Daily Papers

Large-scale kernel ridge regression (KRR) is limited by the need to store a large kernel matrix K_t. To avoid storing the entire matrix K_t, Nystrom methods subsample a subset of columns of the kernel matrix, and efficiently find an approximate KRR solution on the reconstructed matrix. The chosen subsampling distribution in turn affects the statistical and computational tradeoffs. For KRR problems, recent works show that a sampling distribution proportional to the ridge leverage scores (RLSs) provides strong reconstruction guarantees for the approximation. While exact RLSs are as difficult to compute as a KRR solution, we may be able to approximate them well enough. In this paper, we study KRR problems in a sequential setting and introduce the INK-ESTIMATE algorithm, that incrementally computes the RLSs estimates. INK-ESTIMATE maintains a small sketch of K_t, that at each step is used to compute an intermediate estimate of the RLSs. First, our sketch update does not require access to previously seen columns, and therefore a single pass over the kernel matrix is sufficient. Second, the algorithm requires a fixed, small space budget to run dependent only on the effective dimension of the kernel matrix. Finally, our sketch provides strong approximation guarantees on the distance between the true kernel matrix and its approximation, and on the statistical risk of the approximate KRR solution at any time, because all our guarantees hold at any intermediate step.

Digital note-taking is gaining popularity, offering a durable, editable, and easily indexable way of storing notes in the vectorized form, known as digital ink. However, a substantial gap remains between this way of note-taking and traditional pen-and-paper note-taking, a practice still favored by a vast majority. Our work, InkSight, aims to bridge the gap by empowering physical note-takers to effortlessly convert their work (offline handwriting) to digital ink (online handwriting), a process we refer to as Derendering. Prior research on the topic has focused on the geometric properties of images, resulting in limited generalization beyond their training domains. Our approach combines reading and writing priors, allowing training a model in the absence of large amounts of paired samples, which are difficult to obtain. To our knowledge, this is the first work that effectively derenders handwritten text in arbitrary photos with diverse visual characteristics and backgrounds. Furthermore, it generalizes beyond its training domain into simple sketches. Our human evaluation reveals that 87% of the samples produced by our model on the challenging HierText dataset are considered as a valid tracing of the input image and 67% look like a pen trajectory traced by a human.

As text generative models can give increasingly long answers, we tackle the problem of synthesizing long text in digital ink. We show that the commonly used models for this task fail to generalize to long-form data and how this problem can be solved by augmenting the training data, changing the model architecture and the inference procedure. These methods use contrastive learning technique and are tailored specifically for the handwriting domain. They can be applied to any encoder-decoder model that works with digital ink. We demonstrate that our method reduces the character error rate on long-form English data by half compared to baseline RNN and by 16% compared to the previous approach that aims at addressing the same problem. We show that all three parts of the method improve recognizability of generated inks. In addition, we evaluate synthesized data in a human study and find that people perceive most of generated data as real.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

Recent advancements in Digital Document Restoration (DDR) have led to significant breakthroughs in analyzing highly damaged written artifacts. Among those, there has been an increasing interest in applying Artificial Intelligence techniques for virtually unwrapping and automatically detecting ink on the Herculaneum papyri collection. This collection consists of carbonized scrolls and fragments of documents, which have been digitized via X-ray tomography to allow the development of ad-hoc deep learning-based DDR solutions. In this work, we propose a modification of the Fast Fourier Convolution operator for volumetric data and apply it in a segmentation architecture for ink detection on the challenging Herculaneum papyri, demonstrating its suitability via deep experimental analysis. To encourage the research on this task and the application of the proposed operator to other tasks involving volumetric data, we will release our implementation (https://github.com/aimagelab/vffc)

The adoption of tablets with touchscreens and styluses is increasing, and a key feature is converting handwriting to text, enabling search, indexing, and AI assistance. Meanwhile, vision-language models (VLMs) are now the go-to solution for image understanding, thanks to both their state-of-the-art performance across a variety of tasks and the simplicity of a unified approach to training, fine-tuning, and inference. While VLMs obtain high performance on image-based tasks, they perform poorly on handwriting recognition when applied naively, i.e., by rendering handwriting as an image and performing optical character recognition (OCR). In this paper, we study online handwriting recognition with VLMs, going beyond naive OCR. We propose a novel tokenized representation of digital ink (online handwriting) that includes both a time-ordered sequence of strokes as text, and as image. We show that this representation yields results comparable to or better than state-of-the-art online handwriting recognizers. Wide applicability is shown through results with two different VLM families, on multiple public datasets. Our approach can be applied to off-the-shelf VLMs, does not require any changes in their architecture, and can be used in both fine-tuning and parameter-efficient tuning. We perform a detailed ablation study to identify the key elements of the proposed representation.

We show how to transform a non-differentiable rasterizer into a differentiable one with minimal engineering efforts and no external dependencies (no Pytorch/Tensorflow). We rely on Stochastic Gradient Estimation, a technique that consists of rasterizing after randomly perturbing the scene's parameters such that their gradient can be stochastically estimated and descended. This method is simple and robust but does not scale in dimensionality (number of scene parameters). Our insight is that the number of parameters contributing to a given rasterized pixel is bounded. Estimating and averaging gradients on a per-pixel basis hence bounds the dimensionality of the underlying optimization problem and makes the method scalable. Furthermore, it is simple to track per-pixel contributing parameters by rasterizing ID- and UV-buffers, which are trivial additions to a rasterization engine if not already available. With these minor modifications, we obtain an in-engine optimizer for 3D assets with millions of geometry and texture parameters.

The comic production industry requires reference-based line art colorization with high accuracy, efficiency, contextual consistency, and flexible control. A comic page often involves diverse characters, objects, and backgrounds, which complicates the coloring process. Despite advancements in diffusion models for image generation, their application in line art colorization remains limited, facing challenges related to handling extensive reference images, time-consuming inference, and flexible control. We investigate the necessity of extensive contextual image guidance on the quality of line art colorization. To address these challenges, we introduce Cobra, an efficient and versatile method that supports color hints and utilizes over 200 reference images while maintaining low latency. Central to Cobra is a Causal Sparse DiT architecture, which leverages specially designed positional encodings, causal sparse attention, and Key-Value Cache to effectively manage long-context references and ensure color identity consistency. Results demonstrate that Cobra achieves accurate line art colorization through extensive contextual reference, significantly enhancing inference speed and interactivity, thereby meeting critical industrial demands. We release our codes and models on our project page: https://zhuang2002.github.io/Cobra/.

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.

Assessing resection margins is central to pathological specimen evaluation and has profound implications for patient outcomes. Current practice employs physical inking, which is applied variably, and cautery artifacts can obscure the true margin on histological sections. We present a virtual inking network (VIN) that autonomously localizes the surgical cut surface on whole-slide images, reducing reliance on inks and standardizing margin-focused review. VIN uses a frozen foundation model as the feature extractor and a compact two-layer multilayer perceptron trained for patch-level classification of cautery-consistent features. The dataset comprised 120 hematoxylin and eosin (H&E) stained slides from 12 human tonsil tissue blocks, resulting in ~2 TB of uncompressed raw image data, where a board-certified pathologist provided boundary annotations. In blind testing with 20 slides from previously unseen blocks, VIN produced coherent margin overlays that qualitatively aligned with expert annotations across serial sections. Quantitatively, region-level accuracy was ~73.3% across the test set, with errors largely confined to limited areas that did not disrupt continuity of the whole-slide margin map. These results indicate that VIN captures cautery-related histomorphology and can provide a reproducible, ink-free margin delineation suitable for integration into routine digital pathology workflows and for downstream measurement of margin distances.

Painting embodies a unique form of visual storytelling, where the creation process is as significant as the final artwork. Although recent advances in generative models have enabled visually compelling painting synthesis, most existing methods focus solely on final image generation or patch-based process simulation, lacking explicit stroke structure and failing to produce smooth, realistic shading. In this work, we present a differentiable stroke reconstruction framework that unifies painting, stylized texturing, and smudging to faithfully reproduce the human painting-smudging loop. Given an input image, our framework first optimizes single- and dual-color Bezier strokes through a parallel differentiable paint renderer, followed by a style generation module that synthesizes geometry-conditioned textures across diverse painting styles. We further introduce a differentiable smudge operator to enable natural color blending and shading. Coupled with a coarse-to-fine optimization strategy, our method jointly optimizes stroke geometry, color, and texture under geometric and semantic guidance. Extensive experiments on oil, watercolor, ink, and digital paintings demonstrate that our approach produces realistic and expressive stroke reconstructions, smooth tonal transitions, and richly stylized appearances, offering a unified model for expressive digital painting creation. See our project page for more demos: https://yingjiang96.github.io/DiffPaintWebsite/.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to the student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot). The code is available at https://github.com/iclr2024mcmi/ICLRMCMI.

We present MagicColor, a diffusion-based framework for multi-instance sketch colorization. The production of multi-instance 2D line art colorization adheres to an industry-standard workflow, which consists of three crucial stages: the design of line art characters, the coloring of individual objects, and the refinement process. The artists are required to repeat the process of coloring each instance one by one, which is inaccurate and inefficient. Meanwhile, current generative methods fail to solve this task due to the challenge of multi-instance pair data collection. To tackle these challenges, we incorporate three technical designs to ensure precise character detail transcription and achieve multi-instance sketch colorization in a single forward. Specifically, we first propose the self-play training strategy to solve the lack of training data. Then we introduce an instance guider to feed the color of the instance. To achieve accurate color matching, we present fine-grained color matching with edge loss to enhance visual quality. Equipped with the proposed modules, MagicColor enables automatically transforming sketches into vividly-colored images with accurate consistency and multi-instance control. Experiments on our collected datasets show that our model outperforms existing methods regarding chromatic precision. Specifically, our model critically automates the colorization process with zero manual adjustments, so novice users can produce stylistically consistent artwork by providing reference instances and the original line art. Our code and additional details are available at https://yinhan-zhang.github.io/color

Document Image Binarization is a well-known problem in Document Analysis and Computer Vision, although it is far from being solved. One of the main challenges of this task is that documents generally exhibit degradations and acquisition artifacts that can greatly vary throughout the page. Nonetheless, even when dealing with a local patch of the document, taking into account the overall appearance of a wide portion of the page can ease the prediction by enriching it with semantic information on the ink and background conditions. In this respect, approaches able to model both local and global information have been proven suitable for this task. In particular, recent applications of Vision Transformer (ViT)-based models, able to model short and long-range dependencies via the attention mechanism, have demonstrated their superiority over standard Convolution-based models, which instead struggle to model global dependencies. In this work, we propose an alternative solution based on the recently introduced Fast Fourier Convolutions, which overcomes the limitation of standard convolutions in modeling global information while requiring fewer parameters than ViTs. We validate the effectiveness of our approach via extensive experimental analysis considering different types of degradations.

