, including smartphone packing as a high-precision task, laundry folding as a long-horizon deformable-object task, and bimanual pick-and-place involving multi-object perception. Across all tasks, ALOE improves learning efficiency without compromising execution speed, showing that off-policy RL can be reintroduced in a reliable manner for real-world VLA post-training. Videos and additional materials are available at our project website.

Model-agnostic meta-reinforcement learning requires estimating the Hessian matrix of value functions. This is challenging from an implementation perspective, as repeatedly differentiating policy gradient estimates may lead to biased Hessian estimates. In this work, we provide a unifying framework for estimating higher-order derivatives of value functions, based on off-policy evaluation. Our framework interprets a number of prior approaches as special cases and elucidates the bias and variance trade-off of Hessian estimates. This framework also opens the door to a new family of estimates, which can be easily implemented with auto-differentiation libraries, and lead to performance gains in practice.

We present a novel stochastic variational Gaussian process (GP) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for GPs (CVTGP) is defined in terms of the GP prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent GP coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to O(M), enjoys numerical stability, and maintains O(M^3) time- and O(M^2) space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic GP inference methods.

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and κ-hop neighbor truncation under a form of correlation decay property, where κ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of Oleft(T^{-2/3}right). In the sample-based setting, we demonstrate that, with high probability, our algorithm requires mathcal{O}left(ε^{-3.5}right) samples to achieve an ε-FOSP with an approximation error of O(φ_0^{2κ}), where φ_0in (0,1). Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.

We describe the release of reference data towards a challenging long-term localisation and mapping benchmark based on the large-scale Oxford RobotCar Dataset. The release includes 72 traversals of a route through Oxford, UK, gathered in all illumination, weather and traffic conditions, and is representative of the conditions an autonomous vehicle would be expected to operate reliably in. Using post-processed raw GPS, IMU, and static GNSS base station recordings, we have produced a globally-consistent centimetre-accurate ground truth for the entire year-long duration of the dataset. Coupled with a planned online benchmarking service, we hope to enable quantitative evaluation and comparison of different localisation and mapping approaches focusing on long-term autonomy for road vehicles in urban environments challenged by changing weather.

In this paper, we investigate the problem of offline Preference-based Reinforcement Learning (PbRL) with human feedback where feedback is available in the form of preference between trajectory pairs rather than explicit rewards. Our proposed algorithm consists of two main steps: (1) estimate the implicit reward using Maximum Likelihood Estimation (MLE) with general function approximation from offline data and (2) solve a distributionally robust planning problem over a confidence set around the MLE. We consider the general reward setting where the reward can be defined over the whole trajectory and provide a novel guarantee that allows us to learn any target policy with a polynomial number of samples, as long as the target policy is covered by the offline data. This guarantee is the first of its kind with general function approximation. To measure the coverage of the target policy, we introduce a new single-policy concentrability coefficient, which can be upper bounded by the per-trajectory concentrability coefficient. We also establish lower bounds that highlight the necessity of such concentrability and the difference from standard RL, where state-action-wise rewards are directly observed. We further extend and analyze our algorithm when the feedback is given over action pairs.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Given sparse observations of buoy velocities, oceanographers are interested in reconstructing ocean currents away from the buoys and identifying divergences in a current vector field. As a first and modular step, we focus on the time-stationary case - for instance, by restricting to short time periods. Since we expect current velocity to be a continuous but highly non-linear function of spatial location, Gaussian processes (GPs) offer an attractive model. But we show that applying a GP with a standard stationary kernel directly to buoy data can struggle at both current reconstruction and divergence identification, due to some physically unrealistic prior assumptions. To better reflect known physical properties of currents, we propose to instead put a standard stationary kernel on the divergence and curl-free components of a vector field obtained through a Helmholtz decomposition. We show that, because this decomposition relates to the original vector field just via mixed partial derivatives, we can still perform inference given the original data with only a small constant multiple of additional computational expense. We illustrate the benefits of our method with theory and experiments on synthetic and real ocean data.

Systems based on artificial neural networks (ANNs) have achieved state-of-the-art results in many natural language processing tasks. Although ANNs do not require manually engineered features, ANNs have many hyperparameters to be optimized. The choice of hyperparameters significantly impacts models' performances. However, the ANN hyperparameters are typically chosen by manual, grid, or random search, which either requires expert experiences or is computationally expensive. Recent approaches based on Bayesian optimization using Gaussian processes (GPs) is a more systematic way to automatically pinpoint optimal or near-optimal machine learning hyperparameters. Using a previously published ANN model yielding state-of-the-art results for dialog act classification, we demonstrate that optimizing hyperparameters using GP further improves the results, and reduces the computational time by a factor of 4 compared to a random search. Therefore it is a useful technique for tuning ANN models to yield the best performances for natural language processing tasks.

The prediction of ship trajectories is a growing field of study in artificial intelligence. Traditional methods rely on the use of LSTM, GRU networks, and even Transformer architectures for the prediction of spatio-temporal series. This study proposes a viable alternative for predicting these trajectories using only GNSS positions. It considers this spatio-temporal problem as a natural language processing problem. The latitude/longitude coordinates of AIS messages are transformed into cell identifiers using the H3 index. Thanks to the pseudo-octal representation, it becomes easier for language models to learn the spatial hierarchy of the H3 index. The method is compared with a classical Kalman filter, widely used in the maritime domain, and introduces the Fr\'echet distance as the main evaluation metric. We show that it is possible to predict ship trajectories quite precisely up to 8 hours with 30 minutes of context. We demonstrate that this alternative works well enough to predict trajectories worldwide.

Image geolocalization, in which, traditionally, an AI model predicts the precise GPS coordinates of an image is a challenging task with many downstream applications. However, the user cannot utilize the model to further their knowledge other than the GPS coordinate; the model lacks an understanding of the location and the conversational ability to communicate with the user. In recent days, with tremendous progress of large multimodal models (LMMs) proprietary and open-source researchers have attempted to geolocalize images via LMMs. However, the issues remain unaddressed; beyond general tasks, for more specialized downstream tasks, one of which is geolocalization, LMMs struggle. In this work, we propose to solve this problem by introducing a conversational model GAEA that can provide information regarding the location of an image, as required by a user. No large-scale dataset enabling the training of such a model exists. Thus we propose a comprehensive dataset GAEA with 800K images and around 1.6M question answer pairs constructed by leveraging OpenStreetMap (OSM) attributes and geographical context clues. For quantitative evaluation, we propose a diverse benchmark comprising 4K image-text pairs to evaluate conversational capabilities equipped with diverse question types. We consider 11 state-of-the-art open-source and proprietary LMMs and demonstrate that GAEA significantly outperforms the best open-source model, LLaVA-OneVision by 25.69% and the best proprietary model, GPT-4o by 8.28%. Our dataset, model and codes are available

Utility functions or their equivalents (value functions, objective functions, loss functions, reward functions, preference orderings) are a central tool in most current machine learning systems. These mechanisms for defining goals and guiding optimization run into practical and conceptual difficulty when there are independent, multi-dimensional objectives that need to be pursued simultaneously and cannot be reduced to each other. Ethicists have proved several impossibility theorems that stem from this origin; those results appear to show that there is no way of formally specifying what it means for an outcome to be good for a population without violating strong human ethical intuitions (in such cases, the objective function is a social welfare function). We argue that this is a practical problem for any machine learning system (such as medical decision support systems or autonomous weapons) or rigidly rule-based bureaucracy that will make high stakes decisions about human lives: such systems should not use objective functions in the strict mathematical sense. We explore the alternative of using uncertain objectives, represented for instance as partially ordered preferences, or as probability distributions over total orders. We show that previously known impossibility theorems can be transformed into uncertainty theorems in both of those settings, and prove lower bounds on how much uncertainty is implied by the impossibility results. We close by proposing two conjectures about the relationship between uncertainty in objectives and severe unintended consequences from AI systems.

