#01Nov 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.
#02Nov 10, 2026
cs.LG
AutoScaffold: AI-Guided Scaffolding for Reinforcement Learning of Language Models
Zijian Zhang, Rizhen Hu, Jiangweizhi Peng and 4 more
Reinforcement learning with verifiable rewards (RLVR) produces rich training experience, yet outcome rewards reduce each attempt to a single number and leave most of this information unused. Training-time scaffolds, such as strategies or hints added to the prompt during training, offer a natural way to turn this information into guidance, but their design and adaptation are largely left to humans and tailored to specific domains. We introduce AutoScaffold, a unified AI-for-AI framework that turns a student's training experience into adaptive scaffolds, with minimal domain-specific information and no human intervention during training. A frozen teacher periodically examines this experience, diagnoses bottlenecks, and designs scaffolds in two forms: (i) strategies shared across a class of tasks and (ii) hints for individual hard tasks, adjusting the content and amount of support as the student learns. The scaffolds are removed at evaluation. We apply the same framework to ALFWorld, search-based QA, mathematical reasoning, and GPU kernel generation. When evaluated without scaffolds, students trained with AutoScaffold outperform those trained with the corresponding RL baselines in all four domains, with gains of 7.2 points in ALFWorld success and 4.0 points in average QA exact match. On GPU kernel generation, AutoScaffold increases the fraction of tasks with a correct kernel that runs faster than the PyTorch reference by up to 5.0 points. On math, our student surpasses QuestA's reported accuracy using approximately one-third as many student training steps. Analyses show that the teacher identifies a different failure in each task class and shifts its scaffolds from step-by-step workflows to targeted fixes as the student improves, and that its revised scaffolds help the student learn more than keeping the previous scaffold or using no scaffold.
#03Nov 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.
#04Nov 10, 2026
cs.CL
Mechanistic Interpretability Needs a Logic of Inference
Zhimin Hu, Chen Jiang, Hanbo Xie and 2 more
Neural networks are increasingly studied not merely as predictive systems, but as complex systems whose internal computations are themselves objects of scientific inquiry. Recent progress in mechanistic interpretability (MI) has made it possible to identify neurons, features, circuits, population structures, and dynamical patterns associated with model behavior. As these tools improve, attention is shifting from what can be observed inside a model to how those observations support mechanistic explanations. We examine the parallel efforts of neuroscience and MI to address this question and identify recurring inferential bottlenecks when inferring mechanisms from complex neural systems. We propose five principles and organize them into a recursive logic for a more rigorous procedure of mechanistic inference. These principles provide a framework that supports scientific discovery in two senses: it helps turn local interpretability findings into cumulative knowledge of mechanisms within models, and it makes those mechanisms sufficiently precise to generate testable hypotheses about domains beyond the models. Evidence beyond MI is ultimately required to establish what model mechanisms reveal about the world.
#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.