#01Nov 10, 2026
cs.LG
A Theory of Policy Optimization in Post-Training: Coverage Collapse and Reference Resets
Audrey Huang, Nan Jiang, Sham M. Kakade and 3 more
Policy optimization is central to language model post-training, yet principled guidance remains limited. We revisit its theoretical foundations to identify algorithms that learn near-optimal policies using total samples and gradient steps governed by the base model's response coverage, a measure of how readily it generates optimal responses. We call such algorithms coverage-preserving. This guarantee captures the goal of amplifying capabilities accessible through sampling from the base model. (1) Coverage collapse. REINFORCE, the basis for PPO and GRPO, can drive the probability of optimal responses to near zero, even as reward improves. This coverage collapse stalls optimization, and convergence can require exponentially many steps despite good initial coverage. The failure arises even with exact gradients and persists under KL regularization to the base model. (2) Reference resets. We show that repeatedly resetting the KL reference to the most recent policy mitigates coverage collapse. We formalize this intervention in Approximate Policy Mirror Descent (APMD), a meta-algorithm that approximately solves a sequence of KL-regularized RL subproblems. APMD enables stronger regularization, making each subproblem easier to solve, while reference resets allow convergence to global optimality. (3) Coverage-preserving algorithms. For softmax linear policies over pretrained features, we use APMD to establish the first global convergence guarantees showing that widely used families of post-training algorithms are coverage-preserving. These include stylized PPO and GRPO variants with explicit KL regularization and reference resets, and squared-loss algorithms that implement them implicitly, including those used to train the Kimi models. These results clarify how regularization, clipping, and objective choice affect the sampling and optimization costs of post-training.
#02Nov 10, 2026
cs.LG
When Does the Real Wiring Win? Testing connectome structure-function claims against unmeasured physiology
Yeyuan Liu
Connectome-constrained models are often used to argue that a measured wiring diagram outperforms shuffled or rewired wiring, and hence that structure shapes function. Such comparisons can confound wiring with how the models are tuned: a connectome fixes who connects to whom, not the excitability, gains or plasticity rates the model also needs, and modellers often tune these until the real-wiring model works. We separate three estimands: physiology tuned on the real wiring and transferred to nulls (P1), each wiring tuned on its own (P2), and P2 restricted to physiology consistent with independent data (P3). The biases involved are known in machine learning (under-tuned baselines, inherited weights, winner's curse); we measure what they do to biological conclusions, using synthetic ground truth, placebo nulls and three Drosophila circuit models. Some claims survive every protocol we test: segregated reward and punishment dopamine improves learning, and head-direction topography is required for a persistent bump. Others do not. In the mushroom body, the real Kenyon-cell output wiring beats a cross-subtype identity shuffle by 0.09 under P1 and P2 but loses to it by 0.09 under P3 (95% CIs exclude zero; held-out runs confirm). The verdict is set by the share of alpha'beta' cells among active Kenyon cells, which P1 selects low; at the share implied by imaging (about 44%) the real-wiring model fails to learn, exposing a model inadequacy rather than a deficit of the fly's wiring. In flyvis, P1 penalises a mirrored connectome, which has a constructed solution within 0.07 (median) of the real error, more than a spatially shuffled one in 50 of 50 members; the ranking survives ten-fold longer retraining but depends on the checkpoint at fifty-fold. A credible structural claim needs matched optimisation, data-constrained physiology and a model that still works there.
#03Nov 10, 2026
cs.AI
Comparative Analysis of Agent Evaluation Frameworks: Stability, Detection, and Discovery in Enterprise Analytics Agents
Howard Zhang, Chuck Arvin, Logan Brown and 3 more
Deploying LLM-based analytics agents in enterprise settings requires evaluation frameworks that can reliably detect failures across complex, multi-tool workflows. We present a three-phase comparative study of three evaluation frameworks, each representing a distinct evaluation paradigm (trace-based LLM judging, text-only LLM judging with red-teaming, and deterministic heuristics), applied to two analytics agents in a controlled research setting using frozen execution traces. Phase 1 quantifies evaluation harness stability through repeated measurements, finding that 97% of configurations meet the stability threshold and that stability patterns are agent-independent. Phase 2 measures known risk detection on 72 ground-truth test cases, where the trace-based framework achieves the best precision-recall balance (F1=0.90) while text-only evaluation matches on recall but generates 5x more false alarms. Phase 3 evaluates unknown risk discovery, uncovering 24 novel failures with zero overlap between functional testing and security red-teaming. Our results demonstrate that (1) the information available to the evaluation harness determines evaluation quality, (2) functional and security evaluation are complementary, and (3) LLM-based evaluation harnesses surface subtle errors that human reviewers miss. We recommend a two-framework strategy: trace-based evaluation for functional assessment and adversarial red-teaming for security validation.
#04Nov 10, 2026
stat.ML
A Theory of Cross-Validation Variance
Nathaniel S. O'Connell, Jaime L. Speiser
Cross-validation estimates predictive performance by repeatedly splitting the data into training and validation sets, fitting the model on the first and evaluating it on the second. Every observation influences the estimate in two roles, through its own evaluation when it is held out and through the models it helps fit when it trains. The random splits determine its weight in each role. From this representation, we prove an exact finite-sample identity for the variance of the cross-validated estimate. For a given splitting scheme with a common training set size, the variance is a function of these weights, with constants of the model, the metric, and the population. It covers metrics averaged over observations, such as mean squared error, and over case--control pairs, such as the AUC. The identity shows which schemes to use. The variance decomposes into sampling variance, which depends only on the training size, and variance due to the random fold splitting, which arises when the weights change from one draw of the splits to the next. K-fold cross-validation, whose weights are equal across observations by design, is therefore variance optimal at first order; Monte Carlo and bootstrap cross-validation are not. The first-order variance of K-fold does not depend on K, and under reasonable conditions on the model leave-one-out has the smallest variance of any K-fold scheme. For the AUC the same holds for leave-pair-out, which evaluates every case--control pair. Finally, we show the cross-validated estimate is asymptotically normal with the identity's full variance. Together, these results provide a general theoretical foundation for inference on cross-validated performance and establish principles for selecting variance-optimal cross-validation designs.
#05Nov 10, 2026
cs.LG
TorchCurves: Differentiable Parametric Curves
Alex Shtoff
We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curve coefficients can be optimized jointly with the surrounding model or produced by another network. The library provides trainable modules, reusable basis modules, and a functional interface, supporting applications ranging from continuous feature embeddings to Kolmogorov-Arnold networks and functional regression. Its implementation combines classical evaluation algorithms with vectorized PyTorch operations, emphasizing readability and maintainability without custom hardware kernels. Timing experiments compare curve evaluation against NumPy and SciPy and KAN training against EfficientKAN across a range of problem sizes. The results illustrate where this generality remains computationally practical and where overhead is substantial. Library is available on GitHub at https://github.com/alexshtf/torchcurves.