Daily Papers

The concept of deep dictionary learning has been recently proposed. Unlike shallow dictionary learning which learns single level of dictionary to represent the data, it uses multiple layers of dictionaries. So far, the problem could only be solved in a greedy fashion; this was achieved by learning a single layer of dictionary in each stage where the coefficients from the previous layer acted as inputs to the subsequent layer (only the first layer used the training samples as inputs). This was not optimal; there was feedback from shallower to deeper layers but not the other way. This work proposes an optimal solution to deep dictionary learning whereby all the layers of dictionaries are solved simultaneously. We employ the Majorization Minimization approach. Experiments have been carried out on benchmark datasets; it shows that optimal learning indeed improves over greedy piecemeal learning. Comparison with other unsupervised deep learning tools (stacked denoising autoencoder, deep belief network, contractive autoencoder and K-sparse autoencoder) show that our method supersedes their performance both in accuracy and speed.

Message passing neural networks (MPNNs) have emerged as go-to models for learning on graph-structured data in the past decade. Despite their effectiveness, most of such models still incur severe issues such as over-smoothing and -correlation, due to their underlying objective of minimizing the Dirichlet energy and the derived neighborhood aggregation operations. In this paper, we propose the DDSM, a new MPNN model built on an optimization framework that includes the stress majorization and orthogonal regularization for overcoming the above issues. Further, we introduce the diffusion distances for nodes into the framework to guide the new message passing operations and develop efficient algorithms for distance approximations, both backed by rigorous theoretical analyses. Our comprehensive experiments showcase that DDSM consistently and considerably outperforms 15 strong baselines on both homophilic and heterophilic graphs.

Increasing the size of a Transformer model does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, improved generalization ability occurs as the model memorizes the training samples. We present a theoretical framework that sheds light on the memorization process and performance dynamics of transformer-based language models. We model the behavior of Transformers with associative memories using Hopfield networks, such that each transformer block effectively conducts an approximate nearest-neighbor search. Based on this, we design an energy function analogous to that in the modern continuous Hopfield network which provides an insightful explanation for the attention mechanism. Using the majorization-minimization technique, we construct a global energy function that captures the layered architecture of the Transformer. Under specific conditions, we show that the minimum achievable cross-entropy loss is bounded from below by a constant approximately equal to 1. We substantiate our theoretical results by conducting experiments with GPT-2 on various data sizes, as well as training vanilla Transformers on a dataset of 2M tokens.

Most competitive 4-bit LLM research pipelines now open the same way: apply a linear, function-preserving transform (rotation, scaling, permutation, non-orthogonal affine) so the outlier mass sits more favorably against the group scales, and only then round. Yet we are aware of no survey dedicated to this transform stage, and its literature is quietly re-deriving an older theory. We identify and formalize the principle that organizes it, the Great Inversion: allocation-flexible coding rewards energy concentration, whereas the grouped shared-scale quantization a deployed matrix instruction performs rewards within-group flattening. Classical transform coding (1963: decorrelate, allocate bits, quantize) spends different bits per coordinate at a fixed total rate; for a Gaussian source at high rate the Karhunen-Loeve transform's concentration minimizes distortion. A deployed operand tile instead carries one absolute-maximum scale per group and equal bits everywhere, with no allocation; on a uniform grid that objective rewards flattening, approached by Hadamard incoherence. We prove that opposition under within-group majorization: the prescriptions point in opposite directions, each backed by a proof against its own objective, and for a generic spectrum no optimality guarantee transfers. A second axis is the number format: the non-uniform FP4 grid makes flattening buy less, MXFP4's power-of-two block scale still rewards a rotation confined to that block, and NVFP4's mantissa-carrying scale largely removes that pull, so the target pole depends jointly on allocation regime and format. We survey 200 works to a June 2026 cutoff; classify 43 transform methods by structure, data-awareness, searched-versus-constructed, and runtime cost; record, where reported, how they compose with GPTQ rounding; distill a first-choice guide by deployment regime; and close with the open problems it exposes.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Deep clustering, which learns representation and semantic clustering without labels information, poses a great challenge for deep learning-based approaches. Despite significant progress in recent years, most existing methods focus on uniformly distributed datasets, significantly limiting the practical applicability of their methods. In this paper, we propose a more practical problem setting named deep imbalanced clustering, where the underlying classes exhibit an imbalance distribution. To address this challenge, we introduce a novel optimal transport-based pseudo-label learning framework. Our framework formulates pseudo-label generation as a Semantic-regularized Progressive Partial Optimal Transport (SP^2OT) problem, which progressively transports each sample to imbalanced clusters under several prior distribution and semantic relation constraints, thus generating high-quality and imbalance-aware pseudo-labels. To solve SP^2OT, we develop a Majorization-Minimization-based optimization algorithm. To be more precise, we employ the strategy of majorization to reformulate the SP^2OT problem into a Progressive Partial Optimal Transport problem, which can be transformed into an unbalanced optimal transport problem with augmented constraints and can be solved efficiently by a fast matrix scaling algorithm. Experiments on various datasets, including a human-curated long-tailed CIFAR100, challenging ImageNet-R, and large-scale subsets of fine-grained iNaturalist2018 datasets, demonstrate the superiority of our method.

