#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
stat.ME
One Curve, Different Weights: AUC, the Brier Score, Decision-Weighted AUC, and the Policy Youden Index
Yegor Baranovski
AUC and the Brier score are standard summaries of a binary risk score, yet they can rank models differently. We introduce a weighted AUC, AUC$_π$, which weights each pair of observations by how differently a decision maker with probability of acting $π$ treats them. We show that all three are built on weighted averages of one curve, the Youden index $J(t) = \mathrm{TPR}(t) - \mathrm{FPR}(t)$ across cutoffs $t$, and that the averages differ in the weights they put on the cutoffs. Each weights a cutoff by how much something rises across it: for AUC, the distribution of all scores; for the Brier score, the true probability $\mathbb{E}[Y \mid S]$; for AUC$_π$, the decision maker's probability of acting. Up to normalization, AUC$_π$ is the Brier skill score of the ideal forecast with its weight moved to the cutoffs the decision maker cares about. We also show that weighting pairs by $|π(s) - π(s')|$ is, up to scale, the only pair weight fixed in advance that makes a pair-weighted AUC an average of the Youden curve for every score distribution. As a ranking measure, AUC weights every model the same way. Hand (2009) shows that it can also be read as an average over cost thresholds, and in that reading each model weights the thresholds differently. The numerator of AUC$_π$, which we call the policy Youden index, is the expected share of class 1 a fixed policy acts on minus the expected share of class 0. It judges every model by the same policy and so avoids this; the full ratio AUC$_π$ does not.
#03Nov 10, 2026
cs.LG
Uncertainty-Aware Hybrid Offline Reinforcement Learning with Online Action Selection Enabled by Sparse Gaussian-Process Critics
Marco Chan, Christos Evripidou, Liqiu Dong and 2 more
Start-ups and grade changes remain largely operator-driven, while developing and maintaining dynamic models for model-based control requires substantial engineering effort. Hybrid Offline Learning and Online Optimisation (HOFLON) uses one-step offline reinforcement learning to select actions from historical transition data. In its original implementation, the online objective combines the predicted return from a tree-ensemble critic with an adversarial-autoencoder (AAE) penalty for unfamiliar state-action pairs. We examine the effect of this penalty and replace the critic and AAE with a sparse variational Gaussian-process (sGP) critic. Actions maximise $μ- κσ$, an uncertainty-adjusted estimate of the return from one action followed by the historical operating practice. On the HOFLON polymerisation-reactor benchmark, removing the AAE from HOFLON led to 4 failed start-ups in 15 runs over five critics. At its published weight, the variation in the AAE penalty is four orders of magnitude smaller than the variation in the tree-ensemble critic. Nevertheless, it changes actions when the predicted returns of competing candidates are nearly equal, and paired runs with and without the penalty diverged from the first move. With a Matérn-5/2 sGP critic, $κ= 0$ led to failure in 13 of 15 runs, whereas with $κ= 3$ none of 15 runs (five critics, three noise realisations) failed. The median and lowest returns were 13,464 and 13,398 (HOFLON: 13,393 and 12,411). A squared-exponential sGP critic with learned inducing inputs needed $κ\geq 3$ to remain within the empirical data support in steady state, and then settled with a temperature offset of 2.0 K.
#04Nov 10, 2026
cs.AI
ReTrace: Distilling Tool-Using Agents into Planner-Free Workflows
Kaiyuan Hou, Yang Ping Kuo, Indranil Bhattacharya and 6 more
Business process automation runs the same Standard Operating Procedure (SOP) again and again on new inputs. Large Language Model (LLM) agents can follow an SOP written in natural language, but they call an LLM to choose every step of every run, which adds latency and cost at scale. We present ReTrace, which turns an SOP and a few logged agent runs into a reusable workflow in which code, not an LLM, selects the next step. The agent's reasoning, the explanation it writes with each tool call, often states why it took an action; the tool calls alone do not. ReTrace extracts the condition behind each step, merges these conditions across runs into a compact rule document, and generates an executable workflow from it. Only this last stage depends on the platform, so rule documents can be compiled for different orchestration platforms. On $79$ procedures from our production platform, ReTrace workflows reach $93.8\%$ completion, against $96.8\%$ for the agent, at $24\%$ lower cost per task. On $τ^2$-Bench, they reach $75.8\%$ task success (agent: $80.6\%$) and run in $1.3$s instead of $170$s; three rounds of repair on training failures lift $k{=}2$ workflows from $66.7\%$ to $81.2\%$. On eight SOP-Bench procedures, ReTrace without repair trails few-shot generation ($80.6\%$ vs. $83.6\%$), but repair from labeled training failures lifts it to $87.8\%$ at $0.40$s per task, compared to $85.5\%$ in $46.6$s for the agent.
#05Nov 10, 2026
cs.LG
REAL Loss: Optimizing Real Expected Acceptance Length for Speculative Decoding
Yu Tian
Speculative decoding accelerates LLM inference by having a draft model propose multiple tokens for the target model to verify in one pass. The speedup is governed by the expected acceptance length (EAL), yet standard training objectives such as cross-entropy, KL divergence, and total variation focus only on distribution matching or single-step overlap. Recent studies instead propose block-level training objectives, aiming to optimize EAL directly. However, these objectives remain surrogates rather than exact formulations of EAL. For example, some average later acceptance over target-distributed continuations rather than the verification branches selected by accepted tokens, introducing a covariance gap that can reverse the gradient direction. We analyze this gap and derive REAL, a real EAL training loss that uses path weights for unbiased estimation and Rao-Blackwellization for variance reduction. In a controlled loss-level comparison with a Qwen3.6-35B-A3B target and a Domino drafter, REAL outperforms WTV, VSD, DBLast, and the static LK baseline on probabilistic serving acceptance length across 9 task subsets and 5 evaluation seeds. These gains require only a change to the training loss, with no modification to the drafter architecture or inference procedure, demonstrating the practicality of real EAL training. A reference implementation of the REAL loss is available at https://github.com/King-ty/speculators/tree/real-loss.