#01Nov 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.
#02Nov 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.
#03Nov 10, 2026
cs.CV
BoviShift: A Six-Year Multi-Attribute Audit of Visual Cattle Phenotyping Across Animals and Time
Mobasshir Bhuiya Shagor, Nilambar Halder Tonmoy, Md Saef Ullah Miah
Computer vision offers a scalable, non-contact means of estimating livestock traits, but correlated images and video frames make reliable evaluation difficult. Image-random splitting can place views of the same animal in both training and test sets, while deployment further requires transfer to animals captured in future years. We introduce BoviShift, a corpus reconstructed from six consecutive annual cohorts of an operational cattle marketplace collected from 2021 to 2026. It contains 2{,}657 cattle, 10{,}610 still images, and 2{,}566 walk-around videos across nine recorded breed categories. We evaluate three splitting strategies through four configurations: image-random and pooled cattle-disjoint splits over the same development cohorts, followed by separate future-2025 and locked future-2026 evaluations. Using a fixed ResNet-50 multi-task baseline, we assess weight, age, height, breed, and coat color. Differences between image-random and cattle-disjoint splitting are task-dependent rather than a universal leakage penalty. Future-cohort behavior is also attribute- and cohort-specific: breed declines relative to pooled evaluation; mean weight and age performance fails to beat constant baselines in 2025; height remains above baseline; and color transfers well to 2025 but degrades in 2026. Multi-task training improves all five point estimates in a single-seed ablation, still-view aggregation helps selectively, and zero-shot video-frame aggregation exposes a still-to-video domain gap. To our knowledge, BoviShift is the longest-spanning cattle-vision resource combining consecutive annual cohorts with physical and visual attributes.
#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
math.AP
Bayesian inverse problems and epidemic-threshold uncertainty for a heterogeneous SIS reaction-diffusion model
Duc-Lam Duong
We study Bayesian inference of persistence from early observations of a heterogeneous susceptible--infected--susceptible (SIS) reaction--diffusion model with standard incidence. We show that the leading prevalence dynamics depend on the unknown coefficients only through the difference between the transmission and recovery rates and the infected diffusivity. The same pair determines the principal eigenvalue whose sign governs persistence, so early prevalence can inform the threshold even when the individual rates remain uncertain. We prove global weak well-posedness and quantitative parameter stability for the SIS system and use the resulting observation-map estimates to establish Bayesian well-posedness. For an initial infection of size $\varepsilon$, we derive a uniform second-order expansion that describes how the separate rates enter prevalence. Incidence depends explicitly on transmission at leading order. When the noise standard deviation is proportional to $\varepsilon$, we prove $O(\varepsilon)$ convergence in Hellinger distance of the nonlinear posteriors to their low-prevalence limits for both prevalence alone and joint prevalence and incidence data. We bound the principal eigenvalue using the growth rate of the infected $L^2$ norm between two times. This rate gives a lower bound for the full nonlinear system, and the upper bound separates spatial transients from nonlinear saturation. Uniform spectral estimates and bounds on infection size and measurement error give sufficient conditions for persistence and extinction. We also bound the error in posterior persistence probabilities under forward and eigenvalue approximation, accounting for posterior mass near the threshold. Numerical examples illustrate threshold inference and the predicted \(O(\varepsilon)\) convergence of the nonlinear posteriors to their low-prevalence limits in Hellinger distance.