Given the large scale of public functional Magnetic Resonance Imaging (fMRI), e.g., UKBiobank (UKB) and Human Connectome Projects (HCP), brain foundation models are emerging. Although the amount of samples under rich environmental variables is unprecedented, existing brain foundation models learn from fMRI derived from a narrow range of cognitive states stimulated by similar environments, causing the limited robustness demonstrated in various applications and datasets acquired with different pipelines and limited sample size. By capitalizing on the variety of cognitive status as subjects performing explicit tasks, we present the mixture of brain experts, namely BrainMoE, pre-training on tasking fMRI with rich behavioral tasks in addition to resting fMRI for a robust brain foundation model. Brain experts are designed to produce embeddings for different behavioral tasks related to cognition. Afterward, these cognition embeddings are mixed by a cognition adapter via cross-attention so that BrainMoE can handle orthogonal embeddings and be robust on those boutique downstream datasets. We have pre-trained two existing self-regressive architectures and one new supervised architecture as brain experts on 68,251 fMRI scans among UKB and HCP, containing 12 different cognitive states. Then, BrainMoE is evaluated on a variety of applications, including sex, age prediction, human behavior recognition, disease early diagnosis of Autism, Parkinson's disease, Alzheimer's disease, and Schizophrenia, and fMRI-EEG multimodal applications, where promising results in eight datasets from three different pipelines indicate great potential to facilitate current neuroimaging applications in clinical routines.

We examine the quartic Taylor approximation of the word2vecloss around the origin, and we show that both the resulting training dynamics and the final performance on downstream tasks are empirically very similar to those of word2vec. Our main contribution is to analytically solve for both the gradient flow training dynamics and the final word embeddings in terms of only the corpus statistics and training hyperparameters. The solutions reveal that these models learn orthogonal linear subspaces one at a time, each one incrementing the effective rank of the embeddings until model capacity is saturated. Training on Wikipedia, we find that each of the top linear subspaces represents an interpretable topic-level concept. Finally, we apply our theory to describe how linear representations of more abstract semantic concepts emerge during training; these can be used to complete analogies via vector addition.

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-Dojoprovides an interactive environment enabling agents to iteratively experiment, debug, and refine solutions through structured feedback loops. Built upon 200+ real-world Kaggle challenges, MLE-Dojocovers 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 ε > 0 such that the loss value of any gradient flow initialized at most εabove 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 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.

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' 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.

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can be understood through the lens of gradient-variation online learning. In this paper, we investigate online learning with Hölder smooth functions, a general class encompassing both smooth and non-smooth (Lipschitz) functions, and explore its implications for offline optimization.

Causal Representation Learning (CRL) aims to uncover the data-generating process and identify the underlying causal variables and relations, whose evaluation remains inherently challenging due to the requirement of known ground-truth causal variables and causal structure. Existing evaluations often rely on either simplistic synthetic datasets or downstream performance on real-world tasks, generally suffering a dilemma between realism and evaluative precision. In this paper, we introduce a new benchmark for CRL using high-fidelity simulated visual data that retains both realistic visual complexity and, more importantly, access to ground-truth causal generating processes. The dataset comprises around 200 thousand images and 3 million video frames across 24 sub-scenes in four domains: static image generation, dynamic physical simulations, robotic manipulations, and traffic situation analysis. These scenarios range from static to dynamic settings, simple to complex structures, and single to multi-agent interactions, offering a comprehensive testbed that hopefully bridges the gap between rigorous evaluation and real-world applicability. In addition, we provide flexible access to the underlying causal structures, allowing users to modify or configure them to align with the required assumptions in CRL, such as available domain labels, temporal dependencies, or intervention histories. Leveraging this benchmark, we evaluated representative CRL methods across diverse paradigms and offered empirical insights to assist practitioners and newcomers in choosing or extending appropriate CRL frameworks to properly address specific types of real problems that can benefit from the CRL perspective. Welcome to visit our: Project page: https://causal-verse.github.io/