Recent video diffusion models have achieved impressive capabilities as large-scale generative world models. However, these models often struggle with fine-grained physical consistency, exhibiting physically implausible dynamics over time. In this work, we present Phys4D, a pipeline for learning physics-consistent 4D world representations from video diffusion models. Phys4D adopts a three-stage training paradigm that progressively lifts appearance-driven video diffusion models into physics-consistent 4D world representations. We first bootstrap robust geometry and motion representations through large-scale pseudo-supervised pretraining, establishing a foundation for 4D scene modeling. We then perform physics-grounded supervised fine-tuning using simulation-generated data, enforcing temporally consistent 4D dynamics. Finally, we apply simulation-grounded reinforcement learning to correct residual physical violations that are difficult to capture through explicit supervision. To evaluate fine-grained physical consistency beyond appearance-based metrics, we introduce a set of 4D world consistency evaluation that probe geometric coherence, motion stability, and long-horizon physical plausibility. Experimental results demonstrate that Phys4D substantially improves fine-grained spatiotemporal and physical consistency compared to appearance-driven baselines, while maintaining strong generative performance. Our project page is available at https://sensational-brioche-7657e7.netlify.app/

We prove that a minimal Transformer with frozen weights emulates a broad class of algorithms by in-context prompting. We formalize two modes of in-context algorithm emulation. In the *task-specific mode*, for any continuous function $f: \mathbb{R} \to \mathbb{R}$, we show the existence of a single-head softmax attention layer whose forward pass reproduces reproduces functions of the form $f(w^\top x - y)$ to arbitrary precision. This general template subsumes many popular machine learning algorithms (e.g., gradient descent, linear regression, ridge regression). In the *prompt-programmable mode*, we prove universality: a single fixed-weight two-layer softmax attention module emulates all algorithms from the task-specific class (i.e., each implementable by a single softmax attention) via only prompting. Our key idea is to construct prompts that encode an algorithm’s parameters into token representations, creating sharp dot-product gaps that force the softmax attention to follow the intended computation. This construction requires no feed-forward layers and no parameter updates. All adaptation happens through the prompt alone. Numerical results corroborate our theory. These findings forge a direct link between in-context learning and algorithmic emulation, and offer a simple mechanism for large Transformers to serve as prompt-programmable interpreters of algorithms. They illuminate how GPT-style foundation models may swap algorithms via prompts alone, and establish a form of algorithmic universality in modern Transformer models.

Neural population geometry shapes downstream computation. Recent empirical findings in neurobiology suggest that a hyperbolic structure underlies population activity in the hippocampus. Here we provide a theoretical framework for this phenomenon. First, we propose a plausible construction of hippocampal tuning curves that statistically induces hyperbolic geometry. Next, we establish a connection between neural decoding and associative memory by demonstrating that the Modern Hopfield Network update rule computes the minimum mean-squared-error (MMSE) estimator. Finally, we introduce a novel associative memory model defined in hyperbolic space that yields significantly larger capacity than leading models. Our results suggest that animals encode spatial information as a latent hyperbolic cognitive map, improving both memory capacity and decoding accuracy.

Current time series foundation model (TSFM) training corpora largely omit data with certain complexities like irregular temporal sampling. Astronomical time series of stellar fluxes (light curves) are available in immense quantities and exhibit irregular sampling, multiple variates, and heteroskedasticity. We introduce StarEmbed, the first public benchmark for light curves comprised of real observations of 40,000 stars expert-labeled across seven classes and evaluations in clustering, classification, and out-of-distribution (OOD) source detection. We benchmark TSFMs with differing architecture and training strategies as well as domain-specific transformers. Our results demonstrate that the Chronos family, despite being pre-trained on regularly sampled non-astronomical data, yields state-of-the-art (SOTA) performance in light curve clustering and OOD detection. While no TSFM strictly surpasses the classification performance of the long-established domain baseline, they do demonstrate excellent generalization abilities. StarEmbed marks a step toward universal light curve embeddings and improved TSFM performance on challenging data.

