Visual reasoning in multimodal large language models (MLLMs) has primarily been studied in static, fully observable settings, limiting their effectiveness in real-world environments where information is often incomplete due to occlusion or limited field of view. Humans, in contrast, actively explore and interact with their environment--moving, examining, and manipulating objects--to gather information through a closed-loop process integrating perception, reasoning, and action. Inspired by this human capability, we introduce the Active Visual Reasoning (AVR) task, extending visual reasoning to partially observable, interactive environments. AVR necessitates agents to: (1) actively acquire information via sequential physical actions, (2) integrate observations across multiple steps for coherent reasoning, and (3) dynamically adjust decisions based on evolving visual feedback. To rigorously evaluate AVR, we introduce CLEVR-AVR, a simulation benchmark featuring multi-round interactive environments designed to assess both reasoning correctness and information-gathering efficiency. We present AVR-152k, a large-scale dataset offers rich Chain-of-Thought (CoT) annotations detailing iterative reasoning for uncertainty identification, action-conditioned information gain prediction, and information-maximizing action selection, crucial for training agents in a higher-order Markov Decision Process. Building on this, we develop PhysVLM-AVR, an MLLM achieving state-of-the-art performance on CLEVR-AVR, embodied reasoning (OpenEQA, RoboVQA), and passive visual reasoning (GeoMath, Geometry30K). Our analysis also reveals that current embodied MLLMs, despite detecting information incompleteness, struggle to actively acquire and integrate new information through interaction, highlighting a fundamental gap in active reasoning capabilities.

AI audits play a critical role in AI accountability and safety. They are particularly salient in anti-discrimination law. Several areas of anti-discrimination law implicate what is known as the "less discriminatory alternative" (LDA) requirement, under which a protocol is defensible if no less discriminatory model that achieves comparable performance can be found with reasonable effort. Notably, the burden of proving an LDA exists typically falls on the claimant (the party alleging discrimination). This creates a significant hurdle in AI cases, as the claimant would seemingly need to train a less discriminatory yet high-performing model, a task requiring resources and expertise beyond most litigants.

Recent advances in Scientific Machine Learning have shown that second-order methods can enhance the training of Physics-Informed Neural Networks (PINNs), making them a suitable alternative to traditional numerical methods for Partial Differential Equations (PDEs). However, second-order methods induce large memory requirements, making them scale poorly with the model size. In this paper, we define a local Mixture of Experts (MoE) combining the parameter-efficiency of ensemble models and sparse coding to enable the use of second-order training. Our model - PINNBALLS - also features a fully learnable domain decomposition structure, achieved through the use of Adversarial Adaptive Sampling (AAS), which adapts the DD to the PDE and its domain. PINNBALLS achieves better accuracy than the state-of-the-art in scientific machine learning, while maintaining invaluable scalability properties and drawing from a sound theoretical background.

Neural networks learn effective feature representations, which can be transferred to new tasks without additional training. While larger datasets are known to improve feature transfer, the theoretical conditions for the success of such transfer remain unclear. This work investigates feature transfer in networks trained for classification to identify the conditions that enable effective clustering in unseen classes. We first reveal that higher similarity between training and unseen distributions leads to improved Cohesion and Separability. We then show that feature expressiveness is enhanced when inputs are similar to the training classes, while the features of irrelevant inputs remain indistinguishable.

Large Language Models (LLMs), such as OpenAI's o1 and DeepSeek's R1, excel at advanced reasoning tasks like math and coding via Reinforcement Learning with Verifiable Rewards (RLVR), but still struggle with puzzles solvable by humans without domain knowledge. We introduce ENIGMATA, the first comprehensive suite tailored for improving LLMs with puzzle reasoning skills. It includes 36 tasks across 7 categories, each with: 1) a generator that produces unlimited examples with controllable difficulty, and 2) a rule-based verifier for automatic evaluation. This generator-verifier design supports scalable, multi-task RL training, fine-grained analysis, and seamless RLVR integration. We further propose ENIGMATA-Eval, a rigorous benchmark, and develop optimized multi-task RLVR strategies.

Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In parallel, machine learning has seen a surge of interest in understanding how dynamical systems perform computations on time-varying input data. Yet, the link between computation-through-dynamics and representational geometry remains poorly understood. Here, we hypothesise that recurrent neural networks (RNNs) perform computations by dynamically warping their representations of task variables. To test this hypothesis, we develop a Riemannian geometric framework that enables the derivation of the manifold topology and geometry of a dynamical system from the manifold of its inputs. By characterising the time-varying geometry of RNNs, we show that dynamic warping is a fundamental feature of their computations.

Recent advances in large language models (LLMs) have enabled automated dataset labeling with minimal human supervision. While majority voting across multiple LLMs can improve label reliability by mitigating individual model biases, it incurs high computational costs due to repeated querying. In this work, we propose a novel online framework, Cost-aware Majority Voting (CaMVo), for efficient and accurate LLM-based dataset annotation. CaMVo adaptively selects a subset of LLMs for each data instance based on contextual embeddings, balancing confidence and cost without requiring pre-training or ground-truth labels. Leveraging a LinUCB-based selection mechanism and a Bayesian estimator over confidence scores, CaMVo estimates a lower bound on labeling accuracy for each LLM and aggregates responses through weighted majority voting. Our empirical evaluation on the MMLU and IMDBMovie Review datasets demonstrates that CaMVo achieves comparable or superior accuracy to full majority voting while significantly reducing labeling costs. This establishes CaMVo as a practical and robust solution for cost-efficient annotation in dynamic labeling environments.

Normalizing flows are deep generative models that achieve efficient likelihood estimation and sampling through invertible transformations. A key challenge is designing linear layers that enhance expressiveness while enabling efficient computation of the Jacobian determinant and inverse. In this work, we introduce a novel invertible linear layer based on the product of circulant and diagonal matrices. This decomposition provides a parameter-and computation-efficient formulation, reducing the parameter complexity from O(n2)to O(mn)by using mdiagonal matrices together with m 1circulant matrices, while approximating arbitrary linear transformations. Furthermore, leveraging the Fast Fourier Transform (FFT), our method reduces the time complexity of matrix inversion from O(n3) to O(mnlogn) and matrix log-determinant from O(n3) to O(mn), where n is the input dimension. Building upon this, we introduce a novel normalizing flow model called CirculantDiagonal Flow (CDFlow). Empirical results demonstrate that CDFlow excels in density estimation for natural image datasets and effectively models data with inherent periodicity. In terms of computational efficiency, our method speeds up the matrix inverse and log-determinant computations by 1.17 and 4.31, respectively, compared to the general dense matrix, when the number of channels is set to 96.

Large Language Models (LLMs) are increasingly integrated into the software engineering ecosystem. Their test-time compute (TTC) reasoning capabilities show significant potential for understanding program logic and semantics beyond mere token recognition. However, current benchmarks for code reasoning lack a formal, program-centric deductive framework to ensure sound evaluation, and are incapable of assessing whether models genuinely reason about program semantics or merely exploit superficial associations between natural language and code tokens. To bridge this gap, we introduce TF-Bench, a benchmark designed to evaluate LLM reasoning based on type inference in System F, a task we refer to as program semantics reasoning. By employing verified transformations to remove semantically irrelevant natural language, we construct TF-Benchpure, a purely semanticsdriven variant of TF-Bench. Our analysis reveals substantial limitations in state-of-the-art LLMs, with the best-performing LLM (Claude-3.7-sonnet)

Animated QR codes present an exciting frontier for dynamic content delivery and digital interaction. However, despite their potential, there has been no prior work focusing on the generation of animated QR codes that are both visually appealing and universally scannable. In this paper, we introduce AnimateQR, the first generative framework for creating animated QR codes that balance aesthetic flexibility with scannability. Unlike previous methods that focus on static QR codes, AnimateQR leverages hierarchical luminance guidance and progressive spatiotemporal control to produce high-quality dynamic QR codes. Our first innovation is a multi-scale hierarchical control signal that adjusts luminance across different spatial scales, ensuring that the QR code remains decodable while allowing for artistic expression. The second innovation is a progressive control mechanism that dynamically adjusts spatiotemporal guidance throughout the diffusion denoising steps, enabling fine-grained balance between visual quality and scannability. Extensive experimental results demonstrate that AnimateQR achieves state-of-the-art performance in both decoding success rates (96% vs. 56% baseline) and visual quality (user preference: 7.2 vs. 2.3 on a 10-point scale). Codes are availble at https://github.com/mulns/AnimateQR.