Before deployment, an AI system might be evaluated on thousands or even millions of inputs, but after deployment it may encounter billions, so its worst failures may not appear during evaluation. Jones et al. (2025) proposed forecasting how risky the riskiest deployment inputs will be by scoring how close the system comes to failure on each evaluation input and extrapolating from the highest scores. We show that the error of this forecast splits into a noise term, whose distribution is the same for every model up to scale, and terms that depend on the shape of the tail of the model's risk scores. These model-dependent terms can make the forecast under-predict badly, both in theory, whenever the evaluation set lacks a rare kind of input that deployment contains, and in practice: on real user prompts marked as toxic, the forecast under-predicted the probability that a response begins with an offensive word for all eleven language models we tested. Because the shape of this tail is a property of the model, we propose fine-tuning the model itself to make the forecast accurate, using the forecast error as the training loss. In a model organism of jailbreaking and in an RL gridworld with rare traps, our method reduced the held-out squared forecast error by factors of 14 to 60, lowered worst-case risk about as much as direct risk minimization (or more), and preserved the model's primary behavior. For settings in which the model should change as little as possible, we show that training with an alternative safety constraint and an added loss term improved the forecast with far smaller changes to the model. Our method also improved the forecast in RL from sampled returns, in language models of up to 8B parameters, and (with minimal-change training) on the toxic user prompts.
A fundamental limitation of Text-to-Code is that no guarantee can be obtained about the correctness of the generated code. Therefore, to ensure its correctness, the generated code still has to be reviewed, tested, and maintained by developers. However, parsing through LLM-generated code can be tedious and time-consuming, potentially negating the productivity gains promised by AI-coding tools. To address this challenge, we present Viverra, a system that automatically produces formally verified annotations alongside generated code to aid user's understanding of the generated program. Given a natural-language task description, Viverra prompts an LLM to synthesize a C program together with candidate assertions expressing safety and correctness properties. It then verifies those assertions in a compositional and best-effort manner via a portfolio of bounded model checkers. Evaluation on 17 diverse programming tasks suggests that Viverra can efficiently generate code with verified assertions, and that these assertions improve users' performance on code-comprehension tasks in a user study with more than 400 task completions.
Nearest-neighbor methods are fundamental to classical and modern machine learning, yet their geometric properties are typically analyzed under independent sampling. In this paper, we study the nearest-neighbor radii under dependent sampling. We consider strong mixing dependent observations and ask whether dependence changes the scale of nearest-neighbor neighborhoods. We establish distribution-free almost sure convergence under polynomial mixing and sharp non-asymptotic moment bounds under geometric mixing. The moment bounds depend on the local intrinsic dimension rather than the ambient dimension, making the results applicable to high-dimensional data supported on lower-dimensional manifolds. Synthetic experiments and real-world time-series benchmarks illustrate the theory, showing that nearest-neighbor geometry remains informative under dependent sampling.
Language agents are increasingly deployed in professional workflows, yet tutoring remains a high-stakes capability that existing evaluations only partially capture. Effective tutor agents require more than producing correct answers or executing accurate tool calls: they must infer a warranted teaching decision from evidence, adapt support as learner state changes, and carry an instructor's request through a learning-management system (LMS) to a completed, verified intervention. We introduce TeachArena, a source-grounded benchmark that jointly evaluates three complementary surfaces of teaching work: professional pedagogical judgment, situated multi-turn tutoring, and end-to-end LMS teaching workflows. Its 354 tasks are each built around a pedagogical insight, grounded in evidence, and evaluated with matched verifiers over observable turn-level responses, tutoring trajectories, and persistent artifacts or environment states. Across a comprehensive evaluation of frontier models, our findings reveal that current models are generally capable of bounded pedagogical judgment, but still fall short of professional teaching standards in situated tutoring and end-to-end teaching-workflow execution. By unifying teacher judgment, adaptive tutoring, and institutional action in one benchmark, TeachArena provides a measurement foundation for developing tutor agents that can support realistic teaching work.
Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.