Worldwide Geo-localization aims to pinpoint the precise location of images taken anywhere on Earth. This task has considerable challenges due to immense variation in geographic landscapes. The image-to-image retrieval-based approaches fail to solve this problem on a global scale as it is not feasible to construct a large gallery of images covering the entire world. Instead, existing approaches divide the globe into discrete geographic cells, transforming the problem into a classification task. However, their performance is limited by the predefined classes and often results in inaccurate localizations when an image's location significantly deviates from its class center. To overcome these limitations, we propose GeoCLIP, a novel CLIP-inspired Image-to-GPS retrieval approach that enforces alignment between the image and its corresponding GPS locations. GeoCLIP's location encoder models the Earth as a continuous function by employing positional encoding through random Fourier features and constructing a hierarchical representation that captures information at varying resolutions to yield a semantically rich high-dimensional feature suitable to use even beyond geo-localization. To the best of our knowledge, this is the first work employing GPS encoding for geo-localization. We demonstrate the efficacy of our method via extensive experiments and ablations on benchmark datasets. We achieve competitive performance with just 20% of training data, highlighting its effectiveness even in limited-data settings. Furthermore, we qualitatively demonstrate geo-localization using a text query by leveraging CLIP backbone of our image encoder. The project webpage is available at: https://vicentevivan.github.io/GeoCLIP

The advent of autonomous agents is transforming interactions with Graphical User Interfaces (GUIs) by employing natural language as a powerful intermediary. Despite the predominance of Supervised Fine-Tuning (SFT) methods in current GUI agents for achieving spatial localization, these methods face substantial challenges due to their limited capacity to accurately perceive positional data. Existing strategies, such as reinforcement learning, often fail to assess positional accuracy effectively, thereby restricting their utility. In response, we introduce Location Preference Optimization (LPO), a novel approach that leverages locational data to optimize interaction preferences. LPO uses information entropy to predict interaction positions by focusing on zones rich in information. Besides, it further introduces a dynamic location reward function based on physical distance, reflecting the varying importance of interaction positions. Supported by Group Relative Preference Optimization (GRPO), LPO facilitates an extensive exploration of GUI environments and significantly enhances interaction precision. Comprehensive experiments demonstrate LPO's superior performance, achieving SOTA results across both offline benchmarks and real-world online evaluations. Our code will be made publicly available soon, at https://github.com/AIDC-AI/LPO.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

LLM-based function calling enables intelligent agents to interact with external tools and environments, yet autoregressive decoding imposes a fundamental latency bottleneck that limits real-time applications such as embodied intelligence, game AI, and interactive avatars (e.g., 10 Hz control frequency). We observe that function calling differs fundamentally from free-form text generation: structured outputs exhibit substantial token redundancy (delimiters, parameter names), and arguments exhibit weak causal dependencies. Crucially, these two properties must be exploited jointly to achieve real-time performance. We present SimpleTool, which introduces special tokens that serve a dual role: compressing low-entropy tokens (4-6x reduction) while acting as mode selectors that enable independent parallel generation of function name and arguments. This synergistic design achieves 3-6x end-to-end speedup (up to 9.6x) with only +8.2% parallelization overhead. Experiments on five benchmarks across Qwen-series models (0.5B-14B) demonstrate substantial speedup while maintaining competitive or improved accuracy. On Mobile Actions, ST-Qwen-0.5B outperforms Google's FunctionGemma in both accuracy and latency consistency. With quantization on consumer-grade GPU, SimpleTool achieves 61.2ms P50 latency, enabling 16 Hz real-time control at 4B model scale, bridging the gap between LLM function calling and latency-critical real-world deployment.

Cross-view geo-localization (CVGL) aims to establish spatial correspondences between images captured from significantly different viewpoints and constitutes a fundamental technique for visual localization in GNSS-denied environments. Nevertheless, CVGL remains challenging due to severe geometric asymmetry, texture inconsistency across imaging domains, and the progressive degradation of discriminative local information. Existing methods predominantly rely on spatial domain feature alignment, which is inherently sensitive to large scale viewpoint variations and local disturbances. To alleviate these limitations, this paper proposes the Spatial and Frequency Domain Enhancement Network (SFDE), which leverages complementary representations from spatial and frequency domains. SFDE adopts a three branch parallel architecture to model global semantic context, local geometric structure, and statistical stability in the frequency domain, respectively, thereby characterizing consistency across domains from the perspectives of scene topology, multiscale structural patterns, and frequency invariance. The resulting complementary features are jointly optimized in a unified embedding space via progressive enhancement and coupled constraints, enabling the learning of cross-view representations with consistency across multiple granularities. Comprehensive experiments show that SFDE achieves competitive performance and in many cases even surpasses state-of-the-art methods, while maintaining a lightweight and computationally efficient design. {Our code is available at https://github.com/Mashuaishuai669/SFDE

Geolocating images of a ground-level scene entails estimating the location on Earth where the picture was taken, in absence of GPS or other location metadata. Typically, methods are evaluated by measuring the Great Circle Distance (GCD) between a predicted location and ground truth. However, this measurement is limited because it only evaluates a single point, not estimates of regions or score heatmaps. This is especially important in applications to rural, wilderness and under-sampled areas, where finding the exact location may not be possible, and when used in aggregate systems that progressively narrow down locations. In this paper, we introduce a novel metric, Recall vs Area (RvA), which measures the accuracy of estimated distributions of locations. RvA treats image geolocation results similarly to document retrieval, measuring recall as a function of area: For a ranked list of (possibly non-contiguous) predicted regions, we measure the accumulated area required for the region to contain the ground truth coordinate. This produces a curve similar to a precision-recall curve, where "precision" is replaced by square kilometers area, allowing evaluation of performance for different downstream search area budgets. Following directly from this view of the problem, we then examine a simple ensembling approach to global-scale image geolocation, which incorporates information from multiple sources to help address domain shift, and can readily incorporate multiple models, attribute predictors, and data sources. We study its effectiveness by combining the geolocation models GeoEstimation and the current SOTA GeoCLIP, with attribute predictors based on ORNL LandScan and ESA-CCI Land Cover. We find significant improvements in image geolocation for areas that are under-represented in the training set, particularly non-urban areas, on both Im2GPS3k and Street View images.