Manga is a fashionable Japanese-style comic form that is composed of black-and-white strokes and is generally displayed as raster images on digital devices. Typical mangas have simple textures, wide lines, and few color gradients, which are vectorizable natures to enjoy the merits of vector graphics, e.g., adaptive resolutions and small file sizes. In this paper, we propose MARVEL (MAnga's Raster to VEctor Learning), a primitive-wise approach for vectorizing raster mangas by Deep Reinforcement Learning (DRL). Unlike previous learning-based methods which predict vector parameters for an entire image, MARVEL introduces a new perspective that regards an entire manga as a collection of basic primitives\textemdash stroke lines, and designs a DRL model to decompose the target image into a primitive sequence for achieving accurate vectorization. To improve vectorization accuracies and decrease file sizes, we further propose a stroke accuracy reward to predict accurate stroke lines, and a pruning mechanism to avoid generating erroneous and repeated strokes. Extensive subjective and objective experiments show that our MARVEL can generate impressive results and reaches the state-of-the-art level. Our code is open-source at: https://github.com/SwordHolderSH/Mang2Vec.

SymPoint is an initial attempt that utilizes point set representation to solve the panoptic symbol spotting task on CAD drawing. Despite its considerable success, it overlooks graphical layer information and suffers from prohibitively slow training convergence. To tackle this issue, we introduce SymPoint-V2, a robust and efficient solution featuring novel, streamlined designs that overcome these limitations. In particular, we first propose a Layer Feature-Enhanced module (LFE) to encode the graphical layer information into the primitive feature, which significantly boosts the performance. We also design a Position-Guided Training (PGT) method to make it easier to learn, which accelerates the convergence of the model in the early stages and further promotes performance. Extensive experiments show that our model achieves better performance and faster convergence than its predecessor SymPoint on the public benchmark. Our code and trained models are available at https://github.com/nicehuster/SymPointV2.

Digital ink promises to combine the flexibility and aesthetics of handwriting and the ability to process, search and edit digital text. Character recognition converts handwritten text into a digital representation, albeit at the cost of losing personalized appearance due to the technical difficulties of separating the interwoven components of content and style. In this paper, we propose a novel generative neural network architecture that is capable of disentangling style from content and thus making digital ink editable. Our model can synthesize arbitrary text, while giving users control over the visual appearance (style). For example, allowing for style transfer without changing the content, editing of digital ink at the word level and other application scenarios such as spell-checking and correction of handwritten text. We furthermore contribute a new dataset of handwritten text with fine-grained annotations at the character level and report results from an initial user evaluation.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

Given an input painting, we reconstruct a time-lapse video of how it may have been painted. We formulate this as an autoregressive image generation problem, in which an initially blank "canvas" is iteratively updated. The model learns from real artists by training on many painting videos. Our approach incorporates text and region understanding to define a set of painting "instructions" and updates the canvas with a novel diffusion-based renderer. The method extrapolates beyond the limited, acrylic style paintings on which it has been trained, showing plausible results for a wide range of artistic styles and genres.

In this paper, we explore the unique modality of sketch for explainability, emphasising the profound impact of human strokes compared to conventional pixel-oriented studies. Beyond explanations of network behavior, we discern the genuine implications of explainability across diverse downstream sketch-related tasks. We propose a lightweight and portable explainability solution -- a seamless plugin that integrates effortlessly with any pre-trained model, eliminating the need for re-training. Demonstrating its adaptability, we present four applications: highly studied retrieval and generation, and completely novel assisted drawing and sketch adversarial attacks. The centrepiece to our solution is a stroke-level attribution map that takes different forms when linked with downstream tasks. By addressing the inherent non-differentiability of rasterisation, we enable explanations at both coarse stroke level (SLA) and partial stroke level (P-SLA), each with its advantages for specific downstream tasks.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

To address the time-consuming and computationally intensive issues of traditional ART algorithms for flame combustion diagnosis, inspired by flame simulation technology, we propose a novel representation method for flames. By modeling the luminous process of flames and utilizing 2D projection images for supervision, our experimental validation shows that this model achieves an average structural similarity index of 0.96 between actual images and predicted 2D projections, along with a Peak Signal-to-Noise Ratio of 39.05. Additionally, it saves approximately 34 times the computation time and about 10 times the memory compared to traditional algorithms.

The ability to estimate the quality of scientific papers is central to how both humans and AI systems will advance scientific knowledge in the future. However, existing LLM-based estimation methods suffer from high inference cost, whereas the faster direct score regression approach is limited by scale inconsistencies. We present NAIPv2, a debiased and efficient framework for paper quality estimation. NAIPv2 employs pairwise learning within domain-year groups to reduce inconsistencies in reviewer ratings and introduces the Review Tendency Signal (RTS) as a probabilistic integration of reviewer scores and confidences. To support training and evaluation, we further construct NAIDv2, a large-scale dataset of 24,276 ICLR submissions enriched with metadata and detailed structured content. Trained on pairwise comparisons but enabling efficient pointwise prediction at deployment, NAIPv2 achieves state-of-the-art performance (78.2% AUC, 0.432 Spearman), while maintaining scalable, linear-time efficiency at inference. Notably, on unseen NeurIPS submissions, it further demonstrates strong generalization, with predicted scores increasing consistently across decision categories from Rejected to Oral. These findings establish NAIPv2 as a debiased and scalable framework for automated paper quality estimation, marking a step toward future scientific intelligence systems. Code and dataset are released at https://sway.cloud.microsoft/Pr42npP80MfPhvj8.

Assessing sampling uncertainty in extremum estimation can be challenging when the asymptotic variance is not analytically tractable. Bootstrap inference offers a feasible solution but can be computationally costly especially when the model is complex. This paper uses iterates of a specially designed stochastic optimization algorithm as draws from which both point estimates and bootstrap standard errors can be computed in a single run. The draws are generated by the gradient and Hessian computed from batches of data that are resampled at each iteration. We show that these draws yield consistent estimates and asymptotically valid frequentist inference for a large class of regular problems. The algorithm provides accurate standard errors in simulation examples and empirical applications at low computational costs. The draws from the algorithm also provide a convenient way to detect data irregularities.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

We consider the Similarity Sketching problem: Given a universe [u] = {0,ldots, u-1} we want a random function S mapping subsets Asubseteq [u] into vectors S(A) of size t, such that the Jaccard similarity J(A,B) = |Acap B|/|Acup B| between sets A and B is preserved. More precisely, define X_i = [S(A)[i] = S(B)[i]] and X = sum_{iin [t]} X_i. We want E[X_i]=J(A,B), and we want X to be strongly concentrated around E[X] = t cdot J(A,B) (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, large-scale classification, computer vision, similarity search, etc. via the classic MinHash algorithm. The vectors S(A) are also called sketches. Strong concentration is critical, for often we want to sketch many sets B_1,ldots,B_n so that we later, for a query set A, can find (one of) the most similar B_i. It is then critical that no B_i looks much more similar to A due to errors in the sketch. The seminal ttimesMinHash algorithm uses t random hash functions h_1,ldots, h_t, and stores left ( min_{ain A} h_1(A),ldots, min_{ain A} h_t(A) right ) as the sketch of A. The main drawback of MinHash is, however, its O(tcdot |A|) running time, and finding a sketch with similar properties and faster running time has been the subject of several papers. (continued...)

We introduce a differentiable estimator of range-partition entropy, a recent concept from computational geometry that enables algorithms to adapt to the "sortedness" of their input. While range-partition entropy provides strong guarantees in algorithm design, it has not yet been made accessible to deep learning. In this work, we (i) propose the first differentiable approximation of range-partition entropy, enabling its use as a trainable loss or regularizer; (ii) design EntropyNet, a neural module that restructures data into low-entropy forms to accelerate downstream instance-optimal algorithms; and (iii) extend this principle beyond geometry by applying entropy regularization directly to Transformer attention. Across tasks, we demonstrate that differentiable entropy improves efficiency without degrading correctness: in geometry, our method achieves up to 4.1times runtime speedups with negligible error (<0.2%); in deep learning, it induces structured attention patterns that yield 6% higher accuracy at 80% sparsity compared to L1 baselines. Our theoretical analysis provides approximation bounds for the estimator, and extensive ablations validate design choices. These results suggest that entropy-bounded computation is not only theoretically elegant but also a practical mechanism for adaptive learning, efficiency, and structured representation.

Point-based interactive colorization techniques allow users to effortlessly colorize grayscale images using user-provided color hints. However, point-based methods often face challenges when different colors are given to semantically similar areas, leading to color intermingling and unsatisfactory results-an issue we refer to as color collapse. The fundamental cause of color collapse is the inadequacy of points for defining the boundaries for each color. To mitigate color collapse, we introduce a lasso tool that can control the scope of each color hint. Additionally, we design a framework that leverages the user-provided lassos to localize the attention masks. The experimental results show that using a single lasso is as effective as applying 4.18 individual color hints and can achieve the desired outcomes in 30% less time than using points alone.

Diffusion models have recently demonstrated their effectiveness in generating extremely high-quality images and are now utilized in a wide range of applications, including automatic sketch colorization. Although many methods have been developed for guided sketch colorization, there has been limited exploration of the potential conflicts between image prompts and sketch inputs, which can lead to severe deterioration in the results. Therefore, this paper exhaustively investigates reference-based sketch colorization models that aim to colorize sketch images using reference color images. We specifically investigate two critical aspects of reference-based diffusion models: the "distribution problem", which is a major shortcoming compared to text-based counterparts, and the capability in zero-shot sequential text-based manipulation. We introduce two variations of an image-guided latent diffusion model utilizing different image tokens from the pre-trained CLIP image encoder and propose corresponding manipulation methods to adjust their results sequentially using weighted text inputs. We conduct comprehensive evaluations of our models through qualitative and quantitative experiments as well as a user study.

Serving LLMs requires substantial memory due to the storage requirements of Key-Value (KV) embeddings in the KV cache, which grows with sequence length. An effective approach to compress KV cache is quantization. However, traditional quantization methods face significant memory overhead due to the need to store quantization constants (at least a zero point and a scale) in full precision per data block. Depending on the block size, this overhead can add 1 or 2 bits per quantized number. We introduce QJL, a new quantization approach that consists of a Johnson-Lindenstrauss (JL) transform followed by sign-bit quantization. In contrast to existing methods, QJL eliminates memory overheads by removing the need for storing quantization constants. We propose an asymmetric estimator for the inner product of two vectors and demonstrate that applying QJL to one vector and a standard JL transform without quantization to the other provides an unbiased estimator with minimal distortion. We have developed an efficient implementation of the QJL sketch and its corresponding inner product estimator, incorporating a lightweight CUDA kernel for optimized computation. When applied across various LLMs and NLP tasks to quantize the KV cache to only 3 bits, QJL demonstrates a more than fivefold reduction in KV cache memory usage without compromising accuracy, all while achieving faster runtime. Codes are available at https://github.com/amirzandieh/QJL.

