Reinforcement learning (RL) has become the dominant paradigm for improving the performance of language models on complex reasoning tasks. Despite the substantial empirical gains demonstrated by RL-based training methods like GRPO, a granular understanding of why and how RL enhances performance is still lacking. To bridge this gap, we introduce SPARKLE, a fine-grained analytic framework to dissect the effects of RL across three key dimensions: (1) plan following and execution, (2) knowledge integration, and (3) chain of subproblems. Using this framework, we gain insights beyond mere accuracy.

Unfolding networks are interpretable networks emerging from iterative algorithms, incorporate prior knowledge of data structure, and are designed to solve inverse problems like compressed sensing, which deals with recovering data from noisy, missing observations. Compressed sensing finds applications in critical domains, from medical imaging to cryptography, where adversarial robustness is crucial to prevent catastrophic failures. However, a solid theoretical understanding of the performance of unfolding networks in the presence of adversarial attacks is still in its infancy. In this paper, we study the adversarial generalization of unfolding networks when perturbed with l2-norm constrained attacks, generated by the fast gradient sign method. Particularly, we choose a family of state-ofthe-art overaparameterized unfolding networks and deploy a new framework to estimate their adversarial Rademacher complexity. Given this estimate, we provide adversarial generalization error bounds for the networks under study, which are tight with respect to the attack level. To our knowledge, this is the first theoretical analysis on the adversarial generalization of unfolding networks. We further present a series of experiments on real-world data, with results corroborating our derived theory, consistently for all data. Finally, we observe that the family's overparameterization can be exploited to promote adversarial robustness, shedding light on how to efficiently robustify neural networks.

Transformers have emerged as a powerful neural network architecture capable of tackling a wide range of learning tasks. In this work, we provide a theoretical analysis of their ability to automatically extract structure from data in an unsupervised setting. In particular, we demonstrate their suitability for clustering when the input data is generated from a Gaussian mixture model. To this end, we study a simplified two-head attention layer and define a population risk whose minimization with unlabeled data drives the head parameters to align with the true mixture centroids. This phenomenon highlights the ability of attention-based layers to capture underlying distributional structure. We further examine an attention layer with key, query, and value matrices fixed to the identity, and show that, even without any trainable parameters, it can perform in-context quantization, revealing the surprising capacity of transformer-based methods to adapt dynamically to input-specific distributions.

Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of transformers has not been well understood in theory. In this paper, we study the capability and interpretability of transformers in learning a family of classic statistical models, namely random walks on circles. We theoretically demonstrate that, after training with gradient descent, a one-layer transformer model can achieve optimal accuracy in predicting random walks. Importantly, our analysis reveals that the trained model is interpretable: the trained softmax attention serves as a token selector, focusing on the direct parent state; subsequently, the value matrix executes a onestep probability transition to predict the location of the next state based on this parent state. We also show that certain edge cases not covered by our theory are indeed failure cases, demonstrating that our theoretical conditions are tight. By investigating these success and failure cases, it is revealed that gradient descent with small initialization may fail or struggle to converge to a good solution in certain simple tasks even beyond random walks. Experiments are conducted to support our theoretical findings.

In this work, we address the task of table image to LaTeX code generation, with the goal of automating the reconstruction of high-quality, publication-ready tables from visual inputs. A central challenge of this task lies in accurately handling complex tables--those with large sizes, deeply nested structures, and semantically rich or irregular cell content--where existing methods often fail. We begin with a comprehensive analysis, identifying key challenges and highlighting the limitations of current evaluation protocols. To overcome these issues, we propose a reinforced multimodal large language model (MLLM) framework, where a pre-trained MLLM is fine-tuned on a large-scale table-to-LaTeX dataset. To further improve generation quality, we introduce a dual-reward reinforcement learning strategy based on Group Relative Policy Optimization (GRPO). Unlike standard approaches that optimize purely over text outputs, our method incorporates both a structure-level reward on LaTeX code and a visual fidelity reward computed from rendered outputs, enabling direct optimization of the visual output quality. We adopt a hybrid evaluation protocol combining TEDS-Structure and CW-SSIM, and show that our method achieves state-of-the-art performance, particularly on structurally complex tables, demonstrating the effectiveness and robustness of our approach.