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

Function calling is a core capability of large language models, essential for AI agents. Existing benchmarks such as the Berkeley Function Calling Leaderboard (BFCL), tau^2-Bench (arXiv:2506.07982), and ACEBench (arXiv:2501.12851) evaluate argument correctness but do not test adherence to format instructions embedded in parameter descriptions, such as enclosing values in double quotes or using ISO date formats. We introduce IFEval-FC, a benchmark inspired by IFEval (arXiv:2311.07911) that assesses precise instruction following in function calling. IFEval-FC encodes verifiable formats directly within JSON schema descriptions, for example specifying that a value must not contain punctuation. It includes 750 test cases, each consisting of a function with an embedded format for one of its input parameters and a corresponding user query. Evaluation is fully algorithmic, ensuring objectivity, reproducibility, and scalability. Our results show that even state-of-the-art proprietary models, including GPT-5 and Claude 4.1 Opus, frequently fail to follow basic formatting rules, highlighting a practical limitation for real-world agent systems. The complete codebase and data are publicly available at https://github.com/Skripkon/IFEval-FC.

The analysis of non-stationary time-series data requires insight into its local and global patterns with physical interpretability. However, traditional smoothing algorithms, such as B-splines, Savitzky-Golay filtering, and Empirical Mode Decomposition (EMD), lack the ability to perform parametric optimization with guaranteed continuity. In this paper, we propose Functional Continuous Decomposition (FCD), a JAX-accelerated framework that performs parametric, continuous optimization on a wide range of mathematical functions. By using Levenberg-Marquardt optimization to achieve up to C^1 continuous fitting, FCD transforms raw time-series data into M modes that capture different temporal patterns from short-term to long-term trends. Applications of FCD include physics, medicine, financial analysis, and machine learning, where it is commonly used for the analysis of signal temporal patterns, optimized parameters, derivatives, and integrals of decomposition. Furthermore, FCD can be applied for physical analysis and feature extraction with an average SRMSE of 0.735 per segment and a speed of 0.47s on full decomposition of 1,000 points. Finally, we demonstrate that a Convolutional Neural Network (CNN) enhanced with FCD features, such as optimized function values, parameters, and derivatives, achieved 16.8% faster convergence and 2.5% higher accuracy over a standard CNN.

In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The key innovation of our analysis is a novel notion called Gradient-Normalized Smoothness, which characterizes the maximum radius of a ball around the current point that yields a good relative approximation of the gradient field. Our theory establishes a natural intrinsic connection between Hessian approximation and the linearization of the gradient. Importantly, Gradient-Normalized Smoothness does not depend on the specific problem class of the objective functions, while effectively translating local information about the gradient field and Hessian approximation into the global behavior of the method. This new concept equips approximate second-order algorithms with universal global convergence guarantees, recovering state-of-the-art rates for functions with H\"older-continuous Hessians and third derivatives, quasi-self-concordant functions, as well as smooth classes in first-order optimization. These rates are achieved automatically and extend to broader classes, such as generalized self-concordant functions. We demonstrate direct applications of our results for global linear rates in logistic regression and softmax problems with approximate Hessians, as well as in non-convex optimization using Fisher and Gauss-Newton approximations.

Recent advances in cross-view geo-localization (CVGL) methods have shown strong potential for supporting unmanned aerial vehicle (UAV) navigation in GNSS-denied environments. However, existing work predominantly focuses on matching UAV views to onboard map tiles, which introduces an inherent trade-off between accuracy and storage overhead, and overlooks the importance of the UAV's heading during navigation. Moreover, the substantial discrepancies and varying overlaps in cross-view scenarios have been insufficiently considered, limiting their generalization to real-world scenarios. In this paper, we present Bearing-UAV, a purely vision-driven cross-view navigation method that jointly predicts UAV absolute location and heading from neighboring features, enabling accurate, lightweight, and robust navigation in the wild. Our method leverages global and local structural features and explicitly encodes relative spatial relationships, making it robust to cross-view variations, misalignment, and feature-sparse conditions. We also present Bearing-UAV-90k, a multi-city benchmark for evaluating cross-view localization and navigation. Extensive experiments show encouraging results that Bearing-UAV yields lower localization error than previous matching/retrieval paradigm across diverse terrains. Our code and dataset will be made publicly available.

We introduce and analyze distance preservation games (DPGs). In DPGs, agents express ideal distances to other agents and need to choose locations in the unit interval while preserving their ideal distances as closely as possible. We analyze the existence and computation of location profiles that are jump stable (i.e., no agent can benefit by moving to another location) or welfare optimal for DPGs, respectively. Specifically, we prove that there are DPGs without jump stable location profiles and identify important cases where such outcomes always exist and can be computed efficiently. Similarly, we show that finding welfare optimal location profiles is NP-complete and present approximation algorithms for finding solutions with social welfare close to optimal. Finally, we prove that DPGs have a price of anarchy of at most 2.

Verifiable delay functions have found a lot of applications in blockchain technology in recent times. Continuous verifiable delay functions are an improvement over the basic notion of VDFs with recursive capabilities. We are proposing the application of VDF for constructing more space time-efficient provers and simulators required for the iterative non-interactive zero-knowledge systems.

Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting the flexibility of data-driven discovery, while many deep-learning pipelines treat functions as fixed-grid vectors, ignoring inherent continuity. In this paper, we introduce Functional Attention with a Mixture-of-Experts (FAME), an end-to-end, fully data-driven framework for function-on-function regression. FAME forms continuous attention by coupling a bidirectional neural controlled differential equation with MoE-driven vector fields to capture intra-functional continuity, and further fuses change to inter-functional dependencies via multi-head cross attention. Extensive experiments on synthetic and real-world functional-regression benchmarks show that FAME achieves state-of-the-art accuracy, strong robustness to arbitrarily sampled discrete observations of functions.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

We show that the GPS tags contained in photo metadata provide a useful control signal for image generation. We train GPS-to-image models and use them for tasks that require a fine-grained understanding of how images vary within a city. In particular, we train a diffusion model to generate images conditioned on both GPS and text. The learned model generates images that capture the distinctive appearance of different neighborhoods, parks, and landmarks. We also extract 3D models from 2D GPS-to-image models through score distillation sampling, using GPS conditioning to constrain the appearance of the reconstruction from each viewpoint. Our evaluations suggest that our GPS-conditioned models successfully learn to generate images that vary based on location, and that GPS conditioning improves estimated 3D structure.

Integral reinforcement learning (IntRL) demands the precise computation of the utility function's integral at its policy evaluation (PEV) stage. This is achieved through quadrature rules, which are weighted sums of utility functions evaluated from state samples obtained in discrete time. Our research reveals a critical yet underexplored phenomenon: the choice of the computational method -- in this case, the quadrature rule -- can significantly impact control performance. This impact is traced back to the fact that computational errors introduced in the PEV stage can affect the policy iteration's convergence behavior, which in turn affects the learned controller. To elucidate how computation impacts control, we draw a parallel between IntRL's policy iteration and Newton's method applied to the Hamilton-Jacobi-Bellman equation. In this light, computational error in PEV manifests as an extra error term in each iteration of Newton's method, with its upper bound proportional to the computational error. Further, we demonstrate that when the utility function resides in a reproducing kernel Hilbert space (RKHS), the optimal quadrature is achievable by employing Bayesian quadrature with the RKHS-inducing kernel function. We prove that the local convergence rates for IntRL using the trapezoidal rule and Bayesian quadrature with a Mat\'ern kernel to be O(N^{-2}) and O(N^{-b}), where N is the number of evenly-spaced samples and b is the Mat\'ern kernel's smoothness parameter. These theoretical findings are finally validated by two canonical control tasks.

