Recent works have introduced new equivariant neural networks, motivated by their improved generalization compared to traditional deep neural networks. While experiments support this advantage, the theoretical understanding of their generalization properties remains limited. In this paper, we analyze the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with the ReLU activation function through the lens of Vapnik-Chervonenkis (VC) dimension theory. We investigate how architectural factors--such as the number of layers, weights, and input dimensions--affect the VC dimension. A key challenge in our analysis is proving a lower bound on the VC dimension, for which we introduce new techniques, establishing a novel connection between GCNNs and standard deep neural networks. Additionally, we compare our derived bounds to those known for fully connected neural networks. Our results extend previous findings on the VC dimension of continuous GCNNs with two layers, offering new insights into their generalization behavior, particularly their dependence on input resolution.

Pretrained Transformers demonstrate remarkable in-context learning (ICL) capabilities, enabling them to adapt to new tasks from demonstrations without parameter updates. However, theoretical studies often rely on simplified architectures (e.g., omitting MLPs), plain data models (e.g., linear regression with isotropic inputs), and single-source training--limiting their relevance to realistic settings. In this work, we study ICL in pretrained Transformers with nonlinear MLP heads on nonlinear tasks drawn from multiple data sources with heterogeneous input, task, and noise distributions. We analyze a model where the MLP comprises two layers, with the first layer trained via a single gradient step and the second layer fully optimized. Under high-dimensional asymptotics, we prove that such models are equivalent in ICL error to structured polynomial predictors, leveraging results from the theory of Gaussian universality and orthogonal polynomials. This equivalence reveals that nonlinear MLPs meaningfully enhance ICL performance--particularly on nonlinear tasks--compared to linear baselines.

Robust routing under uncertainty is central to real-world logistics, yet most benchmarks assume static, idealized settings. We present \texttt{SVRPBench}, the first open benchmark to capture high-fidelity stochastic dynamics in vehicle routing at urban scale. Spanning more than 500 instances with up to 1000 customers, it simulates realistic delivery conditions: time-dependent congestion, log-normal delays, probabilistic accidents, and empirically grounded time windows for residential and commercial clients. Our pipeline generates diverse, constraint-rich scenarios, including multi-depot and multi-vehicle setups. Benchmarking reveals that state-of-the-art RL solvers like POMO and AM degrade by over 20\% under distributional shift, while classical and metaheuristic methods remain robust. To enable reproducible research, we release the dataset ( Huggingface) and evaluation suite ( Github). SVRPBench challenges the community to design solvers that generalize beyond synthetic assumptions and adapt to real-world uncertainty.

In multi-armed bandits with network interference (MABNI), the action taken by one node can influence the rewards of others, creating complex interdependence. While existing research on MABNI largely concentrates on minimizing regret, it often overlooks the crucial concern that an excessive emphasis on the optimal arm can undermine the inference accuracy for sub-optimal arms. Although initial efforts have been made to address this trade-off in single-unit scenarios, these challenges have become more pronounced in the context of MABNI. In this paper, we establish, for the first time, a theoretical Pareto frontier characterizing the trade-off between regret minimization and inference accuracy in adversarial (design-based) MABNI. We further introduce an anytime-valid asymptotic confidence sequence along with a corresponding algorithm, $\texttt{EXP3-N-CS}$, specifically designed to balance the trade-off between regret minimization and inference accuracy in this setting.

Reinforcement learning (RL) has recently emerged as a compelling approach for enhancing the reasoning capabilities of large language models (LLMs), where an LLM generator serves as a policy guided by a verifier (reward model). However, current RL post-training methods for LLMs typically use verifiers that are fixed (rule-based or frozen pretrained) or trained discriminatively via supervised fine-tuning (SFT). Such designs are susceptible to reward hacking and generalize poorly beyond their training distributions. To overcome these limitations, we propose Tango, a novel framework that uses RL to concurrently train both an LLM generator and a verifier in an interleaved manner. A central innovation of Tango is its generative, process-level LLM verifier, which is trained via RL and co-evolves with the generator. Importantly, the verifier is trained solely based on outcome-level verification correctness rewards without requiring explicit process-level annotations. This generative RL-trained verifier exhibits improved robustness and superior generalization compared to deterministic or SFT-trained verifiers, fostering effective mutual reinforcement with the generator. Extensive experiments demonstrate that both components of Tango achieve state-of-the-art results among 7B/8B-scale models: the generator attains best-in-class performance across five competition-level math benchmarks and four challenging out-of-domain reasoning tasks, while the verifier leads on the ProcessBench dataset.

