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Machine learning models often achieve high average accuracy in the training data while performing poorly on test data due to subpopulation shift. A common data-centric solution is to enforce balanced subgroup proportions, but full balance can be costly, infeasible, and not always necessary. In this work, we study whether balanced training data is the unique optimal configuration for robust subpopulation generalization. We extend a Gaussian feature-model framework to theoretically characterize the performance landscape across general training subgroup distributions. We show that multiple configurations, including substantially imbalanced ones, can perform comparably to the balanced one. We further derive gradient-based directions for adjusting subgroup proportions to improve adjusted accuracy and worst-group accuracy more efficiently. These findings suggest that strategically allocating data offers a more flexible and principled path to robust performance than simple balancing. The code is available at https://github.com/zhaoyingpan/subpop-data-allocation.

Stochastic differential equations (SDEs) describe stochastic processes across a wide range of scientific domains, including physics, biology, and finance. Although individual numerical integration steps are inexpensive, observing meaningful events or transitions can require millions of sequential steps, resulting in substantial wall-clock simulation time and poor hardware utilization. Deep learning offers an alternative by amortizing many integration steps into a single neural network forward pass, potentially enabling much faster simulation. However, existing supervised approaches typically require long simulated trajectory data, which restricts their applicability. In this work, we introduce Kolmogorov-Chapman Maps (KC-Maps), a method for learning the transition kernel of an SDE that relies only on the trajectory-free marginal samples together with the known drift and diffusion coefficients. Given an initial time and state of a process, KC-Maps models its distribution integrated to any given time, corresponding to the weak solution of the SDE. To recover the correct dynamics, KC-Maps satisfies two key properties: (i) it satisfies the boundary conditions, which we incorporate directly into the neural network architecture, and (ii) it respects the Kolmogorov--Chapman equation, which provides an efficient training objective. We empirically demonstrate that KC-Maps learns to integrate the dynamics of peptide molecular systems and outperforms classical molecular dynamics in terms of GPU-hours.

Machine learning interatomic potentials (MLIPs) are commonly trained and evaluated by their ability to reproduce first-principles energies and forces. Practical value, however, is often determined by downstream processes such as structural relaxation. Much of MLIP literature is motivated by the expectation that improving force accuracy will produce correspondingly better downstream behavior. Although this expectation is natural, it may not hold in practice due to model inaccuracies. Here, we demonstrate that force accuracy and relaxation accuracy can be driven in opposite directions. Starting from pretrained MLIPs, we differentiate through relaxation trajectories and optimize the the final structures. This intervention produces increases in force-prediction errors while substantially reducing structural errors. Importantly, this represents a trade-off between two aspects of physical fidelity: the learned forces become less faithful to first-principles forces, while the resulting relaxed structures become more faithful to first-principles predictions. Rather than observing a discrepancy between local quality and downstream performance, we demonstrate that this discrepancy can be induced through optimization. Our findings suggest that MLIPs need not be optimized as approximations of first-principles forces, but can instead learn task-specific vector fields that guide relaxation trajectories toward more accurate final structures. By propagating supervision through complete relaxation trajectories, our framework captures dependencies between successive predictions that are absent when structure--force pairs are treated independently. More broadly, these results demonstrate that conventional force metrics can provide an incomplete assessment of downstream performance and highlights the importance of evaluating scientific machine-learning models within computational workflows.

We introduce OCRia-1, a 4B vision-language model (VLM) for document parsing that excels at preserving table structure, extracting chart data and retaining text formatting. OCRia-1 handles content that has traditionally been challenging in document parsing: merged cells and spanning headers, tables with thousands of cells, chart data, and meaningful text formatting such as bold, italics, subscripts and superscripts, preserving details needed for business-critical document analysis. At the time of this report, it achieves the highest scores on tables, charts and text formatting among the systems evaluated, including a 35B model and Mistral OCR 4.1. Its mean ParseBench score over the four dimensions we evaluate is 0.87, against 0.75 for the next-best system. We emphasize data quality and reward design in training OCRia-1. Synthetic pages provide exact ground truth for long tables and rich formatting, while real pages are transcribed using a pipeline grounded in the PDF text layer. We attribute OCRia-1's performance primarily to careful data curation that prioritizes quality and diversity over quantity. Dimension-specific rewards evaluate table reconstruction, chart-data extraction and text-formatting fidelity. We train the model on the curated data using supervised fine-tuning (SFT), then refine it through reinforcement learning with verifiable rewards (RLVR). To our knowledge, OCRia-1 is the fastest published document-parsing VLM in its class, decoding at about 4,700 tokens per second with a single request on one B200 GPU, about nine times faster than the base model on stock vLLM. This is achieved through a block-diffusion speculator, quantization and custom kernels.