The integration of large language models (LLMs) with function calling has emerged as a crucial capability for enhancing their practical utility in real-world applications. However, effectively combining reasoning processes with accurate function execution remains a significant challenge. Traditional training approaches often struggle to balance the detailed reasoning steps with the precision of function calls, leading to suboptimal performance. To address these limitations, we introduce FunReason, a novel framework that enhances LLMs' function calling capabilities through an automated data refinement strategy and a Self-Refinement Multiscale Loss (SRML) approach. FunReason leverages LLMs' natural reasoning abilities to generate high-quality training examples, focusing on query parseability, reasoning coherence, and function call precision. The SRML approach dynamically balances the contribution of reasoning processes and function call accuracy during training, addressing the inherent trade-off between these two critical aspects. FunReason achieves performance comparable to GPT-4o while effectively mitigating catastrophic forgetting during fine-tuning. FunReason provides a comprehensive solution for enhancing LLMs' function calling capabilities by introducing a balanced training methodology and a data refinement pipeline. For code and dataset, please refer to our repository at GitHub https://github.com/BingguangHao/FunReason

Despite the significant advancements in pre-training methods for point cloud understanding, directly capturing intricate shape information from irregular point clouds without reliance on external data remains a formidable challenge. To address this problem, we propose GPSFormer, an innovative Global Perception and Local Structure Fitting-based Transformer, which learns detailed shape information from point clouds with remarkable precision. The core of GPSFormer is the Global Perception Module (GPM) and the Local Structure Fitting Convolution (LSFConv). Specifically, GPM utilizes Adaptive Deformable Graph Convolution (ADGConv) to identify short-range dependencies among similar features in the feature space and employs Multi-Head Attention (MHA) to learn long-range dependencies across all positions within the feature space, ultimately enabling flexible learning of contextual representations. Inspired by Taylor series, we design LSFConv, which learns both low-order fundamental and high-order refinement information from explicitly encoded local geometric structures. Integrating the GPM and LSFConv as fundamental components, we construct GPSFormer, a cutting-edge Transformer that effectively captures global and local structures of point clouds. Extensive experiments validate GPSFormer's effectiveness in three point cloud tasks: shape classification, part segmentation, and few-shot learning. The code of GPSFormer is available at https://github.com/changshuowang/GPSFormer.

We propose a delay-agnostic asynchronous coordinate update algorithm (DEGAS) for computing operator fixed points, with applications to asynchronous optimization. DEGAS includes novel asynchronous variants of ADMM and block-coordinate descent as special cases. We prove that DEGAS converges under both bounded and unbounded delays under delay-free parameter conditions. We also validate by theory and experiments that DEGAS adapts well to the actual delays. The effectiveness of DEGAS is demonstrated by numerical experiments on classification problems.

Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the "General Catalogue of Variable Stars" and similar catalogs. We apply a recent method NAV ("New Algol Variable") to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to make a periodogram analysis. However, the number of parameters needed drastically increases with decreasing width of minimum. In the NAV algorithm, the special shape of minimum is used, so the number of parameters is limited to 10 (if the period and initial epoch are fixed) or 12 (not fixed). We illustrate the NAV method by application to a recently discovered Algol-type eclipsing variable 2MASS J11080308-6145589 (in the field of previously known variable star RS Car) and compare results to that obtained using the TP fits. For this system, the statistically optimal number of parameters is 44, but the fit is still worse than that of the NAV fit. Application to the system GSC 3692-00624 argues that the NAV fit is better than the TP one even for the case of EW-type stars with much wider eclipses. Model parameters are listed.

The evaluation of navigation instructions remains a persistent challenge in Vision-and-Language Navigation (VLN) research. Traditional reference-based metrics such as BLEU and ROUGE fail to capture the functional utility of spatial directives, specifically whether an instruction successfully guides a navigator to the intended destination. Although existing VLN agents could serve as evaluators, their reliance on high-fidelity visual simulators introduces licensing constraints and computational costs, and perception errors further confound linguistic quality assessment. This paper introduces GROKE(Graph-based Reasoning over OSM Knowledge for instruction Evaluation), a vision-free training-free hierarchical LLM-based framework for evaluating navigation instructions using OpenStreetMap data. Through systematic ablation studies, we demonstrate that structured JSON and textual formats for spatial information substantially outperform grid-based and visual graph representations. Our hierarchical architecture combines sub-instruction planning with topological graph navigation, reducing navigation error by 68.5% compared to heuristic and sampling baselines on the Map2Seq dataset. The agent's execution success, trajectory fidelity, and decision patterns serve as proxy metrics for functional navigability given OSM-visible landmarks and topology, establishing a scalable and interpretable evaluation paradigm without visual dependencies. Code and data are available at https://anonymous.4open.science/r/groke.

Most value function learning algorithms in reinforcement learning are based on the mean squared (projected) Bellman error. However, squared errors are known to be sensitive to outliers, both skewing the solution of the objective and resulting in high-magnitude and high-variance gradients. To control these high-magnitude updates, typical strategies in RL involve clipping gradients, clipping rewards, rescaling rewards, or clipping errors. While these strategies appear to be related to robust losses -- like the Huber loss -- they are built on semi-gradient update rules which do not minimize a known loss. In this work, we build on recent insights reformulating squared Bellman errors as a saddlepoint optimization problem and propose a saddlepoint reformulation for a Huber Bellman error and Absolute Bellman error. We start from a formalization of robust losses, then derive sound gradient-based approaches to minimize these losses in both the online off-policy prediction and control settings. We characterize the solutions of the robust losses, providing insight into the problem settings where the robust losses define notably better solutions than the mean squared Bellman error. Finally, we show that the resulting gradient-based algorithms are more stable, for both prediction and control, with less sensitivity to meta-parameters.