We provide a systematic recipe for translating ReLU approximation results to softmax attention mechanism. This recipe covers many common approximation targets. Importantly, it yields target-specific, economic resource bounds beyond universal approximation statements. We showcase the recipe on multiplication, reciprocal computation, and min/max primitives. These results provide new analytical tools for analyzing softmax transformer models.

We give a comprehensive theoretical analysis of transformers as time series pre- diction models, with a focus on MOIRAI (Woo et al., 2024). We study its ap- proximation and generalization capabilities. First, we demonstrate that there exist transformers that fit an autoregressive model on input univariate time series via gradient descent. We then analyze MOIRAI, one of the state-of-the-art multivariate time series prediction models capable of modeling arbitrary number of covariates. We prove that MOIRAI is capable of automatically fitting autoregressive models with an arbitrary number of covariates, offering insights into its design and em- pirical success. For generalization, we establish learning bounds for pretraining when the data satisfies Dobrushin’s condition. Experiments support our theoretical findings, highlighting the efficacy of using transformers for time series forecasting.

We propose Sci2Pol-Bench and Sci2Pol-Corpus, the first benchmark and training dataset for evaluating and fine-tuning large language models (LLMs) on policy brief generation from a scientific paper. We build Sci2Pol-Bench on a five-stage taxonomy to mirror the human writing process: (i) Autocompletion, (ii) Understanding, (iii) Summarization, (iv) Generation, and (v) Verification. It features 18 tasks in multiple-choice and open-ended formats. Specifically, for the Generation stage, we show that BERTScore and ROUGE scores fail to capture the quality of brief writing, and introduce a new LLM-based evaluation metric aligned with expert judgement. Using this benchmark, we evaluate 13 leading open-source and commercial LLMs to uncover key limitations. To improve LLM performance on brief writing, we curate the Sci2Pol-Corpus for fine-tuning. We start by linking each cited scientific paper to its corresponding policy document, drawn from 5.6 million policy records. This produces 140,000 candidate pairs. We then employ an LLM-as-a-judge to filter high-quality examples, followed by in-context polishing using three expert-written samples as references. This process yields a final set of 639 new pairs. Finally, we fine-tune three models on Sci2Pol-Corpus: LLaMA-3.1-8B, Gemma-12B, and Gemma-27B. Fine-tuning leads to consistent performance improvements across Sci2Pol-Bench. Notably, after fine-tuning, Gemma-27B surpasses the much larger GPT-4o and DeepSeek-V3 (671B). These demonstrate the effectiveness of our corpus in bridging the gap between science and policy.

The choice of batch size in minibatch stochastic gradient optimization is critical for both optimization and generalization performance in large-scale model training. Although large-batch training is arguably the dominant paradigm in large-scale deep learning because of hardware advances, model generalization often deteriorates relative to small-batch training, leading to the so-called “generalization gap.” To mitigate this issue, we investigate adaptive batch size strategies derived from adaptive sampling methods, which were originally developed for stochastic gradient descent. Given the strong interplay between learning rates and batch sizes, together with the prevalence of adaptive gradient methods in deep learning, we emphasize the need for adaptive batch size strategies in these settings. We introduce AdAdaGrad and its scalar variant AdAdaGrad-Norm, which progressively increase batch sizes during training while performing updates with AdaGrad and AdaGrad-Norm, respectively. We prove that AdAdaGrad-Norm converges with high probability at a rate of O(1/K) to a first-order stationary point of a smooth nonconvex function within K iterations. AdAdaGrad also exhibits similar convergence properties when combined with a novel coordinate-wise variant of our adaptive batch size strategy. We corroborate our theoretical claims with image-classification experiments that highlight the merits of the proposed schemes in terms of both training efficiency and model generalization. Our work highlights the potential of adaptive batch size strategies for adaptive gradient optimizers in large-scale model training.