The remarkable success of diffusion and flow-matching models has ignited a surge of works on adapting them at test time for controlled generation tasks. Examples range from image editing to restoration, compression and personalization. However, due to the iterative nature of the sampling process in those models, it is computationally impractical to use gradient-based optimization to directly control the image generated at the end of the process. As a result, existing methods typically resort to manipulating each timestep separately. Here we introduce FlowOpt - a zero-order (gradient-free) optimization framework that treats the entire flow process as a black box, enabling optimization through the whole sampling path without backpropagation through the model. Our method is both highly efficient and allows users to monitor the intermediate optimization results and perform early stopping if desired. We prove a sufficient condition on FlowOpt's step-size, under which convergence to the global optimum is guaranteed. We further show how to empirically estimate this upper bound so as to choose an appropriate step-size. We demonstrate how FlowOpt can be used for image editing, showcasing two options: (i) inversion (determining the initial noise that generates a given image), and (ii) directly steering the edited image to be similar to the source image while conforming to a target text prompt. In both cases, FlowOpt achieves state-of-the-art results while using roughly the same number of neural function evaluations (NFEs) as existing methods. Code and examples are available on the project's webpage.

We consider the optimization problem of the form min_{x in R^d} f(x) triangleq E_{xi} [F(x; xi)], where the component F(x;xi) is L-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently proposed gradient-free method requires at most O( L^4 d^{3/2} epsilon^{-4} + Delta L^3 d^{3/2} delta^{-1} epsilon^{-4}) stochastic zeroth-order oracle complexity to find a (delta,epsilon)-Goldstein stationary point of objective function, where Delta = f(x_0) - inf_{x in R^d} f(x) and x_0 is the initial point of the algorithm. This paper proposes a more efficient algorithm using stochastic recursive gradient estimators, which improves the complexity to O(L^3 d^{3/2} epsilon^{-3}+ Delta L^2 d^{3/2} delta^{-1} epsilon^{-3}).

Text-to-image generation has recently witnessed remarkable achievements. We introduce a text-conditional image diffusion model, termed RAPHAEL, to generate highly artistic images, which accurately portray the text prompts, encompassing multiple nouns, adjectives, and verbs. This is achieved by stacking tens of mixture-of-experts (MoEs) layers, i.e., space-MoE and time-MoE layers, enabling billions of diffusion paths (routes) from the network input to the output. Each path intuitively functions as a "painter" for depicting a particular textual concept onto a specified image region at a diffusion timestep. Comprehensive experiments reveal that RAPHAEL outperforms recent cutting-edge models, such as Stable Diffusion, ERNIE-ViLG 2.0, DeepFloyd, and DALL-E 2, in terms of both image quality and aesthetic appeal. Firstly, RAPHAEL exhibits superior performance in switching images across diverse styles, such as Japanese comics, realism, cyberpunk, and ink illustration. Secondly, a single model with three billion parameters, trained on 1,000 A100 GPUs for two months, achieves a state-of-the-art zero-shot FID score of 6.61 on the COCO dataset. Furthermore, RAPHAEL significantly surpasses its counterparts in human evaluation on the ViLG-300 benchmark. We believe that RAPHAEL holds the potential to propel the frontiers of image generation research in both academia and industry, paving the way for future breakthroughs in this rapidly evolving field. More details can be found on a project webpage: https://raphael-painter.github.io/.

The lottery ticket hypothesis (LTH) has increased attention to pruning neural networks at initialization. We study this problem in the linear setting. We show that finding a sparse mask at initialization is equivalent to the sketching problem introduced for efficient matrix multiplication. This gives us tools to analyze the LTH problem and gain insights into it. Specifically, using the mask found at initialization, we bound the approximation error of the pruned linear model at the end of training. We theoretically justify previous empirical evidence that the search for sparse networks may be data independent. By using the sketching perspective, we suggest a generic improvement to existing algorithms for pruning at initialization, which we show to be beneficial in the data-independent case.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

On-line handwritten character segmentation is often associated with handwriting recognition and even though recognition models include mechanisms to locate relevant positions during the recognition process, it is typically insufficient to produce a precise segmentation. Decoupling the segmentation from the recognition unlocks the potential to further utilize the result of the recognition. We specifically focus on the scenario where the transcription is known beforehand, in which case the character segmentation becomes an assignment problem between sampling points of the stylus trajectory and characters in the text. Inspired by the k-means clustering algorithm, we view it from the perspective of cluster assignment and present a Transformer-based architecture where each cluster is formed based on a learned character query in the Transformer decoder block. In order to assess the quality of our approach, we create character segmentation ground truths for two popular on-line handwriting datasets, IAM-OnDB and HANDS-VNOnDB, and evaluate multiple methods on them, demonstrating that our approach achieves the overall best results.

Recent advances in generative AI have accelerated the production of ultra-high-resolution visual content, posing significant challenges for efficient compression and real-time decoding on end-user devices. Inspired by 3D Gaussian Splatting, recent 2D Gaussian image models improve representation efficiency, yet existing methods struggle to balance compression ratio and reconstruction fidelity in ultra-high-resolution scenarios. To address this issue, we propose SmartSplat, a highly adaptive and feature-aware GS-based image compression framework that supports arbitrary image resolutions and compression ratios. SmartSplat leverages image-aware features such as gradients and color variances, introducing a Gradient-Color Guided Variational Sampling strategy together with an Exclusion-based Uniform Sampling scheme to improve the non-overlapping coverage of Gaussian primitives in pixel space. In addition, we propose a Scale-Adaptive Gaussian Color Sampling method to enhance color initialization across scales. Through joint optimization of spatial layout, scale, and color initialization, SmartSplat efficiently captures both local structures and global textures using a limited number of Gaussians, achieving high reconstruction quality under strong compression. Extensive experiments on DIV8K and a newly constructed 16K dataset demonstrate that SmartSplat consistently outperforms state-of-the-art methods at comparable compression ratios and exceeds their compression limits, showing strong scalability and practical applicability. The code is publicly available at https://github.com/lif314/SmartSplat.

Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a kernel function and a subset size k, our goal is to sample k out of n items with probability proportional to the determinant of the kernel matrix induced by the subset (a.k.a. k-DPP). Existing k-DPP sampling algorithms require an expensive preprocessing step which involves multiple passes over all n items, making it infeasible for large datasets. A naïve heuristic addressing this problem is to uniformly subsample a fraction of the data and perform k-DPP sampling only on those items, however this method offers no guarantee that the produced sample will even approximately resemble the target distribution over the original dataset. In this paper, we develop an algorithm which adaptively builds a sufficiently large uniform sample of data that is then used to efficiently generate a smaller set of k items, while ensuring that this set is drawn exactly from the target distribution defined on all n items. We show empirically that our algorithm produces a k-DPP sample after observing only a small fraction of all elements, leading to several orders of magnitude faster performance compared to the state-of-the-art.

This study addresses the challenge of accurately segmenting 3D Gaussian Splatting from 2D masks. Conventional methods often rely on iterative gradient descent to assign each Gaussian a unique label, leading to lengthy optimization and sub-optimal solutions. Instead, we propose a straightforward yet globally optimal solver for 3D-GS segmentation. The core insight of our method is that, with a reconstructed 3D-GS scene, the rendering of the 2D masks is essentially a linear function with respect to the labels of each Gaussian. As such, the optimal label assignment can be solved via linear programming in closed form. This solution capitalizes on the alpha blending characteristic of the splatting process for single step optimization. By incorporating the background bias in our objective function, our method shows superior robustness in 3D segmentation against noises. Remarkably, our optimization completes within 30 seconds, about 50times faster than the best existing methods. Extensive experiments demonstrate the efficiency and robustness of our method in segmenting various scenes, and its superior performance in downstream tasks such as object removal and inpainting. Demos and code will be available at https://github.com/florinshen/FlashSplat.

The emergence of large language models (LLMs) has significantly pushed the frontiers of program synthesis. Advancement of LLM-based program synthesis calls for a thorough evaluation of LLM-generated code. Most evaluation frameworks focus on the (functional) correctness of generated code; efficiency, as an important measure of code quality, has been overlooked in existing evaluations. In this work, we develop ENAMEL (EfficeNcy AutoMatic EvaLuator), a rigorous and high-standard benchmark for evaluating the capability of LLMs in generating efficient code. Firstly, we propose a new efficiency metric called eff@k, which generalizes the pass@k metric from correctness to efficiency and appropriately handles right-censored execution time. Furthermore, we derive an unbiased and variance-reduced estimator of eff@k via Rao--Blackwellization; we also provide a numerically stable implementation for the new estimator. Secondly, to set a high-standard for efficiency evaluation, we employ a human expert to design best algorithms and implementations as our reference solutions of efficiency, many of which are much more efficient than existing canonical solutions in HumanEval and HumanEval+. Moreover, to ensure a rigorous evaluation, we employ a human expert to curate strong test case generators to filter out wrong code and differentiate suboptimal algorithms. An extensive study across 30 popular LLMs using our benchmark ENAMEL shows that LLMs still fall short of generating expert-level efficient code. Using two subsets of our problem set, we demonstrate that such deficiency is because current LLMs struggle in designing advanced algorithms and are barely aware of implementation optimization. Our benchmark is publicly available at https://github.com/q-rz/enamel .

Cutting out an object and estimating its opacity mask, known as image matting, is a key task in image and video editing. Due to the highly ill-posed issue, additional inputs, typically user-defined trimaps or scribbles, are usually needed to reduce the uncertainty. Although effective, it is either time consuming or only suitable for experienced users who know where to place the strokes. In this work, we propose a decomposed-uncertainty-guided matting (dugMatting) algorithm, which explores the explicitly decomposed uncertainties to efficiently and effectively improve the results. Basing on the characteristic of these uncertainties, the epistemic uncertainty is reduced in the process of guiding interaction (which introduces prior knowledge), while the aleatoric uncertainty is reduced in modeling data distribution (which introduces statistics for both data and possible noise). The proposed matting framework relieves the requirement for users to determine the interaction areas by using simple and efficient labeling. Extensively quantitative and qualitative results validate that the proposed method significantly improves the original matting algorithms in terms of both efficiency and efficacy.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

As sketch research has collectively matured over time, its adaptation for at-mass commercialisation emerges on the immediate horizon. Despite an already mature research endeavour for photos, there is no research on the efficient inference specifically designed for sketch data. In this paper, we first demonstrate existing state-of-the-art efficient light-weight models designed for photos do not work on sketches. We then propose two sketch-specific components which work in a plug-n-play manner on any photo efficient network to adapt them to work on sketch data. We specifically chose fine-grained sketch-based image retrieval (FG-SBIR) as a demonstrator as the most recognised sketch problem with immediate commercial value. Technically speaking, we first propose a cross-modal knowledge distillation network to transfer existing photo efficient networks to be compatible with sketch, which brings down number of FLOPs and model parameters by 97.96% percent and 84.89% respectively. We then exploit the abstract trait of sketch to introduce a RL-based canvas selector that dynamically adjusts to the abstraction level which further cuts down number of FLOPs by two thirds. The end result is an overall reduction of 99.37% of FLOPs (from 40.18G to 0.254G) when compared with a full network, while retaining the accuracy (33.03% vs 32.77%) -- finally making an efficient network for the sparse sketch data that exhibit even fewer FLOPs than the best photo counterpart.

Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is particularly effective in handling high-dimensional inner products and matrix multiplication, in applications of image analysis and large-scale supervised learning.

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any non-negative integer D for the total number of nestings. Standard Monte Carlo methods typically cost at least O(varepsilon^{-(2+D)}) and sometimes O(varepsilon^{-2(1+D)}) to obtain an estimator up to varepsilon-error. More advanced methods, such as multilevel Monte Carlo, currently only exist for D = 1. In this paper, we propose a novel Monte Carlo estimator called READ, which stands for "Recursive Estimator for Arbitrary Depth.'' Our estimator has an optimal computational cost of O(varepsilon^{-2}) for every fixed D under suitable assumptions, and a nearly optimal computational cost of O(varepsilon^{-2(1 + delta)}) for any 0 < delta < frac12 under much more general assumptions. Our estimator is also unbiased, which makes it easy to parallelize. The key ingredients in our construction are an observation of the problem's recursive structure and the recursive use of the randomized multilevel Monte Carlo method.

This paper presents VQ-SGen, a novel algorithm for high-quality creative sketch generation. Recent approaches have framed the task as pixel-based generation either as a whole or part-by-part, neglecting the intrinsic and contextual relationships among individual strokes, such as the shape and spatial positioning of both proximal and distant strokes. To overcome these limitations, we propose treating each stroke within a sketch as an entity and introducing a vector-quantized (VQ) stroke representation for fine-grained sketch generation. Our method follows a two-stage framework - in stage one, we decouple each stroke's shape and location information to ensure the VQ representation prioritizes stroke shape learning. In stage two, we feed the precise and compact representation into an auto-decoding Transformer to incorporate stroke semantics, positions, and shapes into the generation process. By utilizing tokenized stroke representation, our approach generates strokes with high fidelity and facilitates novel applications, such as text or class label conditioned generation and sketch completion. Comprehensive experiments demonstrate our method surpasses existing state-of-the-art techniques on the CreativeSketch dataset, underscoring its effectiveness.

Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not employ any training signal, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models, in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors, each subject to an unknown positive multiplicative factor (or gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable, carefully chosen initialisation point. An analysis of this algorithm allows us to show that it converges to the exact solution provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Interestingly, we show that this requirement grows linearly (up to log factors) in the number of unknowns of the problem. This sample complexity is found both in absence of prior information, as well as when subspace priors are available for both the signal and gains, allowing a further reduction of the number of observations required for our recovery guarantees to hold. Moreover, in the presence of noise we show how our descent algorithm yields a solution whose accuracy degrades gracefully with the amount of noise affecting the measurements. Finally, we present some numerical experiments in an imaging context, where our algorithm allows for a simple solution to blind calibration of the gains in a sensor array.

Existing vector quantization (VQ) methods struggle with scalability, largely attributed to the instability of the codebook that undergoes partial updates during training. The codebook is prone to collapse as utilization decreases, due to the progressively widening distribution gap between non-activated codes and visual features. To solve the problem, we propose Index Backpropagation Quantization (IBQ), a new VQ method for the joint optimization of all codebook embeddings and the visual encoder. Applying a straight-through estimator on the one-hot categorical distribution between the encoded feature and codebook, all codes are differentiable and maintain a consistent latent space with the visual encoder. IBQ enables scalable training of visual tokenizers and, for the first time, achieves a large-scale codebook (2^{18}) with high dimension (256) and high utilization. Experiments on the standard ImageNet benchmark demonstrate the scalability and superiority of IBQ, achieving competitive results on both reconstruction (1.00 rFID) and autoregressive visual generation (2.05 gFID). The code and models are available at https://github.com/TencentARC/SEED-Voken.

Generating accurate glyphs for visual text rendering is essential yet challenging. Existing methods typically enhance text rendering by training on a large amount of high-quality scene text images, but the limited coverage of glyph variations and excessive stylization often compromise glyph accuracy, especially for complex or out-of-domain characters. Some methods leverage reinforcement learning to alleviate this issue, yet their reward models usually depend on text recognition systems that are insensitive to fine-grained glyph errors, so images with incorrect glyphs may still receive high rewards. Inspired by Direct Preference Optimization (DPO), we propose GlyphPrinter, a preference-based text rendering method that eliminates reliance on explicit reward models. However, the standard DPO objective only models overall preference between two samples, which is insufficient for visual text rendering where glyph errors typically occur in localized regions. To address this issue, we construct the GlyphCorrector dataset with region-level glyph preference annotations and propose Region-Grouped DPO (R-GDPO), a region-based objective that optimizes inter- and intra-sample preferences over annotated regions, substantially enhancing glyph accuracy. Furthermore, we introduce Regional Reward Guidance, an inference strategy that samples from an optimal distribution with controllable glyph accuracy. Extensive experiments demonstrate that the proposed GlyphPrinter outperforms existing methods in glyph accuracy while maintaining a favorable balance between stylization and precision.

One tough problem of image inpainting is to restore complex structures in the corrupted regions. It motivates interactive image inpainting which leverages additional hints, e.g., sketches, to assist the inpainting process. Sketch is simple and intuitive to end users, but meanwhile has free forms with much randomness. Such randomness may confuse the inpainting models, and incur severe artifacts in completed images. To address this problem, we propose a two-stage image inpainting method termed SketchRefiner. In the first stage, we propose using a cross-correlation loss function to robustly calibrate and refine the user-provided sketches in a coarse-to-fine fashion. In the second stage, we learn to extract informative features from the abstracted sketches in the feature space and modulate the inpainting process. We also propose an algorithm to simulate real sketches automatically and build a test protocol with different applications. Experimental results on public datasets demonstrate that SketchRefiner effectively utilizes sketch information and eliminates the artifacts due to the free-form sketches. Our method consistently outperforms the state-of-the-art ones both qualitatively and quantitatively, meanwhile revealing great potential in real-world applications. Our code and dataset are available.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

We introduce VectorPainter, a novel framework designed for reference-guided text-to-vector-graphics synthesis. Based on our observation that the style of strokes can be an important aspect to distinguish different artists, our method reforms the task into synthesize a desired vector graphics by rearranging stylized strokes, which are vectorized from the reference images. Specifically, our method first converts the pixels of the reference image into a series of vector strokes, and then generates a vector graphic based on the input text description by optimizing the positions and colors of these vector strokes. To precisely capture the style of the reference image in the vectorized strokes, we propose an innovative vectorization method that employs an imitation learning strategy. To preserve the style of the strokes throughout the generation process, we introduce a style-preserving loss function. Extensive experiments have been conducted to demonstrate the superiority of our approach over existing works in stylized vector graphics synthesis, as well as the effectiveness of the various components of our method.

Point-interactive image colorization aims to colorize grayscale images when a user provides the colors for specific locations. It is essential for point-interactive colorization methods to appropriately propagate user-provided colors (i.e., user hints) in the entire image to obtain a reasonably colorized image with minimal user effort. However, existing approaches often produce partially colorized results due to the inefficient design of stacking convolutional layers to propagate hints to distant relevant regions. To address this problem, we present iColoriT, a novel point-interactive colorization Vision Transformer capable of propagating user hints to relevant regions, leveraging the global receptive field of Transformers. The self-attention mechanism of Transformers enables iColoriT to selectively colorize relevant regions with only a few local hints. Our approach colorizes images in real-time by utilizing pixel shuffling, an efficient upsampling technique that replaces the decoder architecture. Also, in order to mitigate the artifacts caused by pixel shuffling with large upsampling ratios, we present the local stabilizing layer. Extensive quantitative and qualitative results demonstrate that our approach highly outperforms existing methods for point-interactive colorization, producing accurately colorized images with a user's minimal effort. Official codes are available at https://pmh9960.github.io/research/iColoriT

Paging is a prototypical problem in the area of online algorithms. It has also played a central role in the development of learning-augmented algorithms -- a recent line of research that aims to ameliorate the shortcomings of classical worst-case analysis by giving algorithms access to predictions. Such predictions can typically be generated using a machine learning approach, but they are inherently imperfect. Previous work on learning-augmented paging has investigated predictions on (i) when the current page will be requested again (reoccurrence predictions), (ii) the current state of the cache in an optimal algorithm (state predictions), (iii) all requests until the current page gets requested again, and (iv) the relative order in which pages are requested. We study learning-augmented paging from the new perspective of requiring the least possible amount of predicted information. More specifically, the predictions obtained alongside each page request are limited to one bit only. We consider two natural such setups: (i) discard predictions, in which the predicted bit denotes whether or not it is ``safe'' to evict this page, and (ii) phase predictions, where the bit denotes whether the current page will be requested in the next phase (for an appropriate partitioning of the input into phases). We develop algorithms for each of the two setups that satisfy all three desirable properties of learning-augmented algorithms -- that is, they are consistent, robust and smooth -- despite being limited to a one-bit prediction per request. We also present lower bounds establishing that our algorithms are essentially best possible.

The evaluation of generative models for natural image tasks has been extensively studied. Similar protocols and metrics are used in cases with unique particularities, such as Handwriting Generation, even if they might not be completely appropriate. In this work, we introduce three measures tailored for HTG evaluation, HTG_{HTR} , HTG_{style} , and HTG_{OOV} , and argue that they are more expedient to evaluate the quality of generated handwritten images. The metrics rely on the recognition error/accuracy of Handwriting Text Recognition and Writer Identification models and emphasize writing style, textual content, and diversity as the main aspects that adhere to the content of handwritten images. We conduct comprehensive experiments on the IAM handwriting database, showcasing that widely used metrics such as FID fail to properly quantify the diversity and the practical utility of generated handwriting samples. Our findings show that our metrics are richer in information and underscore the necessity of standardized evaluation protocols in HTG. The proposed metrics provide a more robust and informative protocol for assessing HTG quality, contributing to improved performance in HTR. Code for the evaluation protocol is available at: https://github.com/koninik/HTG_evaluation.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

We propose a method for scene-level sketch-to-photo synthesis with text guidance. Although object-level sketch-to-photo synthesis has been widely studied, whole-scene synthesis is still challenging without reference photos that adequately reflect the target style. To this end, we leverage knowledge from recent large-scale pre-trained generative models, resulting in text-guided sketch-to-photo synthesis without the need for reference images. To train our model, we use self-supervised learning from a set of photographs. Specifically, we use a pre-trained edge detector that maps both color and sketch images into a standardized edge domain, which reduces the gap between photograph-based edge images (during training) and hand-drawn sketch images (during inference). We implement our method by fine-tuning a latent diffusion model (i.e., Stable Diffusion) with sketch and text conditions. Experiments show that the proposed method translates original sketch images that are not extracted from color images into photos with compelling visual quality.

