Recursive Flow Matching

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20$\times$ speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.

Generative OOD-regularized Model-based Policy Optimization

We study sequential decision-making with offline reinforcement learning (RL). Traditional offline RL policies may result in out-of-distribution (OOD) actions when training relies only on sparse offline representations. To ensure safe offline policies in a sparse state-action space, we explore how density estimation models can be integrated into model-based RL methods to avoid the OOD regions. Generative models are capable of explicitly modeling the density in sparse state-action spaces. Building on this, we introduce Generative OOD-regularized Model-based Policy Optimization (GORMPO), a density-regularized offline RL algorithm that uses generative density modeling to restrict policy updates to high-density areas of the dataset. Furthermore, we examine whether better OOD detection corresponds to better model-based offline policies. We compare (1) the OOD detection capabilities of various density estimators and (2) their performance within the GORMPO framework on a real-world medical dataset and sparse offline RL datasets. We theoretically guarantee GORMPO's performance under mild assumptions. Empirically, GORMPO outperforms state-of-the-art baselines by 17% on a real-world medical dataset and enhances the base model on the offline RL datasets. Our empirical findings show that better OOD detection generally results in improved policies in environments with stable dynamics, while conservative penalties with poor density estimation are favored when dynamics are uncertain.

Manifold-Guided Attention Steering

Large language models frequently produce errors in reasoning tasks despite possessing the underlying knowledge required for correct reasoning. One possible approach to improve reasoning consistency is through activation steering. However, existing activation steering approaches apply fixed, pre-computed correction vectors, ignoring where the model currently sits along its generation trajectory; the result is indiscriminate perturbation that disrupts already-correct steps as freely as erroneous ones. We propose Manifold-Guided Attention Steering (MAGS), a trajectory-aware inference-time intervention grounded in a geometric observation: the output activations of specific attention heads diverge from a low-dimensional correctness manifold at the point of error, and this deviation compounds through subsequent steps. For each identified attention head, we learn a low-dimensional subspace from contrastive pairs of correct and incorrect traces that capture the directions along which error behavior deviates from correct behavior. During inference, we monitor each head's proximity to this manifold and apply a targeted projection correction when deviation exceeds a learned threshold, steering the attention output back toward the correct subspace before the error propagates. MAGS consistently outperforms both unsteered baselines and static steering approaches across benchmarks spanning mathematical reasoning (MATH-500, GSM8K), code generation (HumanEval, MBPP), and molecular generation (SMILES), suggesting that correctness manifolds are a general feature of LLM attention geometry.

ToolMol: Evolutionary Agentic Framework for Multi-objective Drug Discovery

Advances in large language models (LLMs) have recently opened new and promising avenues for small-molecule drug discovery. Yet existing LLM-based approaches for molecular generation often suffer from high rates of invalid and low-quality ligand candidates, a result of the syntactic limitations of current models with regard to molecular strings. In this paper, we introduce $\texttt{ToolMol}$, an evolutionary agentic framework for de novo drug design. $\texttt{ToolMol}$ combines a multi-objective genetic algorithm with an agentic LLM operator that iteratively updates the ligand population. We build a comprehensive toolbox of RDKit-backed functions that allows our agentic operator to consisently make precise ligand modifications. $\texttt{ToolMol}$ achieves state-of-the-art performance on multi-objective property optimization tasks, discovering drug-like and synthesizable ligands that have $>10\%$ stronger predicted binding affinity compared to existing methods, evaluated on three protein targets. $\texttt{ToolMol}$ ligands additionally achieve state-of-the-art results in gold-standard Absolute Binding Free Energy scores, gaining over existing methods by over $35\%$. By studying chain-of-thought reasoning traces, we observe that tool-calling enables the model to more faithfully execute its planned modifications, efficiently exploiting the strong chemical prior knowledge in LLMs.

U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster

AI-based weather forecasting now rivals traditional physics-based ensembles, but state-of-the-art (SOTA) models rely on specialized architectures and massive computational budgets, creating a high barrier to entry. We demonstrate that such complexity is unnecessary for frontier performance. We introduce U-Cast, a probabilistic forecaster built on a standard U-Net backbone trained with a simple recipe: deterministic pre-training on Mean Absolute Error followed by short probabilistic fine-tuning on the Continuous Ranked Probability Score (CRPS) using Monte Carlo Dropout for stochasticity. As a result, our model matches or exceeds the probabilistic skill of GenCast and IFS ENS at 1.5$^\circ\$ resolution while reducing training compute by over 10$\times$ compared to leading CRPS-based models and inference latency by over 10$\times$ compared to diffusion-based models. U-Cast trains in under 12 H200 GPU-days and generates a 60-step ensemble forecast in 11 seconds. These results suggest that scalable, general-purpose architectures paired with efficient training curricula can match complex domain-specific designs at a fraction of the cost, opening the training of frontier probabilistic weather models to the broader community. Our code is available at: https://github.com/Rose-STL-Lab/u-cast.