A comparative analysis of the special shapes (patterns, profiles) of the eclipses applied for the phenomenological modeling of the light curves of eclipsing binary stars is conducted. Families of functions are considered, generalizing local approximations (Andronov, 2010, 2012) and the functions theoretically unlimited in a width, based on a Gaussian (Mikulasek, 2015). For an analysis, the light curve of the star V0882 Car = 2MASS J11080308 - 6145589 of the classic Algol - subtype (\beta Persei) is used. By analyzing dozens of modified functions with additional parameters, it was chosen the 14 best ones according to the criterion of the least sum of squares of deviations. The best are the functions with an additional parameter, describing profiles, which are limited in phase.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

Geometry problem solving (GPS) is a high-level mathematical reasoning requiring the capacities of multi-modal fusion and geometric knowledge application. Recently, neural solvers have shown great potential in GPS but still be short in diagram presentation and modal fusion. In this work, we convert diagrams into basic textual clauses to describe diagram features effectively, and propose a new neural solver called PGPSNet to fuse multi-modal information efficiently. Combining structural and semantic pre-training, data augmentation and self-limited decoding, PGPSNet is endowed with rich knowledge of geometry theorems and geometric representation, and therefore promotes geometric understanding and reasoning. In addition, to facilitate the research of GPS, we build a new large-scale and fine-annotated GPS dataset named PGPS9K, labeled with both fine-grained diagram annotation and interpretable solution program. Experiments on PGPS9K and an existing dataset Geometry3K validate the superiority of our method over the state-of-the-art neural solvers. Our code, dataset and appendix material are available at https://github.com/mingliangzhang2018/PGPS.

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

Onboard sensors, such as cameras and thermal sensors, have emerged as effective alternatives to Global Positioning System (GPS) for geo-localization in Unmanned Aerial Vehicle (UAV) navigation. Since GPS can suffer from signal loss and spoofing problems, researchers have explored camera-based techniques such as Visual Geo-localization (VG) using satellite RGB imagery. Additionally, thermal geo-localization (TG) has become crucial for long-range UAV flights in low-illumination environments. This paper proposes a novel thermal geo-localization framework using satellite RGB imagery, which includes multiple domain adaptation methods to address the limited availability of paired thermal and satellite images. The experimental results demonstrate the effectiveness of the proposed approach in achieving reliable thermal geo-localization performance, even in thermal images with indistinct self-similar features. We evaluate our approach on real data collected onboard a UAV. We also release the code and Boson-nighttime, a dataset of paired satellite-thermal and unpaired satellite images for thermal geo-localization with satellite imagery. To the best of our knowledge, this work is the first to propose a thermal geo-localization method using satellite RGB imagery in long-range flights.

While a number of existing approaches for building foundation model agents rely on prompting or fine-tuning with human demonstrations, it is not sufficient in dynamic environments (e.g., mobile device control). On-policy reinforcement learning (RL) should address these limitations, but collecting actual rollouts in an environment is often undesirable in truly open-ended agentic problems such as mobile device control or interacting with humans, where each unit of interaction is associated with a cost. In such scenarios, a method for policy learning that can utilize off-policy experience by learning a trained action-value function is much more effective. In this paper, we develop an approach, called Digi-Q, to train VLM-based action-value Q-functions which are then used to extract the agent policy. We study our approach in the mobile device control setting. Digi-Q trains the Q-function using offline temporal-difference (TD) learning, on top of frozen, intermediate-layer features of a VLM. Compared to fine-tuning the whole VLM, this approach saves us compute and enhances scalability. To make the VLM features amenable for representing the Q-function, we need to employ an initial phase of fine-tuning to amplify coverage over actionable information needed for value function. Once trained, we use this Q-function via a Best-of-N policy extraction operator that imitates the best action out of multiple candidate actions from the current policy as ranked by the value function, enabling policy improvement without environment interaction. Digi-Q outperforms several prior methods on user-scale device control tasks in Android-in-the-Wild, attaining 21.2% improvement over prior best-performing method. In some cases, our Digi-Q approach already matches state-of-the-art RL methods that require interaction. The project is open-sourced at https://github.com/DigiRL-agent/digiq

Recent advancements in foundation models have enhanced AI systems' capabilities in autonomous tool usage and reasoning. However, their ability in location or map-based reasoning - which improves daily life by optimizing navigation, facilitating resource discovery, and streamlining logistics - has not been systematically studied. To bridge this gap, we introduce MapEval, a benchmark designed to assess diverse and complex map-based user queries with geo-spatial reasoning. MapEval features three task types (textual, API-based, and visual) that require collecting world information via map tools, processing heterogeneous geo-spatial contexts (e.g., named entities, travel distances, user reviews or ratings, images), and compositional reasoning, which all state-of-the-art foundation models find challenging. Comprising 700 unique multiple-choice questions about locations across 180 cities and 54 countries, MapEval evaluates foundation models' ability to handle spatial relationships, map infographics, travel planning, and navigation challenges. Using MapEval, we conducted a comprehensive evaluation of 28 prominent foundation models. While no single model excelled across all tasks, Claude-3.5-Sonnet, GPT-4o, and Gemini-1.5-Pro achieved competitive performance overall. However, substantial performance gaps emerged, particularly in MapEval, where agents with Claude-3.5-Sonnet outperformed GPT-4o and Gemini-1.5-Pro by 16% and 21%, respectively, and the gaps became even more amplified when compared to open-source LLMs. Our detailed analyses provide insights into the strengths and weaknesses of current models, though all models still fall short of human performance by more than 20% on average, struggling with complex map images and rigorous geo-spatial reasoning. This gap highlights MapEval's critical role in advancing general-purpose foundation models with stronger geo-spatial understanding.

Accurate geo-localization of Unmanned Aerial Vehicles (UAVs) is crucial for outdoor applications including search and rescue operations, power line inspections, and environmental monitoring. The vulnerability of Global Navigation Satellite Systems (GNSS) signals to interference and spoofing necessitates the development of additional robust localization methods for autonomous navigation. Visual Geo-localization (VG), leveraging onboard cameras and reference satellite maps, offers a promising solution for absolute localization. Specifically, Thermal Geo-localization (TG), which relies on image-based matching between thermal imagery with satellite databases, stands out by utilizing infrared cameras for effective nighttime localization. However, the efficiency and effectiveness of current TG approaches, are hindered by dense sampling on satellite maps and geometric noises in thermal query images. To overcome these challenges, we introduce STHN, a novel UAV thermal geo-localization approach that employs a coarse-to-fine deep homography estimation method. This method attains reliable thermal geo-localization within a 512-meter radius of the UAV's last known location even with a challenging 11\% size ratio between thermal and satellite images, despite the presence of indistinct textures and self-similar patterns. We further show how our research significantly enhances UAV thermal geo-localization performance and robustness against geometric noises under low-visibility conditions in the wild. The code is made publicly available.

In goal-reaching reinforcement learning (RL), the optimal value function has a particular geometry, called quasimetric structure. This paper introduces Quasimetric Reinforcement Learning (QRL), a new RL method that utilizes quasimetric models to learn optimal value functions. Distinct from prior approaches, the QRL objective is specifically designed for quasimetrics, and provides strong theoretical recovery guarantees. Empirically, we conduct thorough analyses on a discretized MountainCar environment, identifying properties of QRL and its advantages over alternatives. On offline and online goal-reaching benchmarks, QRL also demonstrates improved sample efficiency and performance, across both state-based and image-based observations.