Structured State-Space Duality (SSD) [Dao Gu, ICML 2024] is an equivalence between a simple Structured State-Space Model (SSM) and a masked attention mechanism. In particular, a state-space model with a scalar-times-identity state matrix is equivalent to a masked self-attention with a 1-semiseparable causal mask. Consequently, the same sequence transformation (model) has two algorithmic realizations: as a linear-time O(T) recurrence or as a quadratic-time O(T^2) attention. In this note, we formalize and generalize this duality: (i) we extend SSD from the scalar-identity case to general diagonal SSMs (diagonal state matrices); (ii) we show that these diagonal SSMs match the scalar case's training complexity lower bounds while supporting richer dynamics; (iii) we establish a necessary and sufficient condition under which an SSM is equivalent to 1-semiseparable masked attention; and (iv) we show that such duality fails to extend to standard softmax attention due to rank explosion. Together, these results tighten bridge between recurrent SSMs and Transformers, and widen the design space for expressive yet efficient sequence models.

Physical events are not understood by their names alone, but by the causal state changes that compose them. A clip-level label such as "bounce" can be correct while hiding the process that makes the event physically valid, from support loss and contact onset to rebound and settling. To make this hidden process explicit, we introduce Atomic Physical Transitions (APTs): minimal, temporally localized state changes that bind a visible cue to an active physical mechanism and before/after dynamical regimes. An APT chain represents a video as an ordered causal transition sequence rather than a single aggregate event label: event labels tell what happened; APT chains explain why it happened. To make APTs learnable by VLMs, we construct mixed-source APT data from human annotations and simulator ground truth, covering 14 transition types across contact, gravity, friction, and rotation/stability, with 27,303 timed instances over 1,246 trials. Using this data, we find that current VLMs miss transition-level physics, with zero-shot recall at most 14

Can Vision Language Models (VLMs) imagine the full scene from just a few views, like humans do? Humans form spatial mental models, internal representations of unseen space, to reason about layout, perspective, and motion. Our new MindCube benchmark with 21,154 questions across 3,268 images exposes this critical gap, where existing VLMs exhibit near-random performance. Using MindCube, we systematically evaluate how well VLMs build robust spatial mental models through representing positions (cognitive mapping), orientations (perspective-taking), and dynamics (mental simulation for "what-if" movements). We then explore three approaches to help VLMs approximate spatial mental models, including unseen intermediate views, natural language reasoning chains, and cognitive maps. The significant improvement comes from a synergistic approach, "map-then-reason", that jointly trains the model to first generate a cognitive map and then reason upon it. By training models to reason over these internal maps, we boosted accuracy from 37.8% to 60.8% (+23.0%). Adding reinforcement learning pushed performance even further to 70.7% (+32.9%). Our key insight is that such scaffolding of spatial mental models, actively constructing and utilizing internal structured spatial representations with flexible reasoning processes, significantly improves understanding of unobservable space.

We introduce Discrete flow Matching policy Optimization (DoMinO), a unified framework for Reinforcement Learning (RL) fine-tuning Discrete Flow Matching (DFM) models under a broad class of policy gradient methods. Our key idea is to view the DFM sampling procedure as a multi-step Markov Decision Process. This perspective provides a simple and transparent reformulation of fine-tuning reward maximization as a robust RL objective. Consequently, it not only preserves the original DFM samplers but also avoids biased auxiliary estimators and likelihood surrogates used by many prior RL fine-tuning methods. To prevent policy collapse, we also introduce new total-variation regularizers to keep the fine-tuned distribution close to the pretrained one. Theoretically, we establish an upper bound on the discretization error of DoMinO and tractable upper bounds for the regularizers. Experimentally, we evaluate DoMinO on regulatory DNA sequence design. DoMinO achieves stronger predicted enhancer activity and better sequence naturalness than the previous best reward-driven baselines. The regularization further improves alignment with the natural sequence distribution while preserving strong functional performance. These results establish DoMinO as an useful framework for controllable discrete sequence generation.

