Flow Matching is Adaptive to Manifold Structures

Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source distribution (e.g., a standard normal) and a target data distribution. Flow-based methods often exhibit greater training stability and have achieved strong empirical performance in high-dimensional settings where data concentrate near a low-dimensional manifold, such as text-to-image synthesis, video generation, and molecular structure generation. Despite this success, existing theoretical analyses of flow matching assume target distributions with smooth, full-dimensional densities, leaving its effectiveness in manifold-supported settings largely unexplained. To this end, we theoretically analyze flow matching with linear interpolation when the target distribution is supported on a smooth manifold. We establish a non-asymptotic convergence guarantee for the learned velocity field, and then propagate this estimation error through the ODE to obtain statistical consistency of the implicit density estimator induced by the flow-matching objective. The resulting convergence rate is near minimax-optimal, depends only on the intrinsic dimension, and reflects the smoothness of both the manifold and the target distribution. Together, these results provide a principled explanation for how flow matching adapts to intrinsic data geometry and circumvents the curse of dimensionality.

Goal-Oriented Influence-Maximizing Data Acquisition for Learning and Optimization

Active data acquisition is central to many learning and optimization tasks in deep neural networks, yet remains challenging because most approaches rely on predictive uncertainty estimates that are difficult to obtain reliably. To this end, we propose Goal-Oriented Influence- Maximizing Data Acquisition (GOIMDA), an active acquisition algorithm that avoids explicit posterior inference while remaining uncertainty-aware through inverse curvature. GOIMDA selects inputs by maximizing their expected influence on a user-specified goal functional, such as test loss, predictive entropy, or the value of an optimizer-recommended design. Leveraging first-order influence functions, we derive a tractable acquisition rule that combines the goal gradient, training-loss curvature, and candidate sensitivity to model parameters. We show theoretically that, for generalized linear models, GOIMDA approximates predictive-entropy minimization up to a correction term accounting for goal alignment and prediction bias, thereby, yielding uncertainty-aware behavior without maintaining a Bayesian posterior. Empirically, across learning tasks (including image and text classification) and optimization tasks (including noisy global optimization benchmarks and neural-network hyperparameter tuning), GOIMDA consistently reaches target performance with substantially fewer labeled samples or function evaluations than uncertainty-based active learning and Gaussian-process Bayesian optimization baselines.

QuEPT: Quantized Elastic Precision Transformers with One-Shot Calibration for Multi-Bit Switching

Elastic precision quantization enables multi-bit deployment via a single optimization pass, fitting diverse quantization scenarios.Yet, the high storage and optimization costs associated with the Transformer architecture, research on elastic quantization remains limited, particularly for large language models.This paper proposes QuEPT, an efficient post-training scheme that reconstructs block-wise multi-bit errors with one-shot calibration on a small data slice. It can dynamically adapt to various predefined bit-widths by cascading different low-rank adapters, and supports real-time switching between uniform quantization and mixed precision quantization without repeated optimization. To enhance accuracy and robustness, we introduce Multi-Bit Token Merging (MB-ToMe) to dynamically fuse token features across different bit-widths, improving robustness during bit-width switching. Additionally, we propose Multi-Bit Cascaded Low-Rank adapters (MB-CLoRA) to strengthen correlations between bit-width groups, further improve the overall performance of QuEPT. Extensive experiments demonstrate that QuEPT achieves comparable or better performance to existing state-of-the-art post-training quantization methods.Our code is available at https://github.com/xuke225/QuEPT

Causal Representation Meets Stochastic Modeling under Generic Geometry

Learning meaningful causal representations from observations has emerged as a crucial task for facilitating machine learning applications and driving scientific discoveries in fields such as climate science, biology, and physics. This process involves disentangling high-level latent variables and their causal relationships from low-level observations. Previous work in this area that achieves identifiability typically focuses on cases where the observations are either i.i.d. or follow a latent discrete-time process. Nevertheless, many real-world settings require identifying latent variables that are continuous-time stochastic processes (e.g., multivariate point processes). To this end, we develop identifiable causal representation learning for continuous-time latent stochastic point processes. We study its identifiability by analyzing the geometry of the parameter space. Furthermore, we develop MUTATE, an identifiable variational autoencoder framework with a time-adaptive transition module to infer stochastic dynamics. Across simulated and empirical studies, we find that MUTATE can effectively answer scientific questions, such as the accumulation of mutations in genomics and the mechanisms driving neuron spike triggers in response to time-varying dynamics.

Terminal-Bench: Benchmarking Agents on Hard, Realistic Tasks in Command Line Interfaces

AI agents may soon become capable of autonomously completing valuable, long-horizon tasks in diverse domains. Current benchmarks either do not measure real-world tasks, or are not sufficiently difficult to meaningfully measure frontier models. To this end, we present Terminal-Bench 2.0: a carefully curated hard benchmark composed of 89 tasks in computer terminal environments inspired by problems from real workflows. Each task features a unique environment, human-written solution, and comprehensive tests for verification. We show that frontier models and agents score less than 65\% on the benchmark and conduct an error analysis to identify areas for model and agent improvement. We publish the dataset and evaluation harness to assist developers and researchers in future work at https://www.tbench.ai/ .