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. [2022] as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance sigma_{1:T}^2 and the cumulative adversarial variation Sigma_{1:T}^2 for convex functions. They also provide a slightly weaker bound based on the maximal stochastic variance sigma_{max}^2 and the maximal adversarial variation Sigma_{max}^2 for strongly convex functions. Inspired by their work, we investigate the theoretical guarantees of optimistic online mirror descent (OMD) for the SEA model. For convex and smooth functions, we obtain the same O(sigma_{1:T^2}+Sigma_{1:T^2}) regret bound, without the convexity requirement of individual functions. For strongly convex and smooth functions, we establish an O(min{log (sigma_{1:T}^2+Sigma_{1:T}^2), (sigma_{max}^2 + Sigma_{max}^2) log T}) bound, better than their O((sigma_{max}^2 + Sigma_{max}^2) log T) bound. For exp-concave and smooth functions, we achieve a new O(dlog(sigma_{1:T}^2+Sigma_{1:T}^2)) bound. Owing to the OMD framework, we can further extend our result to obtain dynamic regret guarantees, which are more favorable in non-stationary online scenarios. The attained results allow us to recover excess risk bounds of the stochastic setting and regret bounds of the adversarial setting, and derive new guarantees for many intermediate scenarios.

Function calling (FC) empowers large language models (LLMs) and autonomous agents to interface with external tools, a critical capability for solving complex, real-world problems. As this ability becomes increasingly central to advanced AI systems, the need for high-quality, multi-turn training data to develop and refine it cannot be overstated. Existing data synthesis methods, such as random environment sampling or multi-agent role-playing, are not powerful enough to generate high-quality data in real-world environments. Practical challenges come in three folds: targeted model training, isolation of tool architecture, and multi-turn logical dependency. To address these structural deficiencies, we present FunReason-MT, a novel data synthesis framework for real-world multi-turn tool use. FunReason-MT resolves the complexity barrier in multi-turn FC data by employing 1) Environment-API Graph Interactions to gather varied high-quality trajectories, 2) Advanced Tool-Query Synthesis to simplify hard query construction, and 3) Guided Iterative Chain for sophisticated CoT generation. Evaluations on Berkeley Function-Calling Leaderboard (BFCLv3) demonstrate the power of our framework: a 4B model built upon FunReason-MT generated data achieves state-of-the-art performance among comparable-sized models, outperforming most close-source models. Further performance improvements on BFCLv4 confirm that FunReason-MT provides a reliable and robust source for agentic learning.

3D Gaussian Splatting (3DGS) has become a popular solution in SLAM due to its high-fidelity and real-time novel view synthesis performance. However, some previous 3DGS SLAM methods employ a differentiable rendering pipeline for tracking, lack geometric priors in outdoor scenes. Other approaches introduce separate tracking modules, but they accumulate errors with significant camera movement, leading to scale drift. To address these challenges, we propose a robust RGB-only outdoor 3DGS SLAM method: S3PO-GS. Technically, we establish a self-consistent tracking module anchored in the 3DGS pointmap, which avoids cumulative scale drift and achieves more precise and robust tracking with fewer iterations. Additionally, we design a patch-based pointmap dynamic mapping module, which introduces geometric priors while avoiding scale ambiguity. This significantly enhances tracking accuracy and the quality of scene reconstruction, making it particularly suitable for complex outdoor environments. Our experiments on the Waymo, KITTI, and DL3DV datasets demonstrate that S3PO-GS achieves state-of-the-art results in novel view synthesis and outperforms other 3DGS SLAM methods in tracking accuracy. Project page: https://3dagentworld.github.io/S3PO-GS/.

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions ge5 using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state-space where such a tipping point might exist. We illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian Process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favors models without tipping points -- leading to harvest policies that guarantee extinction. The GPDP performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective, and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, since it does not underestimate the uncertainty outside of the observed data.

We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We see how the property of convergence of global optimisation is a straightforward consequence of searchability. The abstract setting allows us to generalise searchability and continuity to higher-order functions, so that we can formulate novel convergence criteria for regression, derived from the convergence of global optimisation. All the theory and the motivating examples are fully formalised in the proof assistant Agda.

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

Reliable long-range flight of unmanned aerial vehicles (UAVs) in GNSS-denied environments is challenging: integrating odometry leads to drift, loop closures are unavailable in previously unseen areas and embedded platforms provide limited computational power. We present a fully onboard UAV system developed for the SPRIN-D Funke Fully Autonomous Flight Challenge, which required 9 km long-range waypoint navigation below 25 m AGL (Above Ground Level) without GNSS or prior dense mapping. The system integrates perception, mapping, planning, and control with a lightweight drift-correction method that matches LiDAR-derived local heightmaps to a prior geo-data heightmap via gradient-template matching and fuses the evidence with odometry in a clustered particle filter. Deployed during the competition, the system executed kilometer-scale flights across urban, forest, and open-field terrain and reduced drift substantially relative to raw odometry, while running in real time on CPU-only hardware. We describe the system architecture, the localization pipeline, and the competition evaluation, and we report practical insights from field deployment that inform the design of GNSS-denied UAV autonomy.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

This paper presents a nonlinear location estimation to infer the position of a user holding a smartphone. We consider a large location with M number of grid points, each grid point is labeled with a unique fingerprint consisting of the received signal strength (RSS) values measured from N number of Bluetooth Low Energy (BLE) beacons. Given the fingerprint observed by the smartphone, the user's current location can be estimated by finding the top-k similar fingerprints from the list of fingerprints registered in the database. Besides the environmental factors, the dynamicity in holding the smartphone is another source to the variation in fingerprint measurements, yet there are not many studies addressing the fingerprint variability due to dynamic smartphone positions held by human hands during online detection. To this end, we propose a nonlinear location estimation using the kernel method. Specifically, our proposed method comprises of two steps: 1) a beacon selection strategy to select a subset of beacons that is insensitive to the subtle change of holding positions, and 2) a kernel method to compute the similarity between this subset of observed signals and all the fingerprints registered in the database. The experimental results based on large-scale data collected in a complex building indicate a substantial performance gain of our proposed approach in comparison to state-of-the-art methods. The dataset consisting of the signal information collected from the beacons is available online.

While enabling large language models to implement function calling (known as APIs) can greatly enhance the performance of LLMs, function calling is still a challenging task due to the complicated relations between different APIs, especially in a context-learning setting without fine-tuning. This paper proposes a simple yet controllable target-driven approach called Reverse Chain to empower LLMs with capabilities to use external APIs with only prompts. Given that most open-source LLMs have limited tool-use or tool-plan capabilities, LLMs in Reverse Chain are only employed to implement simple tasks, e.g., API selection and argument completion, and a generic rule is employed to implement a controllable multiple functions calling. In this generic rule, after selecting a final API to handle a given task via LLMs, we first ask LLMs to fill the required arguments from user query and context. Some missing arguments could be further completed by letting LLMs select another API based on API description before asking user. This process continues until a given task is completed. Extensive numerical experiments indicate an impressive capability of Reverse Chain on implementing multiple function calling. Interestingly enough, the experiments also reveal that tool-use capabilities of the existing LLMs, e.g., ChatGPT, can be greatly improved via Reverse Chain.

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.

