Prompt Augmentation Scales up GRPO Training on Mathematical Reasoning

Reinforcement learning algorithms such as group-relative policy optimization (GRPO) have demonstrated strong potential for improving the mathematical reasoning capabilities of large language models. However, prior work has consistently observed an entropy collapse phenomenon during reinforcement post-training, characterized by a monotonic decrease in policy entropy that ultimately leads to training instability and collapse. As a result, most existing approaches restrict training to short horizons (typically 5-20 epochs), limiting sustained exploration and hindering further policy improvement. In addition, nearly all prior work relies on a single, fixed reasoning prompt or template during training. In this work, we introduce prompt augmentation, a training strategy that instructs the model to generate reasoning traces under diverse templates and formats, thereby increasing rollout diversity. We show that, without a KL regularization term, prompt augmentation enables stable scaling of training duration under a fixed dataset and allows the model to tolerate low-entropy regimes without premature collapse. Empirically, a Qwen2.5-Math-1.5B model trained with prompt augmentation on the MATH Level 3-5 dataset achieves state-of-the-art performance, reaching 44.5 per-benchmark accuracy and 51.3 per-question accuracy on standard mathematical reasoning benchmarks, including AIME24, AMC, MATH500, Minerva, and OlympiadBench. The code and model checkpoints are available at https://github.com/wenquanlu/prompt-augmentation-GRPO.

A Lightweight Library for Energy-Based Joint-Embedding Predictive Architectures

We present EB-JEPA, an open-source library for learning representations and world models using Joint-Embedding Predictive Architectures (JEPAs). JEPAs learn to predict in representation space rather than pixel space, avoiding the pitfalls of generative modeling while capturing semantically meaningful features suitable for downstream tasks. Our library provides modular, self-contained implementations that illustrate how representation learning techniques developed for image-level self-supervised learning can transfer to video, where temporal dynamics add complexity, and ultimately to action-conditioned world models, where the model must additionally learn to predict the effects of control inputs. Each example is designed for single-GPU training within a few hours, making energy-based self-supervised learning accessible for research and education. We provide ablations of JEA components on CIFAR-10. Probing these representations yields 91% accuracy, indicating that the model learns useful features. Extending to video, we include a multi-step prediction example on Moving MNIST that demonstrates how the same principles scale to temporal modeling. Finally, we show how these representations can drive action-conditioned world models, achieving a 97% planning success rate on the Two Rooms navigation task. Comprehensive ablations reveal the critical importance of each regularization component for preventing representation collapse. Code is available at https://github.com/facebookresearch/eb_jepa.

Rectified LpJEPA: Joint-Embedding Predictive Architectures with Sparse and Maximum-Entropy Representations

Joint-Embedding Predictive Architectures (JEPA) learn view-invariant representations and admit projection-based distribution matching for collapse prevention. Existing approaches regularize representations towards isotropic Gaussian distributions, but inherently favor dense representations and fail to capture the key property of sparsity observed in efficient representations. We introduce Rectified Distribution Matching Regularization (RDMReg), a sliced two-sample distribution-matching loss that aligns representations to a Rectified Generalized Gaussian (RGG) distribution. RGG enables explicit control over expected $\ell_0$ norm through rectification, while preserving maximum-entropy up to rescaling under expected $\ell_p$ norm constraints. Equipping JEPAs with RDMReg yields Rectified LpJEPA, which strictly generalizes prior Gaussian-based JEPAs. Empirically, Rectified LpJEPA learns sparse, non-negative representations with favorable sparsity-performance trade-offs and competitive downstream performance on image classification benchmarks, demonstrating that RDMReg effectively enforces sparsity while preserving task-relevant information.

VideoGPA: Distilling Geometry Priors for 3D-Consistent Video Generation

While recent video diffusion models (VDMs) produce visually impressive results, they fundamentally struggle to maintain 3D structural consistency, often resulting in object deformation or spatial drift. We hypothesize that these failures arise because standard denoising objectives lack explicit incentives for geometric coherence. To address this, we introduce VideoGPA (Video Geometric Preference Alignment), a data-efficient self-supervised framework that leverages a geometry foundation model to automatically derive dense preference signals that guide VDMs via Direct Preference Optimization (DPO). This approach effectively steers the generative distribution toward inherent 3D consistency without requiring human annotations. VideoGPA significantly enhances temporal stability, physical plausibility, and motion coherence using minimal preference pairs, consistently outperforming state-of-the-art baselines in extensive experiments.

LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics

Learning manipulable representations of the world and its dynamics is central to AI. Joint-Embedding Predictive Architectures (JEPAs) offer a promising blueprint, but lack of practical guidance and theory has led to ad-hoc R&D. We present a comprehensive theory of JEPAs and instantiate it in {\bf LeJEPA}, a lean, scalable, and theoretically grounded training objective. First, we identify the isotropic Gaussian as the optimal distribution that JEPAs' embeddings should follow to minimize downstream prediction risk. Second, we introduce a novel objective--{\bf Sketched Isotropic Gaussian Regularization} (SIGReg)--to constrain embeddings to reach that ideal distribution. Combining the JEPA predictive loss with SIGReg yields LeJEPA with numerous theoretical and practical benefits: (i) single trade-off hyperparameter, (ii) linear time and memory complexity, (iii) stability across hyper-parameters, architectures (ResNets, ViTs, ConvNets) and domains, (iv) heuristics-free, e.g., no stop-gradient, no teacher-student, no hyper-parameter schedulers, and (v) distributed training-friendly implementation requiring only $\approx$50 lines of code. Our empirical validation covers 10+ datasets, 60+ architectures, all with varying scales and domains. As an example, using imagenet-1k for pretraining and linear evaluation with frozen backbone, LeJEPA reaches 79\% with a ViT-H/14. We hope that the simplicity and theory-friendly ecosystem offered by LeJEPA will reestablish self-supervised pre-training as a core pillar of AI research (\href{https://github.com/rbalestr-lab/lejepa}{GitHub repo}).

