#01Oct 22, 2026
math.SG
SympFormer: Inertial Attention Blocks from Damped Hamiltonian Dynamics on Spaces of Probability Measures
Viktor Stein, Levin Maier, Wuchen Li and 1 more
The attention mechanism underpins modern large language models, yet their dynamics remain only partially understood. Recent perspectives interpret attention blocks as interacting particle systems, whose mean-field limits correspond to gradient flows of energy functionals on spaces of probability densities on $\mathbb R^d$ equipped with Wasserstein-type metrics. We extend this viewpoint by deriving accelerated attention blocks from inertial, Nesterov-type damped Hamiltonian dynamics on these density spaces, developing the geometry and differential calculus needed to make the construction rigorous. In particular, we introduce a local-mobility geometry for the Otto-Wasserstein and softmax-Wasserstein settings, and a quotient Stein geometry that resolves the degeneracy of the linear-attention kernel to yield a well-defined metric and differential calculus. We provide rigorous foundations when softmax attention admits a gradient-flow formulation and when its inertial counterpart admits a damped Hamiltonian on explicitly characterized domains. For linear attention, we obtain a finite-dimensional solution theory with sharp conditions for global existence versus finite-time second-moment blow-up. We further prove a quantitative link between continuous moment blow-up and the discrete-layer depth at which token norms cross a prescribed threshold. Finally, motivated by the finite-token geometry, we propose geometric corrections to token and momentum updates. In decoder-only, nanoGPT-style experiments on TinyStories and OpenWebText, these corrections lower validation negative log-likelihood on next-token prediction relative to momentum-only controls.
#02Oct 22, 2026
cs.CV
BrickWright: Agentic Creation of Physically Feasible Brick Builds
Ava Pun, Kevin Dai, Sally Chen and 7 more
Frontier coding agents are becoming increasingly adept at 3D modeling. Yet, they still face challenges when building objects meant to be assembled in the physical world, often creating invalid assemblies with floating, colliding, or disconnected parts. We argue that providing agents with tools for assembling builds and verifying their physical feasibility is sufficient for them to produce physically valid assemblies that still adhere to input prompts. Focusing on the domain of LEGO brick builds, we present BrickWright, a framework for generating physically feasible brick builds from text or image prompts using pre-trained agents, where a build is physically feasible if it uses only real parts, has no colliding or floating parts, and forms a connected structure if possible. BrickWright guides agents to create builds by writing code with BrickLayer, a Python toolkit with two main components: an ergonomic brick assembly API that halves inference cost compared to working in raw LDraw, and a validator that provides feedback on physical feasibility. Whereas baseline agents achieve physical validity rates ranging from only 9% (GPT-6 Luna) to 69% (GPT-6 Astra), BrickWright-guided agents achieve 100% validity on a sample of 512 prompts, while improving prompt adherence for lightweight agents and maintaining it for stronger agents. Additionally, they outperform specialized models on the text-to-brick task. Code is available on our project page: https://avalovelace1.github.io/brickwright/
#03Oct 22, 2026
cs.LG
Causal Chain of Thought: Mitigating Attention Leakage via Context Isolation
Gabriele Dominici, Teague McMillan, Fazl Barez and 2 more
Chain-of-thought (CoT) prompting elicits step-by-step rationales that appear to explain model predictions, but there is no guarantee these steps causally drive the final answer. In standard autoregressive generation, dense attention allows each reasoning step to attend to the full context, enabling the model to derive answers through direct lookup while generating plausible-sounding but post-hoc justifications. We introduce CausalCoT, an inference framework that enforces causal transparency by decomposing problems into a directed acyclic graph of atomic sub-questions, evaluating each node in an isolated context containing only its direct causal parents. This Markovian structure removes attention pathways to non-parent content, making downstream predictions sensitive to local reasoning rather than global context leakage. Across a diverse suite of reasoning benchmarks, CausalCoT preserves competitive predictive performance while improving explanation faithfulness, increasing causal sensitivity of intermediate reasoning steps by an average of 12 and up to 21 percentage points over the strongest baseline. The structured dependency graph additionally enables test-time interventions in which local corrections propagate predictably through downstream reasoning.
#04Oct 22, 2026
cs.CL
Bilingual Language Models Capture Cross-Linguistic Influence in Second-Language Reading
Abderrahmane Issam, Irene E. Winther, Stefan L. Frank
While monolingual language model (LM) surprisal is widely established as a predictor of reading times, it cannot capture the non-native (L2) reading dynamics that are shaped by the reader's first language (L1). In this work, we investigate whether the cross-lingual transfer within bilingual models aligns with human L1-driven biases during L2 reading. We evaluate bilingual models on eye-tracking data of readers from 12 diverse L1 backgrounds reading English texts. To isolate L1-specific transfer, we compare bilingual models trained on an L1 that matches the readers' L1 background to both a monolingual English baseline and bilingual models trained on other L1s. We demonstrate that matching the readers' L1 improves the prediction of L2 reading times. This predictive advantage is concentrated in late-stage eye-tracking measures, modulated by L1-L2 script overlap, and peaks among intermediate-proficiency readers. These findings provide evidence that bilingual LMs capture aspects of cross-linguistic influence, and that such influence is present in L2 reading behavior.
#05Oct 22, 2026
stat.ML
Reliable AI-Assisted Decisions via Selective Auditing
Isaac Gibbs, Elise L. Han, Ryan J. Tibshirani and 1 more
We consider online monitoring of an AI system that produces a sequence of decisions. At each round, the system outputs a proposed decision together with a confidence score estimating the trustworthiness of the decision. The decision and confidence score need not be produced by the same model: for example, one agent may propose a decision, while a separate verifier agent evaluates it and outputs a correctness or safety score. Based on this information, we must decide whether to accept the AI decision automatically or consult an expert, such as a human auditor, who reviews the proposal and either accepts or corrects it. We formulate this task as an online constrained optimization problem in which the goal is to minimize the frequency of expert auditing while guaranteeing that the fraction of AI errors that go unaudited stays below a user-defined threshold. We derive a family of algorithms with provable error-control guarantees with no assumptions, including a method that is optimally efficient: it asymptotically attains the best achievable auditing rate for both adversarial and i.i.d. data streams. Experiments on screening harmful requests to large language models, qualitative text annotation, and data labeling show that our methods achieve valid error control in practice while substantially reducing the need for human auditing compared to baselines.