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term rank axes. We define a model as rankable for an attribute if projecting embeddings onto such an axis preserves the attribute's order. Across 7 popular encoders and 9 datasets with attributes like age, crowd count, head pose, aesthetics, and recency, we find that many embeddings are inherently rankable. Surprisingly, a small number of samples, or even just two extreme examples, often suffice to recover meaningful rank axes, without full-scale supervision. These findings open up new use cases for image ranking in vector databases and motivate further study into the structure and learning of rankable embeddings.

Spiking Neural Networks (SNNs) are distinguished from Artificial Neural Networks (ANNs) for their complex neuronal dynamics and sparse binary activations (spikes) inspired by the biological neural system. Traditional neuron models use iterative step-by-step dynamics, resulting in serial computation and slow training speed of SNNs. Recently, parallelizable spiking neuron models have been proposed to fully utilize the massive parallel computing ability of graphics processing units to accelerate the training of SNNs. However, existing parallelizable spiking neuron models involve dense floating operations and can only achieve high long-term dependencies learning ability with a large order at the cost of huge computational and memory costs. To solve the dilemma of performance and costs, we propose the mul-free channel-wise Parallel Spiking Neuron, which is hardware-friendly and suitable for SNNs' resource-restricted application scenarios.

Deep Neural Networks (DNN) have emerged as an effective approach to implementing challenging subproblems. They are increasingly being used as components in critical transportation, medical, and military systems. However, like human-written software, DNNs may have flaws that can lead to unsafe system performance. To confidently deploy DNNs in such systems, strong evidence is needed that they do not contain such flaws. This has led researchers to explore the adaptation and customization of software verification approaches to the problem of neural network verification (NNV). Many dozens of NNV tools have been developed in recent years and as a field these techniques have matured to the point where realistic networks can be analyzed to detect flaws and to prove conformance with specifications. NNV tools are highly-engineered and complex may harbor flaws that cause them to produce unsound results. We identify commonalities in algorithmic approaches taken by NNV tools to define a verifier independent proof format--activation pattern tree proofs (APTP)--and design an algorithm for checking those proofs that is proven correct and optimized to enable scalable checking. We demonstrate that existing verifiers can efficiently generate APTP proofs, and that an APTPcheckersignificantly outperforms prior work on a benchmark of 16 neural networks and 400 NNV problems, and that it is robust to variation in APTP proof structure arising from different NNV tools.

A.1 Details of Dimension Design We argue that multi-dimensional evaluation is significant to visual caption evaluation and is more comprehensive than previous work. So how to choose proper dimensions? We refer to existing VQA benchmarks [62, 63, 64, 65] and visual generation benchmarks [31, 32, 33]. VQA benchmarks usually design various types of questions to include multi-dimensional evaluation and analysis of MLLMs. For instance, MMBench [64] defines 20 ability dimensions, including attribute recognition, attribute comparison, action recognition, spatial relationship, physical property, OCR, object localization, image style, image scene, identity reasoning, etc. MVBench [64] covers 20 challenging video tasks including action, object, position, count, scene, pose, attribute, character, cognition, etc. Due to the flexible design of questions, VQA benchmarks can be naturally built with comprehensive dimensions. Different from the VQA task, the visual caption task does not require specific questions, but inspects the alignment of visual and textual information. Visual generation is the inverse task of visual captioning, as it requires models to generate specific visual content based on detailed textual descriptions. GenEval [31] designs 6 different tasks to evaluate text-to-image alignment, including single object, two object, counting, colors, position, and attribute binding. VBench [32] comprises 16 dimensions, including subject consistency, background consistency, object class, human action, color, spatial relationship, scene, style, etc. We follow their explored dimensions to design proper dimensions for visual captioning. Finally, we design 6 views, covering object, global, text, camera, temporal, and knowledge. The object-related view includes object category, object color, object 1 number, and spatial relation, the global-related view includes scene and style, the text-related view evaluates the OCR capability of captions, the camera-related view covers the camera angle and movement, the temporal-related view contains action and event, and we also design a view to evaluate the knowledge of MLLMs, i.e., character identification. We believe these dimensions contribute to a comprehensive visual caption benchmarking.

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