Policy gradient methods are an appealing approach in reinforcement learning because they directly optimize the cumulative reward and can straightforwardly be used with nonlinear function approximators such as neural networks. The two main challenges are the large number of samples typically required, and the difficulty of obtaining stable and steady improvement despite the nonstationarity of the incoming data. We address the first challenge by using value functions to substantially reduce the variance of policy gradient estimates at the cost of some bias, with an exponentially-weighted estimator of the advantage function that is analogous to TD(lambda). We address the second challenge by using trust region optimization procedure for both the policy and the value function, which are represented by neural networks. Our approach yields strong empirical results on highly challenging 3D locomotion tasks, learning running gaits for bipedal and quadrupedal simulated robots, and learning a policy for getting the biped to stand up from starting out lying on the ground. In contrast to a body of prior work that uses hand-crafted policy representations, our neural network policies map directly from raw kinematics to joint torques. Our algorithm is fully model-free, and the amount of simulated experience required for the learning tasks on 3D bipeds corresponds to 1-2 weeks of real time.

Control barrier functions (CBFs) enable guaranteed safe multi-agent navigation in the continuous domain. The resulting navigation performance, however, is highly sensitive to the underlying hyperparameters. Traditional approaches consider fixed CBFs (where parameters are tuned apriori), and hence, typically do not perform well in cluttered and highly dynamic environments: conservative parameter values can lead to inefficient agent trajectories, or even failure to reach goal positions, whereas aggressive parameter values can lead to infeasible controls. To overcome these issues, in this paper, we propose online CBFs, whereby hyperparameters are tuned in real-time, as a function of what agents perceive in their immediate neighborhood. Since the explicit relationship between CBFs and navigation performance is hard to model, we leverage reinforcement learning to learn CBF-tuning policies in a model-free manner. Because we parameterize the policies with graph neural networks (GNNs), we are able to synthesize decentralized agent controllers that adjust parameter values locally, varying the degree of conservative and aggressive behaviors across agents. Simulations as well as real-world experiments show that (i) online CBFs are capable of solving navigation scenarios that are infeasible for fixed CBFs, and (ii), that they improve navigation performance by adapting to other agents and changes in the environment.

The R-Mode system, an advanced terrestrial integrated navigation system, is designed to address the vulnerabilities of global navigation satellite systems (GNSS) and explore the potential of a complementary navigation system. This study aims to enhance the accuracy of performance simulation for the medium frequency (MF) R-Mode system by modeling the variance of time-of-arrival (TOA) measurements based on actual data. Drawing inspiration from the method used to calculate the standard deviation of time-of-reception (TOR) measurements in Loran, we adapted and applied this approach to the MF R-Mode system. Data were collected from transmitters in Palmi and Chungju, South Korea, and the parameters for modeling the variance of TOA were estimated.

Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy gamma_t = 2/(t+2), obtaining a O(1/t) convergence rate for this class of functions in terms of primal gap and Frank-Wolfe gap, where t is the iteration count. This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work. We also show improved convergence rates for various common cases, e.g., when the feasible region under consideration is uniformly convex or polyhedral.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

In this paper, we examine the solvability of a functional equation in a Lipschitz space. As an application, we use our result to determine the existence and uniqueness of solutions to an equation describing a specific type of choice behavior model for the learning process of the paradise fish. Finally, we present some concrete examples where, using numerical techniques, we obtain approximations to the solution of the functional equation. As the straightforward Picard's iteration can be very expensive, we show that an analytical suboptimal least-squares approximation can be chosen in practice, resulting in very good accuracy.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

We consider offline reinforcement learning (RL) methods in possibly nonstationary environments. Many existing RL algorithms in the literature rely on the stationarity assumption that requires the system transition and the reward function to be constant over time. However, the stationarity assumption is restrictive in practice and is likely to be violated in a number of applications, including traffic signal control, robotics and mobile health. In this paper, we develop a consistent procedure to test the nonstationarity of the optimal Q-function based on pre-collected historical data, without additional online data collection. Based on the proposed test, we further develop a sequential change point detection method that can be naturally coupled with existing state-of-the-art RL methods for policy optimization in nonstationary environments. The usefulness of our method is illustrated by theoretical results, simulation studies, and a real data example from the 2018 Intern Health Study. A Python implementation of the proposed procedure is available at https://github.com/limengbinggz/CUSUM-RL.

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs, we obtain the exact minimax quantile risk for a rich family of error functions and establish the minimaxity of OLS. This improves on the known lower bounds for the special case of square error, and provides us with a lower bound on the minimax quantile risk over larger sets of distributions. Under the square error and a fourth moment assumption on the distribution of inputs, we show that this lower bound is tight over a larger class of problems. Specifically, we prove a matching upper bound on the worst-case quantile risk of a variant of the recently proposed min-max regression procedure, thereby establishing its minimaxity, up to absolute constants. We illustrate the usefulness of our approach by extending this result to all p-th power error functions for p in (2, infty). Along the way, we develop a generic analogue to the classical Bayesian method for lower bounding the minimax risk when working with the quantile risk, as well as a tight characterization of the quantiles of the smallest eigenvalue of the sample covariance matrix.

While Reinforcement Learning from Human Feedback (RLHF) has become the predominant method for controlling language model outputs, it suffers from high computational costs and training instability. Guided decoding, especially value-guided methods, offers a cost-effective alternative by controlling outputs without re-training models. However, the accuracy of the value function is crucial for value-guided decoding, as inaccuracies can lead to suboptimal decision-making and degraded performance. Existing methods struggle with accurately estimating the optimal value function, leading to less effective control. We propose Iterative Value Function Optimization, a novel framework that addresses these limitations through two key components: Monte Carlo Value Estimation, which reduces estimation variance by exploring diverse trajectories, and Iterative On-Policy Optimization, which progressively improves value estimation through collecting trajectories from value-guided policies. Extensive experiments on text summarization, multi-turn dialogue, and instruction following demonstrate the effectiveness of value-guided decoding approaches in aligning language models. These approaches not only achieve alignment but also significantly reduce computational costs by leveraging principled value function optimization for efficient and effective control.

We develop a robust quaternion recurrent neural network (QRNN) for real-time processing of 3D and 4D data with outliers. This is achieved by combining the real-time recurrent learning (RTRL) algorithm and the maximum correntropy criterion (MCC) as a loss function. While both the mean square error and maximum correntropy criterion are viable cost functions, it is shown that the non-quadratic maximum correntropy loss function is less sensitive to outliers, making it suitable for applications with multidimensional noisy or uncertain data. Both algorithms are derived based on the novel generalised HR (GHR) calculus, which allows for the differentiation of real functions of quaternion variables and offers the product and chain rules, thus enabling elegant and compact derivations. Simulation results in the context of motion prediction of chest internal markers for lung cancer radiotherapy, which includes regular and irregular breathing sequences, support the analysis.

This paper investigates the use of prior computation to estimate the value function to improve sample efficiency in on-policy policy gradient methods in reinforcement learning. Our approach is to estimate the value function from prior computations, such as from the Q-network learned in DQN or the value function trained for different but related environments. In particular, we learn a new value function for the target task while combining it with a value estimate from the prior computation. Finally, the resulting value function is used as a baseline in the policy gradient method. This use of a baseline has the theoretical property of reducing variance in gradient computation and thus improving sample efficiency. The experiments show the successful use of prior value estimates in various settings and improved sample efficiency in several tasks.

