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Fast Learning Rates for Physics-Informed Kernel Methods

Theoretical analysis proves finite-sample learning rates for physics-informed kernel estimators, showing differential observations can improve rates from n^-1/4 to n^-1/2.

The paper analyzes a physics-informed kernel estimator combining n value observations and m differential observations for a linear differential operator D, asking how much differential information improves prediction. The authors prove finite-sample bounds, supported by simulations, revealing a two-regime structure: when m is limited the rate depends jointly on n and m, and when m exceeds a problem-dependent threshold the rate saturates to the oracle rate. Examples in Sobolev spaces, including partial Laplacian constraints on the torus and gradient observations on bounded domains, illustrate improvements from the nonparametric n^-1/4 rate to the parametric n^-1/2 rate, plus physically consistent rates in a stronger norm.

arXiv cs.AI / cs.LG / cs.CL · 18h agoAI research

Google Research Introduces Retrieve-for-Train (R4T): An RL-Compiled Diffusion Retriever for 12× to 20× Faster Query Fan-Out

Google Research introduced R4T, an RL-trained fan-out pipeline distilled into a 53.9M-parameter diffusion retriever achieving 12x-20x faster query fan-out.

Google Research introduced Retrieve-for-Train (R4T), which trains a fan-out language model with GRPO plus soft PPO regularization, then distills query fan-out into a 53.9M-parameter diffusion transformer that generates all retrieval embeddings in a single non-autoregressive pass. A three-term reward (groundedness 0.6, diversity 0.2 via Vendi Score, alignment 0.2) prevents paraphrastic collapse and reward hacking during training. On the Polyvore dataset, Gemma3-4B R4T-FOLM averaged 49.1 versus 40.9 for Best-of-N, and the diffusion retriever cut fan-out latency from 1.46s to 0.07s at batch size 8, a consistent 12x-20x speedup over autoregressive methods.

MarkTechPost · 4h agoAI research

Exponential Hardness of Off-Policy Evaluation under History-Dependent Logging

Researchers prove off-policy evaluation under history-dependent logging requires exponentially many episodes, resolving a hardness question for model-based POMDP evaluation.

The paper constructs POMDPs with at most two latent states per stage, three actions, and a three-memory-state logger where evaluating a known deterministic target policy to accuracy 1/8 requires Θ((3/2)^H log(1/δ)) episodes for any horizon H≥3. Coverage and outcome-revealing conditions hold with constants independent of H, yet a reset erases the unknown transition that determines the target value. The authors characterize the resulting statistical experiment exactly, derive a matching optimal estimator, and validate predictions on a two-lane gridworld. This settles the history-dependent-logging, model-based case posed by Zhang and Jiang (arXiv:2503.01134).

arXiv cs.AI / cs.LG / cs.CL · 16h agoAI research

Probabilistic Linear Explanations

Researchers introduce a unified probabilistic explainability framework using sparse anchored linear models that outperforms LIME and MAPLE on relevance error.

The paper proposes probabilistic explanations based on sparse, anchored linear models applicable to both binary classification and continuous regression. It proves that minimizing relevance error for neural-network models is NP-hard and relates it to a tractable fidelity-error surrogate. Solutions are computed via a mixed integer programming formulation with provably optimal empirical solutions and a polynomial-time iterative hard thresholding algorithm with approximation guarantees. Empirical evaluations show lower relevance error than LIME and MAPLE while satisfying anchoring and sparsity constraints by construction.

arXiv cs.AI / cs.LG / cs.CL · 17h agoAI research

Double descent is the principle of least action

A statistical mechanics analysis explains double descent: finite-time diffusion induces effective weight decay that regularizes models as parameters grow.

The paper models stochastic gradient-based training as a particle diffusing over the training-loss energy landscape at an induced temperature, sampling parameters via a Boltzmann distribution. Finite training time carries an effective weight decay, making every parameter a quadratic degree of freedom governed by the equipartition theorem. Adding parameters at fixed training loss lowers the temperature and the L2 norm of the stationary path, increasing effective regularization and explaining the double descent phenomenon.

arXiv cs.AI / cs.LG / cs.CL · 17h agoAI research