Information Routing in Atomistic Foundation Models: How Equivariance Creates Linearly Disentangled Representations

What do atomistic foundation models encode in their intermediate representations, and how is that information organized? We introduce Composition Projection Decomposition (CPD), which uses QR projection to linearly remove composition signal from learned representations and probes the geometric residual. Across eight models from five architectural families on QM9 molecules and Materials Project crystals, we find a disentanglement gradient: tensor product equivariant architectures (MACE) produce representations where geometry is almost fully linearly accessible after composition removal ($R^2_{\text{geom}} = 0.782$ for HOMO-LUMO gap), while handcrafted descriptors (ANI-2x) entangle the same information nonlinearly ($R^2_{\text{geom}} = -0.792$ under Ridge; $R^2 = +0.784$ under MLP). MACE routes target-specific signal through irreducible representation channels -- dipole to $L = 1$, HOMO-LUMO gap to $L = 0$ -- a pattern not observed in ViSNet's vector-scalar architecture under the same probe. We show that gradient boosted tree probes on projected residuals are systematically inflated, recovering $R^2 = 0.68$--$0.95$ on a purely compositional target, and recommend linear probes as the primary metric. Linearly disentangled representations are more sample-efficient under linear probing, suggesting a practical advantage for equivariant architectures beyond raw prediction accuracy.

PAC Guarantees for Reinforcement Learning: Sample Complexity, Coverage, and Structure

When data is scarce or mistakes are costly, average-case metrics fall short. What a practitioner needs is a guarantee: with probability at least $1-δ$, the learned policy is $\varepsilon$-close to optimal after $N$ episodes. This is the PAC promise, and between 2018 and 2025 the RL theory community made striking progress on when such promises can be kept. We survey that progress. Our organizing tool is the Coverage-Structure-Objective (CSO) framework, proposed here, which decomposes nearly every PAC sample complexity result into three factors: coverage (how data were obtained), structure (intrinsic MDP or function-class complexity), and objective (what the learner must deliver). CSO is not a theorem but an interpretive template that identifies bottlenecks and makes cross-setting comparison immediate. The technical core covers tight tabular baselines and the uniform-PAC bridge to regret; structural complexity measures (Bellman rank, witness rank, Bellman-Eluder dimension) governing learnability with function approximation; results for linear, kernel/NTK, and low-rank models; reward-free exploration as upfront coverage investment; and pessimistic offline RL where inherited coverage is the binding constraint. We provide practitioner tools: rate lookup tables indexed by CSO coordinates, Bellman residual diagnostics, coverage estimation with deployment gates, and per-episode policy certificates. A final section catalogs open problems, separating near-term targets from frontier questions where coverage, structure, and computation tangle in ways current theory cannot resolve.

When Does Margin Clamping Affect Training Variance? Dataset-Dependent Effects in Contrastive Forward-Forward Learning

Contrastive Forward-Forward (CFF) learning trains Vision Transformers layer by layer against supervised contrastive objectives. CFF training can be sensitive to random seed, but the sources of this instability are poorly understood. We focus on one implementation detail: the positive-pair margin in the contrastive loss is applied through saturating similarity clamping, $\min(s + m,\, 1)$. We prove that an alternative formulation, subtracting the margin after the log-probability, is gradient-neutral under the mean-over-positives reduction. On CIFAR-10 ($2 \times 2$ factorial, $n{=}7$ seeds per cell), clamping produces $5.90\times$ higher pooled test-accuracy variance ($p{=}0.003$) with no difference in mean accuracy. Analyses of clamp activation rates, layerwise gradient norms, and a reduced-margin probe point to saturation-driven gradient truncation at early layers. The effect does not transfer cleanly to other datasets: on CIFAR-100, SVHN, and Fashion-MNIST, clamping produces equal or lower variance. Two factors account for the discrepancy. First, positive-pair density per batch controls how often saturation occurs. Second, task difficulty compresses seed-to-seed spread when accuracy is high. An SVHN difficulty sweep confirms the interaction on a single dataset, with the variance ratio moving from $0.25\times$ at high accuracy to $16.73\times$ under aggressive augmentation. In moderate-accuracy regimes with many same-class pairs per batch, switching to the gradient-neutral subtraction reference removes this variance inflation at no cost to mean accuracy. Measuring the layer-0 clamp activation rate serves as a simple check for whether the problem applies.

PyHealth 2.0: A Comprehensive Open-Source Toolkit for Accessible and Reproducible Clinical Deep Learning

Difficulty replicating baselines, high computational costs, and required domain expertise create persistent barriers to clinical AI research. To address these challenges, we introduce PyHealth 2.0, an enhanced clinical deep learning toolkit that enables predictive modeling in as few as 7 lines of code. PyHealth 2.0 offers three key contributions: (1) a comprehensive toolkit addressing reproducibility and compatibility challenges by unifying 15+ datasets, 20+ clinical tasks, 25+ models, 5+ interpretability methods, and uncertainty quantification including conformal prediction within a single framework that supports diverse clinical data modalities - signals, imaging, and electronic health records - with translation of 5+ medical coding standards; (2) accessibility-focused design accommodating multimodal data and diverse computational resources with up to 39x faster processing and 20x lower memory usage, enabling work from 16GB laptops to production systems; and (3) an active open-source community of 400+ members lowering domain expertise barriers through extensive documentation, reproducible research contributions, and collaborations with academic health systems and industry partners, including multi-language support via RHealth. PyHealth 2.0 establishes an open-source foundation and community advancing accessible, reproducible healthcare AI. Available at pip install pyhealth.