We introduce MLE-Dojo, a Gym-style framework for systematically reinforcement learning, evaluating, and improving autonomous large language model (LLM) agents in iterative machine learning engineering (MLE) workflows. Unlike existing benchmarks that primarily rely on static datasets or single-attempt evaluations, MLE-Dojo provides an interactive environment enabling agents to iteratively experiment, debug, and refine solutions through structured feedback loops. Built upon 200+ real-world Kaggle challenges, MLE-Dojo covers diverse, open-ended MLE tasks carefully curated to reflect realistic engineering scenarios such as data processing, architecture search, hyperparameter tuning, and code debugging. Its fully executable environment supports comprehensive agent training via both supervised fine-tuning and reinforcement learning, facilitating iterative experimentation, realistic data sampling, and real-time outcome verification. Extensive evaluations of eight frontier LLMs reveal that while current models achieve meaningful iterative improvements, they still exhibit significant limitations in autonomously generating long-horizon solutions and efficiently resolving complex errors.

We study gradient flows for loss landscapes of fully connected feedforward neural networks with commonly used continuously differentiable activation functions such as the logistic, hyperbolic tangent, softplus or GELU function. We prove that the gradient flow either converges to a critical point or diverges to infinity while the loss converges to an asymptotic critical value. Moreover, we prove the existence of a threshold $\varepsilon> 0$ such that the loss value of any gradient flow initialized at most $\varepsilon$ above the optimal level converges to it. For polynomial target functions and sufficiently big architecture and data set, we prove that the optimal loss value is zero and can only be realized asymptotically.

Visual reasoning in multimodal large language models (MLLMs) has primarily been studied in passive, static settings, limiting their effectiveness in real-world physical environments where an embodied agent must contend with incomplete information due to occlusion or a limited field of view. Humans, in contrast, leverage their embodiment to 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 capability, we introduce the Active Visual Reasoning (AVR) task, extending visual reasoning to a paradigm of embodied interaction in partially observable environments. AVR necessitates embodied 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 that 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 embodied 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 -- PINN Balls -- 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. PINN Balls 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.

Cooperative bargaining games are widely used to model resource allocation and conflict resolution. Traditional solutions assume the mediator can access agents' utility function values and gradients. However, there is an increasing number of settings, such as human-AI interactions, where utility values may be inaccessible or incomparable due to unknown, nonaffine transformations. To model such settings, we consider that the mediator has access only to agents' $\textit{most preferred directions}-$normalized utility gradients in the decision space. To this end, we propose a cooperative bargaining algorithm where a mediator has access to only the direction oracle of each agent. We prove that unlike popular approaches such as the Nash and Kalai-Smorodinsky bargaining solutions, our approach is invariant to monotonic nonaffine transformations, and that under strong convexity and smoothness assumptions, this approach enjoys global asymptotic convergence to Pareto stationary solutions. Moreover, we show that the bargaining solutions found by our algorithm also satisfy the axioms of symmetry and (under slightly stronger conditions) independence of irrelevant alternatives, which are popular in the literature. Finally, we conduct experiments in two domains, multi-agent formation assignment and mediated stock portfolio allocation, which validate these theoretical results.

Mental visualization, the ability to construct and manipulate visual representations internally, is a core component of human cognition and plays a vital role in tasks involving reasoning, prediction, and abstraction. Despite the rapid progress of Multimodal Large Language Models (MLLMs), current benchmarks primarily assess passive visual perception, offering limited insight into the more active capability of internally constructing visual patterns to support problem solving. Yet mental visualization is a critical cognitive skill in humans, supporting abilities such as spatial navigation, predicting physical trajectories, and solving complex visual problems through imaginative simulation. To bridge this gap, we introduce Hyperphantasia, a synthetic benchmark designed to evaluate the mental visualization abilities of MLLMs through four carefully constructed puzzles. Each task is procedurally generated and presented at three difficulty levels, enabling controlled analysis of model performance across increasing complexity. Our comprehensive evaluation of state-of-the-art models reveals a substantial gap between the performance of humans and MLLMs. Additionally, we explore the potential of reinforcement learning to improve visual simulation capabilities. Our findings suggest that while some models exhibit partial competence in recognizing visual patterns, robust mental visualization remains an open challenge for current MLLMs.

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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.