Vision-Language Models (VLMs) are increasingly deployed in embodied environments, where they need produce numerical outputs such as action magnitudes and spatial coordinates. Although these numbers appear meaningful, it remains unclear whether these numerical outputs are genuinely grounded in spatial perception. Therefore, in this work, we revisit spatial numerical understanding through SpaceNum, a unified framework that captures two complementary settings: numbers as dynamic transitions during spatial exploration, and numbers as static layouts in spatial reasoning. We formulate two bidirectional tasks, Num2Space and Space2Num, to evaluate how well VLMs map between vision-side spatial structure and language-side numerical representations. We systematically study whether current VLMs truly understand numerical values in spatial settings. Across dynamic transitions and static layouts, we find that models largely fail to ground numbers in spatial meaning and often perform close to random guess. Through error analysis, reasoning trace analysis, and controlled interventions, we show that current VLMs rely heavily on shallow spatial cues, struggle to build stable coordinate-aware representations, and fail to abstract structured spatial layouts from visual observations. We further show that explicit reasoning provides only marginal gains, while tuning can partially improve spatial numerical understanding and transfer to external spatial reasoning benchmarks.

Times series foundation models (TSFMs) have emerged as a promising paradigm for time series analysis and forecasting, showing remarkable generalization performance across different domains. While efforts have been made on hallucinations of foundation models, the hallucinations of TSFMs have been underexplored. In this paper, we formally define TSFM hallucinations in the zero-shot forecasting setting by examining whether a generated forecast exhibits different dynamics from those of the context. Our study reveals that TSFM hallucinations primarily stem from the loss of context information in hidden states during forward propagation. As such, we propose methodologies to identify signal subspaces in TSFMs and magnify their information through intervention. Extensive experiments demonstrate that our proposed intervention approach effectively mitigates hallucinations and improves forecasting performance. Furthermore, the signal strength measure we compute from signal subspaces has strong predictive power of hallucinations and forecasting performance of the model. Our work contributes to deeper understanding of TSFM trustworthiness that could foster future research in this direction.

We provide an exactly solvable example for interpreting In-Context Learning (ICL) with one-layer attention models as conditional retrieval of dense associative memory models. Our main contribution is to interpret ICL as memory reshaping in the modern Hopfield model from a conditional memory set (in-context examples). Specifically, we show that the in-context sequential examples induce an effective reshaping of the energy landscape of a Hopfield model. We integrate this in-context memory reshaping phenomenon into the existing Bayesian model averaging view of ICL [Zhang et al., AISTATS 2025] via the established equivalence between the modern Hopfield model and transformer attention. Under this unique perspective, we not only characterize how in-context examples shape predictions in the Gaussian linear regression case, but also recover the known epsilon-stability generalization bound of the ICL for the one-layer attention model. We also give explanations for three key behaviors of ICL and validate them through experiments.

Self-driving laboratories offer a promising path toward reducing the labor-intensive, time-consuming, and often irreproducible workflows in the biological sciences. Yet their stringent precision requirements demand highly robust models whose training relies on large amounts of annotated data. However, this kind of data is difficult to obtain in routine practice, especially negative samples. In this work, we focus on pipetting, the most critical and precision sensitive action in SDLs. To overcome the scarcity of training data, we build a hybrid pipeline that fuses real and virtual data generation. The real track adopts a human-in-the-loop scheme that couples automated acquisition with selective human verification to maximize accuracy with minimal effort. The virtual track augments the real data using reference-conditioned, prompt-guided image generation, which is further screened and validated for reliability. Together, these two tracks yield a class-balanced dataset that enables robust bubble detection training. On a held-out real test set, a model trained entirely on automatically acquired real images reaches 99.6

We propose the first unified adversarial attack benchmark for Genomic Foundation Models (GFMs), named GenoArmory. Unlike existing GFM benchmarks, GenoArmory offers the first comprehensive evaluation framework to systematically assess the vulnerability of GFMs to adversarial attacks. Methodologically, we evaluate the adversarial robustness of five state-of-the-art GFMs using four widely adopted attack algorithms and three defense strategies. Importantly, our benchmark provides an accessible and comprehensive framework to analyze GFM vulnerabilities with respect to model architecture, quantization schemes, and training datasets. Additionally, we introduce GenoAdv, a new adversarial sample dataset designed to improve GFM safety. Empirically, classification models exhibit greater robustness to adversarial perturbations compared to generative models, highlighting the impact of task type on model vulnerability. Moreover, adversarial attacks frequently target biologically significant genomic regions, suggesting that these models effectively capture meaningful sequence features.