All Substitution Is Local

When does consulting one information source raise the value of another, and when does it diminish it? We study this question for Bayesian decision-makers facing finite actions. The interaction decomposes into two opposing forces: a complement force, measuring how one source moves beliefs to where the other becomes more useful, and a substitute force, measuring how much the current decision is resolved. Their balance obeys a localization principle: substitution requires an observation to cross a decision boundary, though crossing alone does not guarantee it. Whenever posteriors remain inside the current decision region, the substitute force vanishes, and sources are guaranteed to complement each other, even when one source cannot, on its own, change the decision. The results hold for arbitrarily correlated sources and are formalized in Lean 4. Substitution is confined to the thin boundaries where decisions change. Everywhere else, information cooperates. Code and proofs: https://github.com/nidhishs/all-substitution-is-local.

Meta-Learned Adaptive Optimization for Robust Human Mesh Recovery with Uncertainty-Aware Parameter Updates

Human mesh recovery from single images remains challenging due to inherent depth ambiguity and limited generalization across domains. While recent methods combine regression and optimization approaches, they struggle with poor initialization for test-time refinement and inefficient parameter updates during optimization. We propose a novel meta-learning framework that trains models to produce optimization-friendly initializations while incorporating uncertainty-aware adaptive updates during test-time refinement. Our approach introduces three key innovations: (1) a meta-learning strategy that simulates test-time optimization during training to learn better parameter initializations, (2) a selective parameter caching mechanism that identifies and freezes converged joints to reduce computational overhead, and (3) distribution-based adaptive updates that sample parameter changes from learned distributions, enabling robust exploration while quantifying uncertainty. Additionally, we employ stochastic approximation techniques to handle intractable gradients in complex loss landscapes. Extensive experiments on standard benchmarks demonstrate that our method achieves state-of-the-art performance, reducing MPJPE by 10.3 on 3DPW and 8.0 on Human3.6M compared to strong baselines. Our approach shows superior domain adaptation capabilities with minimal performance degradation across different environmental conditions, while providing meaningful uncertainty estimates that correlate with actual prediction errors. Combining meta-learning and adaptive optimization enables accurate mesh recovery and robust generalization to challenging scenarios.