A Survey of Weight Space Learning: Understanding, Representation, and Generation

Neural network weights are typically viewed as the end product of training, while most deep learning research focuses on data, features, and architectures. However, recent advances show that the set of all possible weight values (weight space) itself contains rich structure: pretrained models form organized distributions, exhibit symmetries, and can be embedded, compared, or even generated. Understanding such structures has tremendous impact on how neural networks are analyzed and compared, and on how knowledge is transferred across models, beyond individual training instances. This emerging research direction, which we refer to as Weight Space Learning (WSL), treats neural weights as a meaningful domain for analysis and modeling. This survey provides the first unified taxonomy of WSL. We categorize existing methods into three core dimensions: Weight Space Understanding (WSU), which studies the geometry and symmetries of weights; Weight Space Representation (WSR), which learns embeddings over model weights; and Weight Space Generation (WSG), which synthesizes new weights through hypernetworks or generative models. We further show how these developments enable practical applications, including model retrieval, continual and federated learning, neural architecture search, and data-free reconstruction. By consolidating fragmented progress under a coherent framework, this survey highlights weight space as a learnable, structured domain with growing impact across model analysis, transferring, and weight generation. We release an accompanying resource at https://github.com/Zehong-Wang/Awesome-Weight-Space-Learning.

Time Series, Vision, and Language: Exploring the Limits of Alignment in Contrastive Representation Spaces

The Platonic Representation Hypothesis posits that learned representations from models trained on different modalities converge to a shared latent structure of the world. However, this hypothesis has largely been examined in vision and language, and it remains unclear whether time series participate in such convergence. We first examine this in a trimodal setting and find that independently pretrained time series, vision, and language encoders exhibit near-orthogonal geometry in the absence of explicit coupling. We then apply post-hoc alignment by training projection heads over frozen encoders using contrastive learning, and analyze the resulting representations with respect to geometry, scaling behavior, and dependence on information density and input modality characteristics. Our investigation reveals that overall alignment in contrastive representation spaces improves with model size, but this alignment is asymmetric: time series align more strongly with visual representations than with text, and images can act as effective intermediaries between time series and language. We further see that richer textual descriptions improve alignment only up to a threshold; training on denser captions does not lead to further improvement. Analogous effects are observed for visual representations. Our findings shed light on considerations for building multimodal systems involving non-conventional data modalities beyond vision and language.

Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under $S_n \times SE(3)$ symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.

Assessing Low Back Movement with Motion Tape Sensor Data Through Deep Learning

Back pain is a pervasive issue affecting a significant portion of the population, often worsened by certain movements of the lower back. Assessing these movements is important for helping clinicians prescribe appropriate physical therapy. However, it can be difficult to monitor patients' movements remotely outside the clinic. High-fidelity data from motion capture sensors can be used to classify different movements, but these sensors are costly and impractical for use in free-living environments. Motion Tape (MT), a new fabric-based wearable sensor, addresses these issues by being low cost and portable. Despite these advantages, novelty and variability in sensor stability make the MT dataset small scale and inherent to noise. In this work, we propose the Motion-Tape Augmentation Inference Model (MT-AIM), a deep learning classification pipeline trained on MT data. In order to address the challenges of limited sample size and noise present within the MT dataset, MT-AIM leverages conditional generative models to generate synthetic MT data of a desired movement, as well as predicting joint kinematics as additional features. This combination of synthetic data generation and feature augmentation enables MT-AIM to achieve state-of-the-art accuracy in classifying lower back movements, bridging the gap between physiological sensing and movement analysis.

Think like a Scientist: Physics-guided LLM Agent for Equation Discovery

Explaining observed phenomena through symbolic, interpretable formulas is a fundamental goal of science. Recently, large language models (LLMs) have emerged as promising tools for symbolic equation discovery, owing to their broad domain knowledge and strong reasoning capabilities. However, most existing LLM-based systems try to guess equations directly from data, without modeling the multi-step reasoning process that scientists often follow: first inferring physical properties such as symmetries, then using these as priors to restrict the space of candidate equations. We introduce KeplerAgent, an agentic framework that explicitly follows this scientific reasoning process. The agent coordinates physics-based tools to extract intermediate structure and uses these results to configure symbolic regression engines such as PySINDy and PySR, including their function libraries and structural constraints. Across a suite of physical equation benchmarks, KeplerAgent achieves substantially higher symbolic accuracy and greater robustness to noisy data than both LLM and traditional baselines.