Chain-of-thought (CoT) reasoning with self-consistency improves performance by aggregating multiple sampled reasoning paths. In this setting, correctness is no longer tied to a single reasoning trace but to the aggregation rule over a pool of candidate paths, making aggregation uncertainty the central challenge. This issue is critical where confidently incorrect answers are far more costly than abstentions. We introduce a conformal procedure for CoT reasoning that directly addresses aggregation uncertainty. Our approach replaces majority voting with weighted score aggregation over reasoning paths and calibrates an abstention rule using conformal risk control. This approach leads to finite-sample guarantees on the confident-error rate--the probability that the system answers and is wrong. We further identify score separability as the key condition under which abstention provably improves selective accuracy, and derive closed-form expressions that predict accuracy gains from calibration data alone. The method is fully inference-time, and requires no retraining. Across four benchmarks, four open-source models, and three score classes, realized confident-error rates are consistent with the prescribed targets up to calibration-split and test-set variability. Our method achieves $90.1\%$ selective accuracy on GSM8K by abstaining on fewer than $5\%$ of problems, compared with $82.3\%$ accuracy under majority voting and $87.4\%$ under score-weighted voting without abstention, while conformal risk control keeps the expected rate of confidently wrong answers below $10\%$.
Code agents must both reason over long-horizon repository state and obey strict tool-use protocols. In paired Instruct/Thinking checkpoints, these capabilities are complementary but misaligned. The Instruct model is concise and tool-disciplined, whereas the Thinking model offers stronger planning and recovery behavior but often over-deliberates and degrades agent performance. We present CRANE (Constrained Reasoning Injection for Code Agents via Nullspace Editing), a training-free parameter-editing method that treats the Thinking-Instruct delta as a directional pool of candidate reasoning edits for the Instruct backbone. CRANE combines magnitude thresholding to denoise the delta, a Conservative Taylor Gate to retain edits that are jointly beneficial for reasoning transfer and tool-use preservation, and Graduated Sigmoidal Projection to suppress format-critical update directions. By merging paired Instruct and Thinking checkpoints, CRANE delivers strong gains over either individual model while preserving Instruct-level efficiency: on Roo-Eval it achieves pass1 of 66.2% (+19.5%) for Qwen3-30B-A3B and 81.5% (+8.7%) for Qwen3-Next-80B-A3B; on SWE-bench-Verified it resolves up to 14 additional instances at both scales (122/500 and 180/500); and on Terminal-Bench v2 it improves pass1/pass5 by up to 2.3%/7.8%, reaching 7.6%/17.9% and 14.8%/30.3%, respectively, consistently outperforming alternative merging strategies across all three benchmarks.
We introduce CurveBench, a benchmark for visual topological reasoning. Given an image of disjoint closed curves, a model must recover the tree of adjacent regions rooted at the exterior. The benchmark contains 756 hand-drawn images, ranging from simple configurations to maze-like and densely packed arrangements. Each image has a manually verified reference tree. We evaluate predictions by exact tree matching with the exterior root fixed. Gemini 3.1 Pro, the strongest model in our evaluation, achieves 71.1% exact-match accuracy on CurveBench-Easy and 28.7% on CurveBench-Hard. A Qwen3-VL-8B checkpoint trained using reinforcement learning with verifiable rewards reaches 31.7% on Easy, compared with 21.7% for its Thinking base model at a 16,384-token generation budget. The same comparison yields a gain of 1.1 percentage points on Hard.
Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federated learning and KV cache compression. While dense random rotations yield clean theoretical guarantees, they require $\Theta(d^2)$ time. The randomized Hadamard transform $HD$ reduces this cost to $O(d \log d)$, but its discrete structure complicates analysis and leads to weaker or purely empirical compression guarantees. In this work, we introduce DASHQuant (Dithered Accelerated Single-Hadamard Quantization), a provable variant of this approach. Specifically, the quantizer applies $HD$ to the input vector and adds a random dithering before quantizing, injecting additional randomness at negligible cost. We prove that this approach is unbiased and provides mean squared error bounds that asymptotically match those achievable with truly random rotation matrices. In particular, we prove that a dithered version of TurboQuant, and a special case of EDEN, achieves mean squared error $\bigl(\pi\sqrt{3}/2 + o(1)\bigr) \cdot 4^{-b}$ at $b$ bits per coordinate, where the $o(1)$ term vanishes uniformly over all unit vectors and all dimensions as the number of quantization levels grows.