For many practical applications in wireless communications, we need to recover a structured sparse signal from a linear observation model with dynamic grid parameters in the sensing matrix. Conventional expectation maximization (EM)-based compressed sensing (CS) methods, such as turbo compressed sensing (Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have double-loop iterations, where the inner loop (E-step) obtains a Bayesian estimation of sparse signals and the outer loop (M-step) obtains a point estimation of dynamic grid parameters. This leads to a slow convergence rate. Furthermore, each iteration of the E-step involves a complicated matrix inverse in general. To overcome these drawbacks, we first propose a successive linear approximation VBI (SLA-VBI) algorithm that can provide Bayesian estimation of both sparse signals and dynamic grid parameters. Besides, we simplify the matrix inverse operation based on the majorization-minimization (MM) algorithmic framework. In addition, we extend our proposed algorithm from an independent sparse prior to more complicated structured sparse priors, which can exploit structured sparsity in specific applications to further enhance the performance. Finally, we apply our proposed algorithm to solve two practical application problems in wireless communications and verify that the proposed algorithm can achieve faster convergence, lower complexity, and better performance compared to the state-of-the-art EM-based methods.

The Iterative Closest Point (ICP) algorithm and its variants are a fundamental technique for rigid registration between two point sets, with wide applications in different areas from robotics to 3D reconstruction. The main drawbacks for ICP are its slow convergence as well as its sensitivity to outliers, missing data, and partial overlaps. Recent work such as Sparse ICP achieves robustness via sparsity optimization at the cost of computational speed. In this paper, we propose a new method for robust registration with fast convergence. First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to speed up its convergence. In addition, we introduce a robust error metric based on the Welsch's function, which is minimized efficiently using the MM algorithm with Anderson acceleration. On challenging datasets with noises and partial overlaps, we achieve similar or better accuracy than Sparse ICP while being at least an order of magnitude faster. Finally, we extend the robust formulation to point-to-plane ICP, and solve the resulting problem using a similar Anderson-accelerated MM strategy. Our robust ICP methods improve the registration accuracy on benchmark datasets while being competitive in computational time.

In modern machine learning problems we deal with datasets that are either distributed by nature or potentially large for which distributing the computations is usually a standard way to proceed, since centralized algorithms are in general ineffective. We propose a distributed learning approach for mixtures of experts (MoE) models with an aggregation strategy to construct a reduction estimator from local estimators fitted parallelly to distributed subsets of the data. The aggregation is based on an optimal minimization of an expected transportation divergence between the large MoE composed of local estimators and the unknown desired MoE model. We show that the provided reduction estimator is consistent as soon as the local estimators to be aggregated are consistent, and its construction is performed by a proposed majorization-minimization (MM) algorithm that is computationally effective. We study the statistical and numerical properties for the proposed reduction estimator on experiments that demonstrate its performance compared to namely the global estimator constructed in a centralized way from the full dataset. For some situations, the computation time is more than ten times faster, for a comparable performance. Our source codes are publicly available on Github.

Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we introduce an as-rigid-as-possible regulation term to estimate the deformed normals and propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.