The task of Knowlegde-Based Visual Question Answering (KB-VQA) requires the model to understand visual features and retrieve external knowledge. Retrieval-Augmented Generation (RAG) have been employed to address this problem through knowledge base querying. However, existing work demonstrate two limitations: insufficient interactivity during knowledge retrieval and ineffective organization of retrieved information for Visual-Language Model (VLM). To address these challenges, we propose a three-stage visual language model with Process, Retrieve and Filter (VLM-PRF) framework. For interactive retrieval, VLM-PRF uses reinforcement learning (RL) to guide the model to strategically process information via tool-driven operations. For knowledge filtering, our method trains the VLM to transform the raw retrieved information into into task-specific knowledge. With a dual reward as supervisory signals, VLM-PRF successfully enable model to optimize retrieval strategies and answer generation capabilities simultaneously. Experiments on two datasets demonstrate the effectiveness of our framework.

Network quantization effectively reduces both memory footprints and inference time of deep neural networks, enabling their deployment on resource-constrained devices. To fully utilize the multiple bit-width arithmetic operations of the hardware, mixed-precision quantization (MPQ) is developed to assign different bit-widths to each layer. However, the quantization policy obtained by existing MPQ methods struggles to achieve the objectives of efficiency and generalization simultaneously. In this paper, we propose an efficient and generalizable MPQ based on topological entropy (TE) (GMPQ-TE). Specifically, TE, derived from \textit{topological data analysis}, effectively measures the quantization sensitivity of each layer by using the minibatch of data with the same label. Furthermore, we observe that TE remains consistent across various datasets and shows a strong correlation with both quantized model accuracy and bit-width. Thus, MPQ is formulated as a single-pass linear programming problem, obtaining a generalizable quantization policy in a few seconds (11s on MobileNet-V2). Extensive experiments show that the quantization policy obtained on CIFAR-10 can generalize to ImageNet and PASCAL VOC. GMPQ-TE achieves a competitive accuracy-complexity trade-off compared to state-of-the-art MPQ methods.

Although there is an extensive body of work characterizing the sample complexity of discounted-return offline RL with function approximations, prior work on the average-reward setting has received significantly less attention, and existing approaches rely on restrictive assumptions, such as ergodicity or linearity of the MDP. In this work, we establish the first sample complexity results for average-reward offline RL with function approximation for weakly communicating MDPs, a much milder assumption. To this end, we introduce Anchored Fitted Q-Iteration, which combines the standard Fitted Q-Iteration with an anchor mechanism. We show that the anchor, which can be interpreted as a form of weight decay, is crucial for enabling finite-time analysis in the average-reward setting. We also extend our finite-time analysis to the setup where the dataset is generated from a single-trajectory rather than IID transitions, again leveraging the anchor mechanism.

Text-to-image (T2I) models are capable of generating visually impressive images, yet they often fail to accurately capture specific attributes in user prompts, such as the correct number of objects with the specified colors. The diversity of such errors underscores the need for a hierarchical evaluation framework that can compare prompt adherence abilities of different image generation models. Simultaneously, benchmarks of vision language models (VLMs) have not kept pace with the complexity of scenes that VLMs are used to annotate. In this work, we propose a structured methodology for jointly evaluating T2I models and VLMs by testing whether VLMs can identify 27 specific failure modes in the images generated by T2I models conditioned on challenging prompts. Our second contribution is a dataset of prompts and images generated by 5 T2I models (Flux, SD3-Medium, SD3-Large, SD3.5-Medium, SD3.5-Large) and the corresponding annotations from VLMs (Molmo, InternVL3, Pixtral) annotated by an LLM (Llama3) to test whether VLMs correctly identify the failure mode in a generated image. By analyzing failure modes on a curated set of prompts, we reveal systematic errors in attribute fidelity and object representation. Our findings suggest that current metrics are insufficient to capture these nuanced errors, highlighting the importance of targeted benchmarks for advancing generative model reliability and interpretability.

Inducing reasoning in multimodal large language models (MLLMs) is critical for achieving human-level perception and understanding. Existing methods mainly leverage LLM reasoning to analyze parsed visuals, often limited by static perception stages. This paper introduces Visual Test-Time Scaling (VTTS), a novel approach to enhance MLLMs' reasoning via iterative perception during inference. VTTS mimics humans' hierarchical attention by progressively refining focus on high-confidence spatio-temporal regions, guided by updated textual predictions. Specifically, VTTS employs an Iterative Perception (ITP) mechanism, incorporating reinforcement learning with spatio-temporal supervision to optimize reasoning. To support this paradigm, we also present VTTS-80K, a dataset tailored for iterative perception. These designs allows a MLLM to enhance its performance by increasing its perceptual compute.