Weakly supervised semantic segmentation (WSSS) trains dense pixel-level segmentation models from partial or coarse annotations such as bounding boxes, scribbles, or image-level tags. While recent work leverages foundation models such as the Segment Anything Model (SAM) to generate pseudo-labels, these approaches typically depend on heuristic prompt choices and offer limited ways to incorporate prior knowledge or heterogeneous labels. We address this gap by taking a neurosymbolic perspective: integrating differentiable fuzzy logic with deep segmentation models. Weak annotations and domain-specific priors are unified as continuous logical constraints that fine-tune SAM under weak supervision. The refined foundation model then produces improved pseudo-labels, from which we train a second-stage prompt-free segmentation model. Experiments on Pascal VOC 2012 and the REFUGE2 optic disc/cup segmentation dataset show that our logic-guided fine-tuning yields higher-quality pseudo-labels, leading to state-of-the-art segmentation accuracy that often exceeds densely supervised baselines.
Autonomous agents such as Claude Code and Codex now operate for hours or even days. Understanding their runtime behavior has become critical for downstream tasks such as diagnosing inefficiencies, fixing bugs, and ensuring better oversight. A primary way to gain this understanding is analyzing the reasoning trajectories and execution traces these agents generate. Yet such data remains in unstructured natural-language form, making it difficult for humans to interpret at scale. We introduce Act*ONOMY, a taxonomy for describing and analyzing agent behavior at runtime. Act*ONOMY has two components: (1) the taxonomy itself, developed through Grounded Theory and structured as a three-level hierarchy of 10 actions, 46 subactions, and 120 leaf categories; and (2) an open repository that hosts the living taxonomy, provides an automated analysis pipeline that applies it to agent trajectory analysis, and defines an extension protocol for customization and growth. Our experiments show that Act*ONOMY can be used to compare behavioral profiles across agents and characterize a single agent's behavior across diverse trajectories, surfacing patterns indicative of failure modes. By providing a shared vocabulary, Act*ONOMY aims to help agent researchers, designers, and deployment engineers interpret agent behavior more effectively and consistently, supporting further study of oversight and control.
Measuring the creativity of large language models (LLMs) is essential for designing methods that can improve creativity and for enhancing our scientific understanding of this ability. To accomplish this, it has become common in recent years to administer semantic distance tests of human creativity to LLMs. Although these tests provide a convenient and fully automated way to score aspects of "creativity," their validity as measures of machine creativity has not been established. To address this problem, we conduct the first large-scale, systematic study assessing the effectiveness of semantic distance tests for predicting the creative achievement of LLMs across four target constructs: (a) creative writing, (b) output diversity on open-ended prompts, (c) combinatorial creativity, and (d) scientific ideation. We score each test on two criteria (validity and specificity), and derive a theoretical limit for the maximum attainable specificity and validity a test can achieve. We find that: (1) No test is a significant predictor of output diversity, suggesting that point creativity, the ability to produce a single response connecting semantically distant concepts, and distributional creativity, the ability to produce distinct responses across repeated samples, may dissociate in current LLMs--a pattern we call jagged creativity. (2) The Remote Associates Test is effectively a proxy for general capabilities rather than a specific predictor of creativity in LLMs. (3) Lastly, the Divergent Association Task is the best predictor of creative writing, but no single test predicts all constructs well. In summary, our results prescribe caution when applying psychometric tests and tasks of creativity validated among human populations to LLMs.