MapSAM2: Adapting SAM2 for Automatic Segmentation of Historical Map Images and Time Series

Historical maps are unique and valuable archives that document geographic features across different time periods. However, automated analysis of historical map images remains a significant challenge due to their wide stylistic variability and the scarcity of annotated training data. Constructing linked spatio-temporal datasets from historical map time series is even more time-consuming and labor-intensive, as it requires synthesizing information from multiple maps. Such datasets are essential for applications such as dating buildings, analyzing the development of road networks and settlements, studying environmental changes etc. We present MapSAM2, a unified framework for automatically segmenting both historical map images and time series. Built on a visual foundation model, MapSAM2 adapts to diverse segmentation tasks with few-shot fine-tuning. Our key innovation is to treat both historical map images and time series as videos. For images, we process a set of tiles as a video, enabling the memory attention mechanism to incorporate contextual cues from similar tiles, leading to improved geometric accuracy, particularly for areal features. For time series, we introduce the annotated Siegfried Building Time Series Dataset and, to reduce annotation costs, propose generating pseudo time series from single-year maps by simulating common temporal transformations. Experimental results show that MapSAM2 learns temporal associations effectively and can accurately segment and link buildings in time series under limited supervision or using pseudo videos. We will release both our dataset and code to support future research.

SAFE: A Novel Approach to AI Weather Evaluation through Stratified Assessments of Forecasts over Earth

The dominant paradigm in machine learning is to assess model performance based on average loss across all samples in some test set. This amounts to averaging performance geospatially across the Earth in weather and climate settings, failing to account for the non-uniform distribution of human development and geography. We introduce Stratified Assessments of Forecasts over Earth (SAFE), a package for elucidating the stratified performance of a set of predictions made over Earth. SAFE integrates various data domains to stratify by different attributes associated with geospatial gridpoints: territory (usually country), global subregion, income, and landcover (land or water). This allows us to examine the performance of models for each individual stratum of the different attributes (e.g., the accuracy in every individual country). To demonstrate its importance, we utilize SAFE to benchmark a zoo of state-of-the-art AI-based weather prediction models, finding that they all exhibit disparities in forecasting skill across every attribute. We use this to seed a benchmark of model forecast fairness through stratification at different lead times for various climatic variables. By moving beyond globally-averaged metrics, we for the first time ask: where do models perform best or worst, and which models are most fair? To support further work in this direction, the SAFE package is open source and available at https://github.com/N-Masi/safe

Your Attention Matters: to Improve Model Robustness to Noise and Spurious Correlations

Self-attention mechanisms are foundational to Transformer architectures, supporting their impressive success in a wide range of tasks. While there are many self-attention variants, their robustness to noise and spurious correlations has not been well studied. This study evaluates Softmax, Sigmoid, Linear, Doubly Stochastic, and Cosine attention within Vision Transformers under different data corruption scenarios. Through testing across the CIFAR-10, CIFAR-100, and Imagenette datasets, we show that Doubly Stochastic attention is the most robust. Our findings inform self-attention selection in contexts with imperfect data.

General Methods Make Great Domain-specific Foundation Models: A Case-study on Fetal Ultrasound

With access to large-scale, unlabeled medical datasets, researchers are confronted with two questions: Should they attempt to pretrain a custom foundation model on this medical data, or use transfer-learning from an existing generalist model? And, if a custom model is pretrained, are novel methods required? In this paper we explore these questions by conducting a case-study, in which we train a foundation model on a large regional fetal ultrasound dataset of 2M images. By selecting the well-established DINOv2 method for pretraining, we achieve state-of-the-art results on three fetal ultrasound datasets, covering data from different countries, classification, segmentation, and few-shot tasks. We compare against a series of models pretrained on natural images, ultrasound images, and supervised baselines. Our results demonstrate two key insights: (i) Pretraining on custom data is worth it, even if smaller models are trained on less data, as scaling in natural image pretraining does not translate to ultrasound performance. (ii) Well-tuned methods from computer vision are making it feasible to train custom foundation models for a given medical domain, requiring no hyperparameter tuning and little methodological adaptation. Given these findings, we argue that a bias towards methodological innovation should be avoided when developing domain specific foundation models under common computational resource constraints.

GrokAlign: Geometric Characterisation and Acceleration of Grokking

A key challenge for the machine learning community is to understand and accelerate the training dynamics of deep networks that lead to delayed generalisation and emergent robustness to input perturbations, also known as grokking. Prior work has associated phenomena like delayed generalisation with the transition of a deep network from a linear to a feature learning regime, and emergent robustness with changes to the network's functional geometry, in particular the arrangement of the so-called linear regions in deep networks employing continuous piecewise affine nonlinearities. Here, we explain how grokking is realised in the Jacobian of a deep network and demonstrate that aligning a network's Jacobians with the training data (in the sense of cosine similarity) ensures grokking under a low-rank Jacobian assumption. Our results provide a strong theoretical motivation for the use of Jacobian regularisation in optimizing deep networks -- a method we introduce as GrokAlign -- which we show empirically to induce grokking much sooner than more conventional regularizers like weight decay. Moreover, we introduce centroid alignment as a tractable and interpretable simplification of Jacobian alignment that effectively identifies and tracks the stages of deep network training dynamics. Accompanying \href{https://thomaswalker1.github.io/blog/grokalign.html}{webpage} and \href{https://github.com/ThomasWalker1/grokalign}{code}.