The SIML (abbreviation of Separating Information Maximal Likelihood) method, has been introduced by N. Kunitomo and S. Sato and their collaborators to estimate the integrated volatility of high-frequency data that is assumed to be an It\^o process but with so-called microstructure noise. The SIML estimator turned out to share many properties with the estimator introduced by P. Malliavin and M.E. Mancino. The present paper establishes the consistency and the asymptotic normality under a general sampling scheme but without microstructure noise. Specifically, a fast convergence shown for Malliavin--Mancino estimator by E. Clement and A. Gloter is also established for the SIML estimator.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over- or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance. To better estimate the uncertainty at each iteration, we propose Conformal Information Pursuit (C-IP), an alternative approach to sequential information gain based on conformal prediction sets. More specifically, C-IP leverages a relationship between prediction sets and conditional entropy at each iteration to estimate uncertainty based on the average size of conformal prediction sets. In contrast to conditional entropy, we find that conformal prediction sets are a distribution-free and robust method of measuring uncertainty. Experiments with 20 Questions show that C-IP obtains better predictive performance and shorter query-answer chains compared to previous approaches to IP and uncertainty-based chain-of-thought methods. Furthermore, extending to an interactive medical setting between a doctor and a patient on the MediQ dataset, C-IP achieves competitive performance with direct single-turn prediction while offering greater interpretability.

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

This paper introduces a cost-effective robotic handwriting system designed to replicate human-like handwriting with high precision. Combining a Raspberry Pi Pico microcontroller, 3D-printed components, and a machine learning-based handwriting generation model implemented via TensorFlow, the system converts user-supplied text into realistic stroke trajectories. By leveraging lightweight 3D-printed materials and efficient mechanical designs, the system achieves a total hardware cost of approximately \56, significantly undercutting commercial alternatives. Experimental evaluations demonstrate handwriting precision within \pm$0.3 millimeters and a writing speed of approximately 200 mm/min, positioning the system as a viable solution for educational, research, and assistive applications. This study seeks to lower the barriers to personalized handwriting technologies, making them accessible to a broader audience.

Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower dimensions. In this paper, we propose a novel sketching scheme for the first order method in large-scale distributed learning setting, such that the communication costs between distributed agents are saved while the convergence of the algorithms is still guaranteed. Given gradient information in a high dimension d, the agent passes the compressed information processed by a sketching matrix Rin R^{stimes d} with sll d, and the receiver de-compressed via the de-sketching matrix R^top to ``recover'' the information in original dimension. Using such a framework, we develop algorithms for federated learning with lower communication costs. However, such random sketching does not protect the privacy of local data directly. We show that the gradient leakage problem still exists after applying the sketching technique by presenting a specific gradient attack method. As a remedy, we prove rigorously that the algorithm will be differentially private by adding additional random noises in gradient information, which results in a both communication-efficient and differentially private first order approach for federated learning tasks. Our sketching scheme can be further generalized to other learning settings and might be of independent interest itself.

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in the high-dimensional, undersampled regimes typical of modern experiments. Recent machine learning-based estimators show promise, but their accuracy depends sensitively on dataset size, structure, and hyperparameters, with no accepted tests to detect failures. We close these gaps through a systematic evaluation of classical and neural MI estimators across standard benchmarks and new synthetic datasets tailored to challenging high-dimensional, undersampled regimes. We contribute: (i) a practical protocol for reliable MI estimation with explicit checks for statistical consistency; (ii) confidence intervals (error bars around estimates) that existing neural MI estimator do not provide; and (iii) a new class of probabilistic critics designed for high-dimensional, high-information settings. We demonstrate the effectiveness of our protocol with computational experiments, showing that it consistently matches or surpasses existing methods while uniquely quantifying its own reliability. We show that reliable MI estimation is sometimes achievable even in severely undersampled, high-dimensional datasets, provided they admit accurate low-dimensional representations. This broadens the scope of applicability of neural MI estimators and clarifies when such estimators can be trusted.

Building on recent advances in image generation, we present a fully data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising operations on top of a Gaussian noise distribution. We view the diffusion denoising process as a sequential decision making process, and show that it exhibits compounding errors similar to exposure bias issues in imitation learning problems. To mitigate these issues, we adapt the scheduled sampling algorithm to diffusion training. We conduct experiments on four markup datasets: mathematical formulas (LaTeX), table layouts (HTML), sheet music (LilyPond), and molecular images (SMILES). These experiments each verify the effectiveness of the diffusion process and the use of scheduled sampling to fix generation issues. These results also show that the markup-to-image task presents a useful controlled compositional setting for diagnosing and analyzing generative image models.

Recent remarkable advances in large-scale text-to-image diffusion models have inspired a significant breakthrough in text-to-3D generation, pursuing 3D content creation solely from a given text prompt. However, existing text-to-3D techniques lack a crucial ability in the creative process: interactively control and shape the synthetic 3D contents according to users' desired specifications (e.g., sketch). To alleviate this issue, we present the first attempt for text-to-3D generation conditioning on the additional hand-drawn sketch, namely Control3D, which enhances controllability for users. In particular, a 2D conditioned diffusion model (ControlNet) is remoulded to guide the learning of 3D scene parameterized as NeRF, encouraging each view of 3D scene aligned with the given text prompt and hand-drawn sketch. Moreover, we exploit a pre-trained differentiable photo-to-sketch model to directly estimate the sketch of the rendered image over synthetic 3D scene. Such estimated sketch along with each sampled view is further enforced to be geometrically consistent with the given sketch, pursuing better controllable text-to-3D generation. Through extensive experiments, we demonstrate that our proposal can generate accurate and faithful 3D scenes that align closely with the input text prompts and sketches.

Assessing student handwritten scratchwork is crucial for personalized educational feedback but presents unique challenges due to diverse handwriting, complex layouts, and varied problem-solving approaches. Existing educational NLP primarily focuses on textual responses and neglects the complexity and multimodality inherent in authentic handwritten scratchwork. Current multimodal large language models (MLLMs) excel at visual reasoning but typically adopt an "examinee perspective", prioritizing generating correct answers rather than diagnosing student errors. To bridge these gaps, we introduce ScratchMath, a novel benchmark specifically designed for explaining and classifying errors in authentic handwritten mathematics scratchwork. Our dataset comprises 1,720 mathematics samples from Chinese primary and middle school students, supporting two key tasks: Error Cause Explanation (ECE) and Error Cause Classification (ECC), with seven defined error types. The dataset is meticulously annotated through rigorous human-machine collaborative approaches involving multiple stages of expert labeling, review, and verification. We systematically evaluate 16 leading MLLMs on ScratchMath, revealing significant performance gaps relative to human experts, especially in visual recognition and logical reasoning. Proprietary models notably outperform open-source models, with large reasoning models showing strong potential for error explanation. All evaluation data and frameworks are publicly available to facilitate further research.

Existing handwritten text generation methods often require more than ten handwriting samples as style references. However, in practical applications, users tend to prefer a handwriting generation model that operates with just a single reference sample for its convenience and efficiency. This approach, known as "one-shot generation", significantly simplifies the process but poses a significant challenge due to the difficulty of accurately capturing a writer's style from a single sample, especially when extracting fine details from the characters' edges amidst sparse foreground and undesired background noise. To address this problem, we propose a One-shot Diffusion Mimicker (One-DM) to generate handwritten text that can mimic any calligraphic style with only one reference sample. Inspired by the fact that high-frequency information of the individual sample often contains distinct style patterns (e.g., character slant and letter joining), we develop a novel style-enhanced module to improve the style extraction by incorporating high-frequency components from a single sample. We then fuse the style features with the text content as a merged condition for guiding the diffusion model to produce high-quality handwritten text images. Extensive experiments demonstrate that our method can successfully generate handwriting scripts with just one sample reference in multiple languages, even outperforming previous methods using over ten samples. Our source code is available at https://github.com/dailenson/One-DM.

We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural stationarity measure to zero at the rate O(k^{-1/4}). As a consequence, we obtain the first complexity guarantees for the stochastic proximal point, proximal subgradient, and regularized Gauss-Newton methods for minimizing compositions of convex functions with smooth maps. The guiding principle, underlying the complexity guarantees, is that all algorithms under consideration can be interpreted as approximate descent methods on an implicit smoothing of the problem, given by the Moreau envelope. Specializing to classical circumstances, we obtain the long-sought convergence rate of the stochastic projected gradient method, without batching, for minimizing a smooth function on a closed convex set.

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

We study the classic Text-to-Pattern Hamming Distances problem: given a pattern P of length m and a text T of length n, both over a polynomial-size alphabet, compute the Hamming distance between P and T[i, ., . , i+m-1] for every shift i, under the standard Word-RAM model with Theta(log n)-bit words. - We provide an O(nm) time Las Vegas randomized algorithm for this problem, beating the decades-old O(n m log m) running time [Abrahamson, SICOMP 1987]. We also obtain a deterministic algorithm, with a slightly higher O(nm(log mloglog m)^{1/4}) running time. Our randomized algorithm extends to the k-bounded setting, with running time Obig(n+nk{m}big), removing all the extra logarithmic factors from earlier algorithms [Gawrychowski and Uzna\'{n}ski, ICALP 2018; Chan, Golan, Kociumaka, Kopelowitz and Porat, STOC 2020]. - For the (1+epsilon)-approximate version of Text-to-Pattern Hamming Distances, we give an O(epsilon^{-0.93}n) time Monte Carlo randomized algorithm, beating the previous O(epsilon^{-1}n) running time [Kopelowitz and Porat, FOCS 2015; Kopelowitz and Porat, SOSA 2018]. Our approximation algorithm exploits a connection with 3SUM, and uses a combination of Fredman's trick, equality matrix product, and random sampling; in particular, we obtain new results on approximate counting versions of 3SUM and Exact Triangle, which may be of independent interest. Our exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion; in particular, we obtain a faster algorithm for computing the sumset of two integer sets, in the regime when the universe size is close to quadratic in the number of elements. We also prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3SUM.