Deploying language models as autonomous agents requires more than per-task accuracy: when an agent faces a queue of problems under a finite token budget, it must decide which to attempt, in what order, and how much compute to commit to each, all before any execution feedback is available. This is the prospective form of metacognitive control studied for decades in human cognition, yet whether language models possess it remains largely untested. We introduce TRIAGE, an evaluation framework in which a model receives a task pool and a token budget calibrated to its own baseline cost, and commits to a single ordered plan that jointly encodes selection, sequencing, and per-problem allocation. Plans are scored against an oracle built from the measured solvability and token costs of the model, using triage efficiency normalized between random and oracle performance, together with normalized regret relative to the oracle. We evaluate frontier and open-source models, with and without reasoning enabled, across competition mathematics, graduate-level science, code generation, and expert multidisciplinary knowledge, and find that current language models exhibit substantial gaps in prospective metacognitive control, revealing a previously unmeasured capability dimension with direct implications for resource-efficient agent deployment.
Graph Neural Networks (GNNs) perform computations on graphs by routing the signal between graph regions using a graph shift operator or a message passing scheme. Often, the propagation of the signal leads to a loss of information, where the signal tends to diffuse across the graph instead of being deliberately routed between regions of interest. Two notions that depict this phenomenon are oversmoothing and oversquashing. In this paper, we propose an alternative approach for modeling signal propagation, inspired by quantum mechanics, using the notion of observables. Specifically, we model the place in the graph where the signal lies, how much the signal is concentrated there, and how much of the signal is propagated towards a location of interest when applying a GNN. Using these new concepts, we prove that standard spectral GNNs have poor signal propagation capabilities. We then propose a new type of spectral GNN, termed Schr\"odinger GNN, which we show has a superior capacity to route the signal across the graph.
On-policy distillation (OPD) has become a promising paradigm for reasoning-oriented post-training of large language models (LLMs), especially when combined with reinforcement learning from verifiable rewards (RLVR). Existing OPD methods rely on reverse KL (RKL)-based teacher supervision over trajectories sampled from the student policy. However, we identify a critical limitation: under large teacher--student policy divergence, RL-driven exploration often produces trajectories outside the teacher distribution, resulting in uninformative negative feedback. To address this, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy reasoning distillation method that remains effective under large policy divergence settings. Rather than relying solely on evaluative supervision, TGPO uses teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations. Experiments on reasoning benchmarks show that TGPO consistently outperforms existing RKL-based OPD methods and remains robust across different teacher models.
Camera-conditioned video generation requires positional encoding that remains reliable under changes in camera motion, lens configuration, and scene structure. However, existing attention-level camera encodings either provide ray-only camera signals or rely on pinhole camera geometry, limiting their applicability to general camera control under the Unified Camera Model, including wide-angle and fisheye lenses. To address this limitation, we propose Curved Ray Expectation Positional Encoding (CRePE). CRePE represents each image token as a depth-aware positional distribution along its source ray, providing a Unified Camera Model-compatible positional encoding that naturally captures the curved-ray geometry of wide-angle and fisheye cameras. CRePE is implemented through a Geometric Attention Adapter added to frozen video DiTs, injecting token-wise scene-distance information into selected attention layers and stabilizing it with pseudo supervision from a monocular geometry foundation model. This design leads to more stable camera control with competitive video quality in camera-conditioned video generation under the Unified Camera Model, and the resulting model transfers zero-shot to real fisheye and diverse pinhole videos. Controlled positional-encoding ablations show improvements over a RayRoPE-style endpoint approximation, demonstrating the effectiveness of curved-ray-aware positional encoding, particularly for non-pinhole cameras. Furthermore, by extending the same positional-encoding pathway to external geometry control through Radial MixForcing, CRePE supports external radial-map control for scene-geometry-conditioned generation and source-video motion transfer beyond camera control. Project page: https://crepe-neurips2026.github.io/; code: https://github.com/jinotter3/CRePE.