Meta-probabilistic Modeling

While probabilistic graphical models can discover latent structure in data, their effectiveness hinges on choosing well-specified models. Identifying such models is challenging in practice, often requiring iterative checking and revision through trial and error. To this end, we propose meta-probabilistic modeling (MPM), a meta-learning algorithm that learns generative model structure directly from multiple related datasets. MPM uses a hierarchical architecture where global model specifications are shared across datasets while local parameters remain dataset-specific. For learning and inference, we propose a tractable VAE-inspired surrogate objective, and optimize it through bi-level optimization: local variables are updated analytically via coordinate ascent, while global parameters are trained with gradient-based methods. We evaluate MPM on object-centric image modeling and sequential text modeling, demonstrating that it adapts generative models to data while recovering meaningful latent representations.

On the Identifiability of Regime-Switching Models with Multi-Lag Dependencies

Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting. For SDSs, we establish identifiability of the latent variables up to permutation and scaling via temporal structure, which in turn yields conditions for identifiability of regime-dependent latent causal graphs (up to regime/node permutations). Our results hold in a fully unsupervised setting through architectural and noise assumptions that are directly enforceable via neural network design. We complement the theory with a flexible variational estimator that satisfies the assumptions and validate the results on synthetic benchmarks. Across real-world datasets from neuroscience, finance, and climate, identifiability leads to more trustworthy interpretability analysis, which is crucial for scientific discovery.

Environment-Adaptive Covariate Selection: Learning When to Use Spurious Correlations for Out-of-Distribution Prediction

Out-of-distribution (OOD) prediction is often approached by restricting models to causal or invariant covariates, avoiding non-causal spurious associations that may be unstable across environments. Despite its theoretical appeal, this strategy frequently underperforms empirical risk minimization (ERM) in practice. We investigate the source of this gap and show that such failures naturally arise when only a subset of the true causes of the outcome is observed. In these settings, non-causal spurious covariates can serve as informative proxies for unobserved causes and substantially improve prediction, except under distribution shifts that break these proxy relationships. Consequently, the optimal set of predictive covariates is neither universal nor necessarily exhibits invariant relationships with the outcome across all environments, but instead depends on the specific type of shift encountered. Crucially, we observe that different covariate shifts induce distinct, observable signatures in the covariate distribution itself. Moreover, these signatures can be extracted from unlabeled data in the target OOD environment and used to assess when proxy covariates remain reliable and when they fail. Building on this observation, we propose an environment-adaptive covariate selection (EACS) algorithm that maps environment-level covariate summaries to environment-specific covariate sets, while allowing the incorporation of prior causal knowledge as constraints. Across simulations and applied datasets, EACS consistently outperforms static causal, invariant, and ERM-based predictors under diverse distribution shifts.

Last Layer Empirical Bayes

The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle this task. Both approaches produce predictions by computing an expectation of neural network outputs over some distribution on the corresponding weights; this distribution is given by the posterior in the case of BNNs, and by a mixture of point masses for ensembles. Inspired by recent work showing that the distribution used by ensembles can be understood as a posterior corresponding to a learned data-dependent prior, we propose last layer empirical Bayes (LLEB). LLEB instantiates a learnable prior as a normalizing flow, which is then trained to maximize the evidence lower bound; to retain tractability we use the flow only on the last layer. We show why LLEB is well motivated, and how it interpolates between standard BNNs and ensembles in terms of the strength of the prior that they use. LLEB performs on par with existing approaches, highlighting that empirical Bayes is a promising direction for future research in uncertainty quantification.

Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model

''Grokking'' is a phenomenon where a neural network first memorizes training data and generalizes poorly, but then suddenly transitions to near-perfect generalization after prolonged training. While intriguing, this delayed generalization phenomenon compromises predictability and efficiency. Ideally, models should generalize directly without delay. To this end, this paper proposes GrokTransfer, a simple and principled method for accelerating grokking in training neural networks, based on the key observation that data embedding plays a crucial role in determining whether generalization is delayed. GrokTransfer first trains a smaller, weaker model to reach a nontrivial (but far from optimal) test performance. Then, the learned input embedding from this weaker model is extracted and used to initialize the embedding in the target, stronger model. We rigorously prove that, on a synthetic XOR task where delayed generalization always occurs in normal training, GrokTransfer enables the target model to generalize directly without delay. Moreover, we demonstrate that, across empirical studies of different tasks, GrokTransfer effectively reshapes the training dynamics and eliminates delayed generalization, for both fully-connected neural networks and Transformers.