This study addresses the challenge of estimating average treatment effects (ATEs) for advertising campaigns in online marketplaces where complete randomized experimentation is infeasible. We propose two key innovations: (1) a shrinkage estimator that optimally combines observational and experimental data without assuming smooth treatment effects across campaigns, and (2) a Bayesian adaptive experimental design framework that efficiently selects campaigns for randomized evaluation that minimizes cumulative risk. Our shrinkage estimator achieves lower risk compared to existing methods by balancing bias-variance tradeoffs, while our adaptive design significantly reduces the costs of campaign randomization. We establish theoretical guarantees including asymptotic normality and regret bounds. In an application to Amazon Ads data analyzing 2,583 campaigns, our approach achieves equivalent estimation precision while requiring only half of the randomized experiments needed by random sampling, the standard method widely used in practice today. The proposed method serves as a practical solution for marketplace platforms to efficiently measure advertising effectiveness while managing experimentation costs.

We propose SketchINR, to advance the representation of vector sketches with implicit neural models. A variable length vector sketch is compressed into a latent space of fixed dimension that implicitly encodes the underlying shape as a function of time and strokes. The learned function predicts the xy point coordinates in a sketch at each time and stroke. Despite its simplicity, SketchINR outperforms existing representations at multiple tasks: (i) Encoding an entire sketch dataset into a fixed size latent vector, SketchINR gives 60times and 10times data compression over raster and vector sketches, respectively. (ii) SketchINR's auto-decoder provides a much higher-fidelity representation than other learned vector sketch representations, and is uniquely able to scale to complex vector sketches such as FS-COCO. (iii) SketchINR supports parallelisation that can decode/render sim100times faster than other learned vector representations such as SketchRNN. (iv) SketchINR, for the first time, emulates the human ability to reproduce a sketch with varying abstraction in terms of number and complexity of strokes. As a first look at implicit sketches, SketchINR's compact high-fidelity representation will support future work in modelling long and complex sketches.

We describe a novel attribution method which is grounded in Sensitivity Analysis and uses Sobol indices. Beyond modeling the individual contributions of image regions, Sobol indices provide an efficient way to capture higher-order interactions between image regions and their contributions to a neural network's prediction through the lens of variance. We describe an approach that makes the computation of these indices efficient for high-dimensional problems by using perturbation masks coupled with efficient estimators to handle the high dimensionality of images. Importantly, we show that the proposed method leads to favorable scores on standard benchmarks for vision (and language models) while drastically reducing the computing time compared to other black-box methods -- even surpassing the accuracy of state-of-the-art white-box methods which require access to internal representations. Our code is freely available: https://github.com/fel-thomas/Sobol-Attribution-Method

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent variable models such as Gaussian mixtures are missing. Formally, we are given censored data from a mixture of univariate Gaussians $sum_{i=1}^k w_i N(mu_i,sigma^2), i.e. the sample is observed only if it lies inside a set S. The goal is to learn the weights w_i and the means \mu_i. We propose an algorithm that takes only 1{\varepsilon^{O(k)}} samples to estimate the weights w_i and the means \mu_i within \varepsilon$ error.

Traditional OCR systems (OCR-1.0) are increasingly unable to meet people's usage due to the growing demand for intelligent processing of man-made optical characters. In this paper, we collectively refer to all artificial optical signals (e.g., plain texts, math/molecular formulas, tables, charts, sheet music, and even geometric shapes) as "characters" and propose the General OCR Theory along with an excellent model, namely GOT, to promote the arrival of OCR-2.0. The GOT, with 580M parameters, is a unified, elegant, and end-to-end model, consisting of a high-compression encoder and a long-contexts decoder. As an OCR-2.0 model, GOT can handle all the above "characters" under various OCR tasks. On the input side, the model supports commonly used scene- and document-style images in slice and whole-page styles. On the output side, GOT can generate plain or formatted results (markdown/tikz/smiles/kern) via an easy prompt. Besides, the model enjoys interactive OCR features, i.e., region-level recognition guided by coordinates or colors. Furthermore, we also adapt dynamic resolution and multi-page OCR technologies to GOT for better practicality. In experiments, we provide sufficient results to prove the superiority of our model.

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine learning practitioners, our goal is to accelerate generalization of a model under grokking phenomenon. By regarding a series of gradients of a parameter over training iterations as a random signal over time, we can spectrally decompose the parameter trajectories under gradient descent into two components: the fast-varying, overfitting-yielding component and the slow-varying, generalization-inducing component. This analysis allows us to accelerate the grokking phenomenon more than times 50 with only a few lines of code that amplifies the slow-varying components of gradients. The experiments show that our algorithm applies to diverse tasks involving images, languages, and graphs, enabling practical availability of this peculiar artifact of sudden generalization. Our code is available at https://github.com/ironjr/grokfast.

Recent advancements in Vision-Language Models (VLMs) have opened new possibilities in automatic grading of handwritten student responses, particularly in mathematics. However, a comprehensive study to test the ability of VLMs to evaluate and reason over handwritten content remains absent. To address this gap, we introduce FERMAT, a benchmark designed to assess the ability of VLMs to detect, localize and correct errors in handwritten mathematical content. FERMAT spans four key error dimensions - computational, conceptual, notational, and presentation - and comprises over 2,200 handwritten math solutions derived from 609 manually curated problems from grades 7-12 with intentionally introduced perturbations. Using FERMAT we benchmark nine VLMs across three tasks: error detection, localization, and correction. Our results reveal significant shortcomings in current VLMs in reasoning over handwritten text, with Gemini-1.5-Pro achieving the highest error correction rate (77%). We also observed that some models struggle with processing handwritten content, as their accuracy improves when handwritten inputs are replaced with printed text or images. These findings highlight the limitations of current VLMs and reveal new avenues for improvement. We release FERMAT and all the associated resources in the open-source to drive further research.

We propose a learning-based method to recover normals, specularity, and roughness from a single diffuse image of a material, using microgeometry appearance as our primary cue. Previous methods that work on single images tend to produce over-smooth outputs with artifacts, operate at limited resolution, or train one model per class with little room for generalization. Previous methods that work on single images tend to produce over-smooth outputs with artifacts, operate at limited resolution, or train one model per class with little room for generalization. In contrast, in this work, we propose a novel capture approach that leverages a generative network with attention and a U-Net discriminator, which shows outstanding performance integrating global information at reduced computational complexity. We showcase the performance of our method with a real dataset of digitized textile materials and show that a commodity flatbed scanner can produce the type of diffuse illumination required as input to our method. Additionally, because the problem might be illposed -more than a single diffuse image might be needed to disambiguate the specular reflection- or because the training dataset is not representative enough of the real distribution, we propose a novel framework to quantify the model's confidence about its prediction at test time. Our method is the first one to deal with the problem of modeling uncertainty in material digitization, increasing the trustworthiness of the process and enabling more intelligent strategies for dataset creation, as we demonstrate with an active learning experiment.

Copying an element from a photo and pasting it into a painting is a challenging task. Applying photo compositing techniques in this context yields subpar results that look like a collage --- and existing painterly stylization algorithms, which are global, perform poorly when applied locally. We address these issues with a dedicated algorithm that carefully determines the local statistics to be transferred. We ensure both spatial and inter-scale statistical consistency and demonstrate that both aspects are key to generating quality results. To cope with the diversity of abstraction levels and types of paintings, we introduce a technique to adjust the parameters of the transfer depending on the painting. We show that our algorithm produces significantly better results than photo compositing or global stylization techniques and that it enables creative painterly edits that would be otherwise difficult to achieve.

A significant volume of analog information, i.e., documents and images, have been digitized in the form of scanned copies for storing, sharing, and/or analyzing in the digital world. However, the quality of such contents is severely degraded by various distortions caused by printing, storing, and scanning processes in the physical world. Although restoring high-quality content from scanned copies has become an indispensable task for many products, it has not been systematically explored, and to the best of our knowledge, no public datasets are available. In this paper, we define this problem as Descanning and introduce a new high-quality and large-scale dataset named DESCAN-18K. It contains 18K pairs of original and scanned images collected in the wild containing multiple complex degradations. In order to eliminate such complex degradations, we propose a new image restoration model called DescanDiffusion consisting of a color encoder that corrects the global color degradation and a conditional denoising diffusion probabilistic model (DDPM) that removes local degradations. To further improve the generalization ability of DescanDiffusion, we also design a synthetic data generation scheme by reproducing prominent degradations in scanned images. We demonstrate that our DescanDiffusion outperforms other baselines including commercial restoration products, objectively and subjectively, via comprehensive experiments and analyses.

Creating high quality and realistic materials in computer graphics is a challenging and time-consuming task, which requires great expertise. In this paper, we present MatFuse, a novel unified approach that harnesses the generative power of diffusion models (DM) to simplify the creation of SVBRDF maps. Our DM-based pipeline integrates multiple sources of conditioning, such as color palettes, sketches, and pictures, enabling fine-grained control and flexibility in material synthesis. This design allows for the combination of diverse information sources (e.g., sketch + image embedding), enhancing creative possibilities in line with the principle of compositionality. We demonstrate the generative capabilities of the proposed method under various conditioning settings; on the SVBRDF estimation task, we show that our method yields performance comparable to state-of-the-art approaches, both qualitatively and quantitatively.

Gaussian processes (GP) are a well studied Bayesian approach for the optimization of black-box functions. Despite their effectiveness in simple problems, GP-based algorithms hardly scale to high-dimensional functions, as their per-iteration time and space cost is at least quadratic in the number of dimensions d and iterations t. Given a set of A alternatives to choose from, the overall runtime O(t^3A) is prohibitive. In this paper we introduce BKB (budgeted kernelized bandit), a new approximate GP algorithm for optimization under bandit feedback that achieves near-optimal regret (and hence near-optimal convergence rate) with near-constant per-iteration complexity and remarkably no assumption on the input space or covariance of the GP. We combine a kernelized linear bandit algorithm (GP-UCB) with randomized matrix sketching based on leverage score sampling, and we prove that randomly sampling inducing points based on their posterior variance gives an accurate low-rank approximation of the GP, preserving variance estimates and confidence intervals. As a consequence, BKB does not suffer from variance starvation, an important problem faced by many previous sparse GP approximations. Moreover, we show that our procedure selects at most O(d_{eff}) points, where d_{eff} is the effective dimension of the explored space, which is typically much smaller than both d and t. This greatly reduces the dimensionality of the problem, thus leading to a O(TAd_{eff}^2) runtime and O(A d_{eff}) space complexity.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. Further, we iterate on the two steps again by using the second step's embeddings as new covariates for the next iteration. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples.

Tissue segmentation is a routine preprocessing step to reduce the computational cost of whole slide image (WSI) analysis by excluding background regions. Traditional image processing techniques are commonly used for tissue segmentation, but often require manual adjustments to parameter values for atypical cases, fail to exclude all slide and scanning artifacts from the background, and are unable to segment adipose tissue. Pen marking artifacts in particular can be a potential source of bias for subsequent analyses if not removed. In addition, several applications require the separation of individual cross-sections, which can be challenging due to tissue fragmentation and adjacent positioning. To address these problems, we develop a convolutional neural network for tissue and pen marking segmentation using a dataset of 200 H&E stained WSIs. For separating tissue cross-sections, we propose a novel post-processing method based on clustering predicted centroid locations of the cross-sections in a 2D histogram. On an independent test set, the model achieved a mean Dice score of 0.981pm0.033 for tissue segmentation and a mean Dice score of 0.912pm0.090 for pen marking segmentation. The mean absolute difference between the number of annotated and separated cross-sections was 0.075pm0.350. Our results demonstrate that the proposed model can accurately segment H&E stained tissue cross-sections and pen markings in WSIs while being robust to many common slide and scanning artifacts. The model with trained model parameters and post-processing method are made publicly available as a Python package called SlideSegmenter.