This paper introduces language-based agent control (LBAC), a new programming model for agentic applications that brings techniques from programming languages and language-based security to the problem of agent control. In conventional programming, combinations of static typing and runtime enforcement have long been used to guarantee that well-typed programs satisfy user-specified policies, including policies for access control, information flow, data provenance, and more. The key idea behind LBAC is to extend these guarantees to agentic applications by requiring agents to generate programs that are themselves well-typed in the context of the surrounding scaffolding code. Unsafe programs are rejected by the typechecker before execution, allowing policies to apply uniformly across the entire application, including both agent-generated behavior and developer-written scaffolding. At the same time, LBAC preserves substantial expressiveness: agents may perform arbitrary side-effect-free computation and recursively invoke subagents, which retain full tool access subject to the same--or potentially more restrictive--policies. We demonstrate LBAC with three case studies: I/O sandboxing via filesystem capabilities, data provenance, and information-flow control.
Reconstructing nonlinear dynamical systems (DS) from data (DSR) is a fundamental challenge in science and engineering, but it inherently relies on sequential models. Recent breakthroughs for sequential models have produced algorithms that parallelize computation along sequence length $T$, achieving logarithmic time complexity, $\mathcal{O}(\log T)$. Since sequence lengths have been practically limited due to the linear runtime complexity $\mathcal{O}(T)$ of classical backpropagation through time, this opens new avenues for DSR. This paper studies two prominent classes of parallel-in-time algorithms for this task, both of which leverage parallel associative scans as their core computational primitive. The first class comprises models with linear yet non-autonomous dynamics and a nonlinear readout, such as modern State Space Models (SSMs), while the second consists of general nonlinear models which can be parallelized using the DEER framework. We find that the linear training-time recurrence of the first class of models imposes limitations that often hinder learning of accurate nonlinear dynamics. To address this, we augment DEER with Generalized Teacher Forcing (GTF), a novel variant within the more general nonlinear framework that ensures stable and effective learning of nonlinear dynamics across arbitrary sequence lengths. Using GTF-DEER, we investigate the benefits of training on extremely long sequences ($T$ approaching $10^5$) for DSR. Our results show that access to such long trajectories significantly improves DSR if the data features long time scales. This work establishes GTF-DEER as a robust tool for data-driven discovery and underscores the largely untapped potential of long-sequence learning in modeling complex DS.
Electrocardiography (ECG) is the clinical standard for cardiac assessment but requires dedicated hardware that does not scale to daily-life monitoring. Photoplethysmography (PPG) is ubiquitous in wearables but lacks ECG-specific diagnostic morphology and is corrupted by motion and sensor noise. PPG-to-ECG generation aims to bridge this gap by recovering electrical morphology and timing from peripheral pulse signals. However, existing methods largely rely on statistical alignment and data-driven generation. They fail to explicitly structure the latent space around physiology-aware electro-hemodynamic factors and lack constraints from forward physiological dynamics. To address these challenges, we propose PPG2ECG, a physiology-guided latent rectified flow framework. PPG2ECG introduces an electro-hemodynamic simulator that co-models ECG and PPG through shared cardiac phase dynamics. Guided by this simulator, a Physiology-Aware AutoEncoder learns a structured electro-hemodynamic latent space. Then we integrate this simulator guidance into a PPG-conditioned latent rectified flow, enforcing ECG-side morphology consistency and ECG-to-PPG forward hemodynamic consistency during generative transport. Experiments on the large-scale MC-MED dataset demonstrate that PPG2ECG significantly improves PPG-to-ECG generation and downstream cardiovascular disease classification, proving its ability to generate ECGs that are both signal-faithful and physiologically plausible under the ECG-to-PPG hemodynamic pathway
We introduce Pion, a spectrum-preserving optimizer for large language model (LLM) training based on orthogonal equivalence transformation. Unlike additive optimizers such as Adam and Muon, Pion updates each weight matrix through left and right orthogonal transformations, preserving its singular values throughout training. This yields an optimization mechanism that modulates the geometry of weight matrices while keeping their spectral norm fixed. We derive the Pion update rule, systematically examine its design choices, and analyze its convergence behavior along with several key properties. Empirical results show that Pion offers a stable and competitive alternative to standard optimizers for both LLM pretraining and finetuning.