Autonomous driving involves multiple, often conflicting objectives such as safety, efficiency, and comfort. In reinforcement learning (RL), these objectives are typically combined through weighted summation, which collapses their relative priorities and often yields policies that violate safety-critical constraints. To overcome this limitation, we introduce the Preordered Multi-Objective MDP (Pr-MOMDP), which augments standard MOMDPs with a preorder over reward components. This structure enables reasoning about actions with respect to a hierarchy of objectives rather than a scalar signal. To make this structure actionable, we extend distributional RL with a novel pairwise comparison metric, Quantile Dominance (QD), that evaluates action return distributions without reducing them into a single statistic. Building on QD, we propose an algorithm for extracting optimal subsets, the subset of actions that remain non-dominated under each objective, which allows precedence information to shape both decision-making and training targets. Our framework is instantiated with Implicit Quantile Networks (IQN), establishing a concrete implementation while preserving compatibility with a broad class of distributional RL methods. Experiments in Carla show improved success rates, fewer collisions and off-road events, and deliver statistically more robust policies than IQN and ensemble-IQN baselines. By ensuring policies respect rewards preorder, our work advances safer, more reliable autonomous driving systems.

Non-cooperative game theory provides a robust framework for analyzing distributed resource allocation in multi-user wireless networks, with Iterative Water-Filling (IWF) emerging as a canonical solution for power control problems. Although classical fixed-point theorems guarantee the existence of a Nash Equilibrium (NE) under mild concavity and compactness conditions, the convergence of practical iterative algorithms to that equilibrium remains a challenging endeavor. This challenge intensifies under varying update schedules, interference regimes, and imperfections such as channel estimation errors or feedback delay. In this paper, we present an in-depth examination of IWF in multi-user systems under three different update schemes: (1) synchronous sequential updates, (2) synchronous simultaneous updates, and (3) totally asynchronous updates. We first formulate the water-filling operator in a multi-carrier environment, then recast the iterative process as a fixed-point problem. Using contraction mapping principles, we demonstrate sufficient conditions under which IWF converges to a unique NE and highlight how spectral radius constraints, diagonal dominance, and careful step-size selection are pivotal for guaranteeing convergence. We further discuss robustness to measurement noise, partial updates, and network scaling to emphasize the practical viability of these schemes. This comprehensive analysis unifies diverse threads in the literature while offering novel insights into asynchronous implementations. Our findings enable network designers to ascertain system parameters that foster both stable convergence and efficient spectrum usage.

Training reinforcement learning (RL) agents on robotic tasks typically requires a large number of training samples. This is because training data often consists of noisy trajectories, whether from exploration or human-collected demonstrations, making it difficult to learn value functions that understand the effect of taking each action. On the other hand, recent behavior-cloning (BC) approaches have shown that predicting a sequence of actions enables policies to effectively approximate noisy, multi-modal distributions of expert demonstrations. Can we use a similar idea for improving RL on robotic tasks? In this paper, we introduce a novel RL algorithm that learns a critic network that outputs Q-values over a sequence of actions. By explicitly training the value functions to learn the consequence of executing a series of current and future actions, our algorithm allows for learning useful value functions from noisy trajectories. We study our algorithm across various setups with sparse and dense rewards, and with or without demonstrations, spanning mobile bi-manual manipulation, whole-body control, and tabletop manipulation tasks from BiGym, HumanoidBench, and RLBench. We find that, by learning the critic network with action sequences, our algorithm outperforms various RL and BC baselines, in particular on challenging humanoid control tasks.

Federated optimization studies the problem of collaborative function optimization among multiple clients (e.g. mobile devices or organizations) under the coordination of a central server. Since the data is collected separately by each client and always remains decentralized, federated optimization preserves data privacy and allows for large-scale computing, which makes it a promising decentralized machine learning paradigm. Though it is often deployed for tasks that are online in nature, e.g., next-word prediction on keyboard apps, most works formulate it as an offline problem. The few exceptions that consider federated bandit optimization are limited to very simplistic function classes, e.g., linear, generalized linear, or non-parametric function class with bounded RKHS norm, which severely hinders its practical usage. In this paper, we propose a new algorithm, named Fed-GO-UCB, for federated bandit optimization with generic non-linear objective function. Under some mild conditions, we rigorously prove that Fed-GO-UCB is able to achieve sub-linear rate for both cumulative regret and communication cost. At the heart of our theoretical analysis are distributed regression oracle and individual confidence set construction, which can be of independent interests. Empirical evaluations also demonstrate the effectiveness of the proposed algorithm.

We study distributionally robust expected values under optimal transport distance with a quadratic cost function. In general the duality method, for this computation for the payoff function f, requires the computation of the λc-transform f^{λc}. We show that under the quadratic cost function there exists an intuitive and easily implementable representation of f^{λc}, if f is convex and piecewise linear. We apply this to the robust expected shortfall under the risk-neutral measure of an unhedged call option, from the point of view of the writer, as well as that of a portfolio mixing underlying shares with a call and a put option.

We present MM-Navigator, a GPT-4V-based agent for the smartphone graphical user interface (GUI) navigation task. MM-Navigator can interact with a smartphone screen as human users, and determine subsequent actions to fulfill given instructions. Our findings demonstrate that large multimodal models (LMMs), specifically GPT-4V, excel in zero-shot GUI navigation through its advanced screen interpretation, action reasoning, and precise action localization capabilities. We first benchmark MM-Navigator on our collected iOS screen dataset. According to human assessments, the system exhibited a 91\% accuracy rate in generating reasonable action descriptions and a 75\% accuracy rate in executing the correct actions for single-step instructions on iOS. Additionally, we evaluate the model on a subset of an Android screen navigation dataset, where the model outperforms previous GUI navigators in a zero-shot fashion. Our benchmark and detailed analyses aim to lay a robust groundwork for future research into the GUI navigation task. The project page is at https://github.com/zzxslp/MM-Navigator.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an varepsilon-optimal policy with probability 1-delta under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

Intelligent vehicle cockpits present unique challenges for API Agents, requiring coordination across tightly-coupled subsystems that exceed typical task environments' complexity. Traditional Function Calling (FC) approaches operate statelessly, requiring multiple exploratory calls to build environmental awareness before execution, leading to inefficiency and limited error recovery. We introduce VehicleWorld, the first comprehensive environment for the automotive domain, featuring 30 modules, 250 APIs, and 680 properties with fully executable implementations that provide real-time state information during agent execution. This environment enables precise evaluation of vehicle agent behaviors across diverse, challenging scenarios. Through systematic analysis, we discovered that direct state prediction outperforms function calling for environmental control. Building on this insight, we propose State-based Function Call (SFC), a novel approach that maintains explicit system state awareness and implements direct state transitions to achieve target conditions. Experimental results demonstrate that SFC significantly outperforms traditional FC approaches, achieving superior execution accuracy and reduced latency. We have made all implementation code publicly available on Github https://github.com/OpenMOSS/VehicleWorld.