Tree boosting is a highly effective and widely used machine learning method. In this paper, we describe a scalable end-to-end tree boosting system called XGBoost, which is used widely by data scientists to achieve state-of-the-art results on many machine learning challenges. We propose a novel sparsity-aware algorithm for sparse data and weighted quantile sketch for approximate tree learning. More importantly, we provide insights on cache access patterns, data compression and sharding to build a scalable tree boosting system. By combining these insights, XGBoost scales beyond billions of examples using far fewer resources than existing systems.

As the physical size of recent CMOS image sensors (CIS) gets smaller, the latest mobile cameras are adopting unique non-Bayer color filter array (CFA) patterns (e.g., Quad, Nona, QxQ), which consist of homogeneous color units with adjacent pixels. These non-Bayer sensors are superior to conventional Bayer CFA thanks to their changeable pixel-bin sizes for different light conditions but may introduce visual artifacts during demosaicing due to their inherent pixel pattern structures and sensor hardware characteristics. Previous demosaicing methods have primarily focused on Bayer CFA, necessitating distinct reconstruction methods for non-Bayer patterned CIS with various CFA modes under different lighting conditions. In this work, we propose an efficient unified demosaicing method that can be applied to both conventional Bayer RAW and various non-Bayer CFAs' RAW data in different operation modes. Our Knowledge Learning-based demosaicing model for Adaptive Patterns, namely KLAP, utilizes CFA-adaptive filters for only 1% key filters in the network for each CFA, but still manages to effectively demosaic all the CFAs, yielding comparable performance to the large-scale models. Furthermore, by employing meta-learning during inference (KLAP-M), our model is able to eliminate unknown sensor-generic artifacts in real RAW data, effectively bridging the gap between synthetic images and real sensor RAW. Our KLAP and KLAP-M methods achieved state-of-the-art demosaicing performance in both synthetic and real RAW data of Bayer and non-Bayer CFAs.

Stable Diffusion and ControlNet have achieved excellent results in the field of image generation and synthesis. However, due to the granularity and method of its control, the efficiency improvement is limited for professional artistic creations such as comics and animation production whose main work is secondary painting. In the current workflow, fixing characters and image styles often need lengthy text prompts, and even requires further training through TextualInversion, DreamBooth or other methods, which is very complicated and expensive for painters. Therefore, we present a new method in this paper, Stable Diffusion Reference Only, a images-to-image self-supervised model that uses only two types of conditional images for precise control generation to accelerate secondary painting. The first type of conditional image serves as an image prompt, supplying the necessary conceptual and color information for generation. The second type is blueprint image, which controls the visual structure of the generated image. It is natively embedded into the original UNet, eliminating the need for ControlNet. We released all the code for the module and pipeline, and trained a controllable character line art coloring model at https://github.com/aihao2000/stable-diffusion-reference-only, that achieved state-of-the-art results in this field. This verifies the effectiveness of the structure and greatly improves the production efficiency of animations, comics, and fanworks.

Generative AI has matured to a point where large-scale models can generate text that seems indistinguishable from human-written text and remarkably photorealistic images. Automatically measuring how close the distribution of generated data is to the target real data distribution is a key step in diagnosing existing models and developing better models. We present MAUVE, a family of comparison measures between pairs of distributions such as those encountered in the generative modeling of text or images. These scores are statistical summaries of divergence frontiers capturing two types of errors in generative modeling. We explore four approaches to statistically estimate these scores: vector quantization, non-parametric estimation, classifier-based estimation, and parametric Gaussian approximations. We provide statistical bounds for the vector quantization approach. Empirically, we find that the proposed scores paired with a range of f-divergences and statistical estimation methods can quantify the gaps between the distributions of human-written text and those of modern neural language models by correlating with human judgments and identifying known properties of the generated texts. We conclude the paper by demonstrating its applications to other AI domains and discussing practical recommendations.

Large Language Models (LLMs) have demonstrated great capabilities in solving a wide range of tasks in a resource-efficient manner through prompting, which does not require task-specific training, but suffers from performance fluctuation when there are multiple prompt candidates. Previous works have introduced gradient-free probability-based prompt selection methods that aim to choose the optimal prompt among the candidates for a given task but fail to provide a comprehensive and fair comparison between each other. In this paper, we propose a unified framework to interpret and evaluate the existing probability-based prompt selection methods by performing extensive experiments on 13 common NLP tasks. We find that all existing methods can be unified into some variant of the method that maximizes the mutual information between the input and the corresponding model output (denoted as MI). Using the finding, we develop several variants of MI and increases the effectiveness of the best prompt selection method from 87.79% to 94.98%, measured as the ratio of the performance of the selected prompt to that of the optimal oracle prompt. Furthermore, we propose a novel calibration method called Calibration by Marginalization (CBM) that is orthogonal to existing methods and helps increase the prompt selection effectiveness of the best method by 99.44%. The code and datasets used in our work will be released at https://github.com/soheeyang/unified-prompt-selection.

Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic or non-smooth neurons? I.e., can we "back-propagate" through these stochastic neurons? We examine this question, existing approaches, and compare four families of solutions, applicable in different settings. One of them is the minimum variance unbiased gradient estimator for stochatic binary neurons (a special case of the REINFORCE algorithm). A second approach, introduced here, decomposes the operation of a binary stochastic neuron into a stochastic binary part and a smooth differentiable part, which approximates the expected effect of the pure stochatic binary neuron to first order. A third approach involves the injection of additive or multiplicative noise in a computational graph that is otherwise differentiable. A fourth approach heuristically copies the gradient with respect to the stochastic output directly as an estimator of the gradient with respect to the sigmoid argument (we call this the straight-through estimator). To explore a context where these estimators are useful, we consider a small-scale version of {\em conditional computation}, where sparse stochastic units form a distributed representation of gaters that can turn off in combinatorially many ways large chunks of the computation performed in the rest of the neural network. In this case, it is important that the gating units produce an actual 0 most of the time. The resulting sparsity can be potentially be exploited to greatly reduce the computational cost of large deep networks for which conditional computation would be useful.

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.

Derived from diffusion models, MangaNinjia specializes in the task of reference-guided line art colorization. We incorporate two thoughtful designs to ensure precise character detail transcription, including a patch shuffling module to facilitate correspondence learning between the reference color image and the target line art, and a point-driven control scheme to enable fine-grained color matching. Experiments on a self-collected benchmark demonstrate the superiority of our model over current solutions in terms of precise colorization. We further showcase the potential of the proposed interactive point control in handling challenging cases, cross-character colorization, multi-reference harmonization, beyond the reach of existing algorithms.

Real-world text can be damaged by corrosion issues caused by environmental or human factors, which hinder the preservation of the complete styles of texts, e.g., texture and structure. These corrosion issues, such as graffiti signs and incomplete signatures, bring difficulties in understanding the texts, thereby posing significant challenges to downstream applications, e.g., scene text recognition and signature identification. Notably, current inpainting techniques often fail to adequately address this problem and have difficulties restoring accurate text images along with reasonable and consistent styles. Formulating this as an open problem of text image inpainting, this paper aims to build a benchmark to facilitate its study. In doing so, we establish two specific text inpainting datasets which contain scene text images and handwritten text images, respectively. Each of them includes images revamped by real-life and synthetic datasets, featuring pairs of original images, corrupted images, and other assistant information. On top of the datasets, we further develop a novel neural framework, Global Structure-guided Diffusion Model (GSDM), as a potential solution. Leveraging the global structure of the text as a prior, the proposed GSDM develops an efficient diffusion model to recover clean texts. The efficacy of our approach is demonstrated by thorough empirical study, including a substantial boost in both recognition accuracy and image quality. These findings not only highlight the effectiveness of our method but also underscore its potential to enhance the broader field of text image understanding and processing. Code and datasets are available at: https://github.com/blackprotoss/GSDM.

Given a grayscale photograph as input, this paper attacks the problem of hallucinating a plausible color version of the photograph. This problem is clearly underconstrained, so previous approaches have either relied on significant user interaction or resulted in desaturated colorizations. We propose a fully automatic approach that produces vibrant and realistic colorizations. We embrace the underlying uncertainty of the problem by posing it as a classification task and use class-rebalancing at training time to increase the diversity of colors in the result. The system is implemented as a feed-forward pass in a CNN at test time and is trained on over a million color images. We evaluate our algorithm using a "colorization Turing test," asking human participants to choose between a generated and ground truth color image. Our method successfully fools humans on 32% of the trials, significantly higher than previous methods. Moreover, we show that colorization can be a powerful pretext task for self-supervised feature learning, acting as a cross-channel encoder. This approach results in state-of-the-art performance on several feature learning benchmarks.

Kernel online convex optimization (KOCO) is a framework combining the expressiveness of non-parametric kernel models with the regret guarantees of online learning. First-order KOCO methods such as functional gradient descent require only O(t) time and space per iteration, and, when the only information on the losses is their convexity, achieve a minimax optimal O(T) regret. Nonetheless, many common losses in kernel problems, such as squared loss, logistic loss, and squared hinge loss posses stronger curvature that can be exploited. In this case, second-order KOCO methods achieve O(log(Det(K))) regret, which we show scales as O(d_{eff}log T), where d_{eff} is the effective dimension of the problem and is usually much smaller than O(T). The main drawback of second-order methods is their much higher O(t^2) space and time complexity. In this paper, we introduce kernel online Newton step (KONS), a new second-order KOCO method that also achieves O(d_{eff}log T) regret. To address the computational complexity of second-order methods, we introduce a new matrix sketching algorithm for the kernel matrix K_t, and show that for a chosen parameter γleq 1 our Sketched-KONS reduces the space and time complexity by a factor of γ^2 to O(t^2γ^2) space and time per iteration, while incurring only 1/γ times more regret.

We present AI-SARAH, a practical variant of SARAH. As a variant of SARAH, this algorithm employs the stochastic recursive gradient yet adjusts step-size based on local geometry. AI-SARAH implicitly computes step-size and efficiently estimates local Lipschitz smoothness of stochastic functions. It is fully adaptive, tune-free, straightforward to implement, and computationally efficient. We provide technical insight and intuitive illustrations on its design and convergence. We conduct extensive empirical analysis and demonstrate its strong performance compared with its classical counterparts and other state-of-the-art first-order methods in solving convex machine learning problems.

