In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular systems. However, while classical diffusion sampling usually recovers the training distribution, the corresponding energy-based interpretation of the learned score is often inconsistent with this distribution, even for low-dimensional toy systems. We trace this inconsistency to inaccuracies of the learned score at very small diffusion timesteps, where the model must capture the correct evolution of the data distribution. In this regime, diffusion models fail to satisfy the Fokker-Planck equation, which governs the evolution of the score. We interpret this deviation as one source of the observed inconsistencies and propose an energy-based diffusion model with a Fokker-Planck-derived regularization term to enforce consistency. We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins, and by introducing a state-of-the-art transferable Boltzmann emulator for dipeptides that supports simulation and achieves improved consistency and efficient sampling.

Furthermore, we develop a method to eliminate bias in cases where blindly assuming IID is expected to yield a significantly biased estimate.

The Heckman selection model is one of the most well-renounced econometric models in the analysis of data with sample selection. This model is designed to rectify sample selection biases based on the assumption of bivariate normal error terms. However, real data diverge from this assumption in the presence of heavy tails and/or atypical observations. Recently, this assumption has been relaxed via a more flexible Student's t-distribution, which has appealing statistical properties. This paper introduces a novel Heckman selection model using a bivariate contaminated normal distribution for the error terms. We present an efficient ECM algorithm for parameter estimation with closed-form expressions at the E-step based on truncated multinormal distribution formulas. The identifiability of the proposed model is also discussed, and its properties have been examined. Through simulation studies, we compare our proposed model with the normal and Student's t counterparts and investigate the finite-sample properties and the variation in missing rate. Results obtained from two real data analyses showcase the usefulness and effectiveness of our model. The proposed algorithms are implemented in the R package HeckmanEM.

What data should a vision-language model be trained on? To answer this question, many data curation efforts center on the quality of a dataset. However, most of these existing methods are (i) offline, i.e. they produce a static dataset from a set of predetermined filtering criteria, and (ii) concept-agnostic, i.e. they use model-based filters which induce additional data biases. In this work, we go beyond such offline, concept-agnostic methods and advocate for more flexible, task-adaptive online concept-based curation. Our first contribution is DataConcept, a collection of 128M web-crawled image-text pairs annotated with fine-grained details about their concept composition. Building on DataConcept, we introduce Concept-Aware Batch Sampling (CABS), a simple yet effective batch sampling framework that flexibly constructs batches on-the-fly based on specific target distributions. We propose two variants: (i) Diversity Maximization (CABS-DM) to curate batches with a broad coverage of available concepts, and (ii) Frequency Maximization (CABS-FM) to curate batches with high object multiplicity. Through extensive evaluations across 28 benchmarks, we demonstrate that our CABS method significantly benefits CLIP/SigLIP model classes and yields highly performant models. Overall, CABS represents a strong open-source alternative to proprietary online data curation algorithms, enabling practitioners to define custom concept distributions that optimize for specific downstream tasks.

Flow-matching models effectively represent complex distributions, yet estimating expectations of functions of their outputs remains challenging under limited sampling budgets. Independent sampling often yields high-variance estimates, especially when rare but with high-impact outcomes dominate the expectation. W e propose an importance-weighted non-IID sampling framework that jointly draws multiple samples to cover diverse, salient regions of a flow's distribution while maintaining unbiased estimation via estimated importance weights. T o balance diversity and quality, we introduce a score-based regularization for the diversity mechanism, which uses the score function, i.e., the gradient of the log probability, to ensure samples are pushed apart within high-density regions of the data manifold, mitigating off-manifold drift. W e further develop the first approach for importance weighting of non-IID flow samples by learning a residual velocity field that reproduces the marginal distribution of the non-IID samples. Empirically, our method produces diverse, high-quality samples and accurate estimates of both importance weights and expectations, advancing the reliable characterization of flow-matching model outputs. Our code will be publicly available on GitHub.

In semi-decentralized federated learning, devices primarily rely on device-to-device communication but occasionally interact with a central server. Periodically, a sampled subset of devices uploads their local models to the server, which computes an aggregate model. The server can then either (i) share this aggregate model only with the sampled clients (sampled-to-sampled, S2S) or (ii) broadcast it to all clients (sampled-to-all, S2A). Despite their practical significance, a rigorous theoretical and empirical comparison of these two strategies remains absent. We address this gap by analyzing S2S and S2A within a unified convergence framework that accounts for key system parameters: sampling rate, server aggregation frequency, and network connectivity. Our results--both analytical and experimental--reveal distinct regimes where one strategy outperforms the other, depending primarily on the degree of data heterogeneity across devices. These insights lead to concrete design guidelines for practical semi-decentralized FL deployments.

We present a data-domain sampling regime for quantifying CNNs' graphic perception behaviors. This regime lets us evaluate CNNs' ratio estimation ability in bar charts from three perspectives: sensitivity to training-test distribution discrepancies, stability to limited samples, and relative expertise to human observers. After analyzing 16 million trials from 800 CNNs models and 6,825 trials from 113 human participants, we arrived at a simple and actionable conclusion: CNNs can outperform humans and their biases simply depend on the training-test distance. We show evidence of this simple, elegant behavior of the machines when they interpret visualization images. osf.io/gfqc3 provides registration, the code for our sampling regime, and experimental results.

This paper proposes deception as a mechanism for out-of-distribution (OOD) generalization: by learning data representations that make training data appear independent and identically distributed (iid) to an observer, we can identify stable features that eliminate spurious correlations and generalize to unseen domains. We refer to this principle as deceptive risk minimization (DRM) and instantiate it with a practical differentiable objective that simultaneously learns features that eliminate distribution shifts from the perspective of a detector based on conformal martingales while minimizing a task-specific loss. In contrast to domain adaptation or prior invariant representation learning methods, DRM does not require access to test data or a partitioning of training data into a finite number of data-generating domains. We demonstrate the efficacy of DRM on numerical experiments with concept shift and a simulated imitation learning setting with covariate shift in environments that a robot is deployed in.

Furthermore, we develop a method to eliminate bias in cases where blindly assuming IID is expected to yield a significantly biased estimate. Finally, we test the coverage and performance of our methods through simulations.

We consider the problem of persistent client dropout in asynchronous Decentralized Federated Learning (DFL). Asynchronicity and decentralization obfuscate information about model updates among federation peers, making recovery from a client dropout difficult. Access to the number of learning epochs, data distributions, and all the information necessary to precisely reconstruct the missing neighbor's loss functions is limited. We show that obvious mitigations do not adequately address the problem and introduce adaptive strategies based on client reconstruction. We show that these strategies can effectively recover some performance loss caused by dropout. Our work focuses on asynchronous DFL with local regularization and differs substantially from that in the existing literature. We evaluate the proposed methods on tabular and image datasets, involve three DFL algorithms, and three data heterogeneity scenarios (iid, non-iid, class-focused non-iid). Our experiments show that the proposed adaptive strategies can be effective in maintaining robustness of federated learning, even if they do not reconstruct the missing client's data precisely. We also discuss the limitations and identify future avenues for tackling the problem of client dropout.