The explosion of large-scale data in fields such as finance, e-commerce, and social media has outstripped the processing capabilities of single-machine systems, driving the need for distributed statistical inference methods. Traditional approaches to distributed inference often struggle with achieving true sparsity in high-dimensional datasets and involve high computational costs. We propose a novel, two-stage, distributed best subset selection algorithm to address these issues. Our approach starts by efficiently estimating the active set while adhering to the ell_0 norm-constrained surrogate likelihood function, effectively reducing dimensionality and isolating key variables. A refined estimation within the active set follows, ensuring sparse estimates and matching the minimax ell_2 error bound. We introduce a new splicing technique for adaptive parameter selection to tackle subproblems under ell_0 constraints and a Generalized Information Criterion (GIC). Our theoretical and numerical studies show that the proposed algorithm correctly finds the true sparsity pattern, has the oracle property, and greatly lowers communication costs. This is a big step forward in distributed sparse estimation.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

Vector glyphs are the atomic units of digital typography, yet most learning-based pipelines still depend on carefully curated exemplar sheets and raster-to-vector postprocessing, which limits accessibility and editability. We introduce VecGlypher, a single multimodal language model that generates high-fidelity vector glyphs directly from text descriptions or image exemplars. Given a style prompt, optional reference glyph images, and a target character, VecGlypher autoregressively emits SVG path tokens, avoiding raster intermediates and producing editable, watertight outlines in one pass. A typography-aware data and training recipe makes this possible: (i) a large-scale continuation stage on 39K noisy Envato fonts to master SVG syntax and long-horizon geometry, followed by (ii) post-training on 2.5K expert-annotated Google Fonts with descriptive tags and exemplars to align language and imagery with geometry; preprocessing normalizes coordinate frames, canonicalizes paths, de-duplicates families, and quantizes coordinates for stable long-sequence decoding. On cross-family OOD evaluation, VecGlypher substantially outperforms both general-purpose LLMs and specialized vector-font baselines for text-only generation, while image-referenced generation reaches a state-of-the-art performance, with marked gains over DeepVecFont-v2 and DualVector. Ablations show that model scale and the two-stage recipe are critical and that absolute-coordinate serialization yields the best geometry. VecGlypher lowers the barrier to font creation by letting users design with words or exemplars, and provides a scalable foundation for future multimodal design tools.

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

Offline optimization has recently emerged as an increasingly popular approach to mitigate the prohibitively expensive cost of online experimentation. The key idea is to learn a surrogate of the black-box function that underlines the target experiment using a static (offline) dataset of its previous input-output queries. Such an approach is, however, fraught with an out-of-distribution issue where the learned surrogate becomes inaccurate outside the offline data regimes. To mitigate this, existing offline optimizers have proposed numerous conditioning techniques to prevent the learned surrogate from being too erratic. Nonetheless, such conditioning strategies are often specific to particular surrogate or search models, which might not generalize to a different model choice. This motivates us to develop a model-agnostic approach instead, which incorporates a notion of model sharpness into the training loss of the surrogate as a regularizer. Our approach is supported by a new theoretical analysis demonstrating that reducing surrogate sharpness on the offline dataset provably reduces its generalized sharpness on unseen data. Our analysis extends existing theories from bounding generalized prediction loss (on unseen data) with loss sharpness to bounding the worst-case generalized surrogate sharpness with its empirical estimate on training data, providing a new perspective on sharpness regularization. Our extensive experimentation on a diverse range of optimization tasks also shows that reducing surrogate sharpness often leads to significant improvement, marking (up to) a noticeable 9.6% performance boost. Our code is publicly available at https://github.com/cuong-dm/IGNITE

Much research in machine learning involves finding appropriate inductive biases (e.g. convolutional neural networks, momentum-based optimizers, transformers) to promote generalization on tasks. However, quantification of the amount of inductive bias associated with these architectures and hyperparameters has been limited. We propose a novel method for efficiently computing the inductive bias required for generalization on a task with a fixed training data budget; formally, this corresponds to the amount of information required to specify well-generalizing models within a specific hypothesis space of models. Our approach involves modeling the loss distribution of random hypotheses drawn from a hypothesis space to estimate the required inductive bias for a task relative to these hypotheses. Unlike prior work, our method provides a direct estimate of inductive bias without using bounds and is applicable to diverse hypothesis spaces. Moreover, we derive approximation error bounds for our estimation approach in terms of the number of sampled hypotheses. Consistent with prior results, our empirical results demonstrate that higher dimensional tasks require greater inductive bias. We show that relative to other expressive model classes, neural networks as a model class encode large amounts of inductive bias. Furthermore, our measure quantifies the relative difference in inductive bias between different neural network architectures. Our proposed inductive bias metric provides an information-theoretic interpretation of the benefits of specific model architectures for certain tasks and provides a quantitative guide to developing tasks requiring greater inductive bias, thereby encouraging the development of more powerful inductive biases.

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

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.

Watermarking by altering token sampling probabilities based on red-green list is a promising method for tracing the origin of text generated by large language models (LLMs). However, existing watermark methods often struggle with a fundamental dilemma: improving watermark effectiveness (the detectability of the watermark) often comes at the cost of reduced text quality. This trade-off limits their practical application. To address this challenge, we first formalize the problem within a multi-objective trade-off analysis framework. Within this framework, we identify a key factor that influences the dilemma. Unlike existing methods, where watermark strength is typically treated as a fixed hyperparameter, our theoretical insights lead to the development of MorphMarka method that adaptively adjusts the watermark strength in response to changes in the identified factor, thereby achieving an effective resolution of the dilemma. In addition, MorphMark also prioritizes flexibility since it is a model-agnostic and model-free watermark method, thereby offering a practical solution for real-world deployment, particularly in light of the rapid evolution of AI models. Extensive experiments demonstrate that MorphMark achieves a superior resolution of the effectiveness-quality dilemma, while also offering greater flexibility and time and space efficiency.

Text-to-Image (T2I) generation has made significant advancements with the advent of diffusion models. These models exhibit remarkable abilities to produce images based on textual prompts. Current T2I models allow users to specify object colors using linguistic color names. However, these labels encompass broad color ranges, making it difficult to achieve precise color matching. To tackle this challenging task, named color prompt learning, we propose to learn specific color prompts tailored to user-selected colors. Existing T2I personalization methods tend to result in color-shape entanglement. To overcome this, we generate several basic geometric objects in the target color, allowing for color and shape disentanglement during the color prompt learning. Our method, denoted as ColorPeel, successfully assists the T2I models to peel off the novel color prompts from these colored shapes. In the experiments, we demonstrate the efficacy of ColorPeel in achieving precise color generation with T2I models. Furthermore, we generalize ColorPeel to effectively learn abstract attribute concepts, including textures, materials, etc. Our findings represent a significant step towards improving precision and versatility of T2I models, offering new opportunities for creative applications and design tasks. Our project is available at https://moatifbutt.github.io/colorpeel/.

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase retrieval. The key assumption is that the underlying signal lies near the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. We propose a quadratic estimator, and show that it enjoys a statistical rate of order frac{klog L{m}}, where m is the number of samples. We also provide a near-matching algorithm-independent lower bound. Moreover, we provide a variant of the classic power method, which projects the calculated data onto the range of the generative model during each iteration. We show that under suitable conditions, this method converges exponentially fast to a point achieving the above-mentioned statistical rate. We perform experiments on various image datasets for spiked matrix and phase retrieval models, and illustrate performance gains of our method to the classic power method and the truncated power method devised for sparse principal component analysis.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

This paper focuses on the problem of constrained stochastic optimization. A zeroth order Frank-Wolfe algorithm is proposed, which in addition to the projection-free nature of the vanilla Frank-Wolfe algorithm makes it gradient free. Under convexity and smoothness assumption, we show that the proposed algorithm converges to the optimal objective function at a rate Oleft(1/T^{1/3}right), where T denotes the iteration count. In particular, the primal sub-optimality gap is shown to have a dimension dependence of Oleft(d^{1/3}right), which is the best known dimension dependence among all zeroth order optimization algorithms with one directional derivative per iteration. For non-convex functions, we obtain the Frank-Wolfe gap to be Oleft(d^{1/3}T^{-1/4}right). Experiments on black-box optimization setups demonstrate the efficacy of the proposed algorithm.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

We study weight-only post-training quantization (PTQ), which quantizes the weights of a large language model (LLM) without retraining, using little or no calibration data. Weight-only PTQ is crucial for reducing the memory footprint and latency of LLM inference, especially in memory-bound, small-batch inference scenarios, such as personalized inference on edge devices. Despite its importance, irregular weight distributions with heavy-tailed outliers in LLMs complicate quantization, recently motivating rotation-based methods that transform weights into near-Gaussian distributions, which are more regular with fewer outliers, thereby reducing quantization error. In this work, we first derive the information-theoretically optimal bit allocation for Gaussianized weights under given bit budgets, revealing that fine-grained fractional-bit quantizers approaching the Gaussian distortion-rate bound are essential to achieve near-optimal quantization performance. To bridge this theoretical insight and practical implementation, we introduce Q-Palette, a versatile collection of fractional-bit quantizers that range from trellis-coded quantizers offering near-optimal distortion to simpler vector and scalar quantizers optimized for faster inference, all efficiently implemented with optimized CUDA kernels across various bitwidths. Furthermore, leveraging Q-Palette as a foundational component, we propose a novel mixed-scheme quantization framework, jointly optimizing quantizer choices and layer fusion decisions given resource constraints. The code is available at https://github.com/snu-mllab/Q-Palette.

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where (a) the number of unknowns may potentially be larger than the number of observations and (b) f* admits a sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation. In this paper, we use Hutchinson's trace estimator to give a scalable unbiased estimate of the log-density. The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures. We demonstrate our approach on high-dimensional density estimation, image generation, and variational inference, achieving the state-of-the-art among exact likelihood methods with efficient sampling.

Noisy partial label learning (noisy PLL) is an important branch of weakly supervised learning. Unlike PLL where the ground-truth label must conceal in the candidate label set, noisy PLL relaxes this constraint and allows the ground-truth label may not be in the candidate label set. To address this challenging problem, most of the existing works attempt to detect noisy samples and estimate the ground-truth label for each noisy sample. However, detection errors are unavoidable. These errors can accumulate during training and continuously affect model optimization. To this end, we propose a novel framework for noisy PLL with theoretical guarantees, called ``Adjusting Label Importance Mechanism (ALIM)''. It aims to reduce the negative impact of detection errors by trading off the initial candidate set and model outputs. ALIM is a plug-in strategy that can be integrated with existing PLL approaches. Experimental results on benchmark datasets demonstrate that our method can achieve state-of-the-art performance on noisy PLL. \textcolor[rgb]{0.93,0.0,0.47}{Our code can be found in Supplementary Material}.