arXiv subjects

Murdock Aubry

Publications and source records attributed to Murdock Aubry.

6 recordsLinked to original sources

arXiv2026

Instruct-FD: Can Your Full-Duplex Speech System Follow Turn-Taking Instructions?

Current full-duplex (FD) spoken dialogue systems can produce fluid interactions, yet it remains unclear whether they can adapt their turn-taking behavior when explicitly instructed. This is critical for real-world deployment, where conversational policies vary across applications (e.g., proactive tutoring vs. passive counseling). We introduce Instruct-FD, an instruction-conditioned benchmark for evaluating controllable turn management in FD systems. To enable this, we develop a human-validated, scalable synthetic pipeline that generates instruction-conditioned conversations, along with a deployment-agnostic multi-turn evaluation protocol and an LLM-based judge. Benchmarking six state-of-the-art full-duplex systems reveals a substantial gap in instruction-following turn management: the best model achieves only 64.4% adherence. Performance is highly uneven across behaviors and scenarios, with proactive behaviors such as model backchanneling and interruption remaining particularly challenging. These findings establish instruction-following turn management as a crucial direction for building adaptable and deployable full-duplex dialogue systems.

cs.CL↗

arXiv2026

Trust the Batch, On- or Off-Policy: Adaptive Policy Optimization for RL Post-Training

Reinforcement learning is structurally harder than supervised learning because the policy changes the data distribution it learns from. The resulting fragility is especially visible in large-model training, where the training and rollout systems differ in numerical precision, sampling, and other implementation details. Existing methods manage this fragility by adding hyper-parameters to the training objective, which makes the algorithm more sensitive to its configuration and requires retuning whenever the task, model scale, or distribution mismatch changes. This fragility traces to two concerns that current objectives entangle through hyper-parameters set before training begins: a trust-region concern, that updates should not move the policy too far from its current value, and an off-policy concern, that data from older or different behavior policies should influence the update only to the extent that it remains reliable. Neither concern is a constant to set in advance, and their severity is reflected in the policy-ratio distribution of the current batch. We present a simple yet effective batch-adaptive objective that replaces fixed clipping with the normalized effective sample size of the policy ratios. The same statistic caps the score-function weight and sets the strength of an off-policy regularizer, so the update stays close to the usual on-policy score-function update when ratios are nearly uniform, and tightens automatically when stale or mismatched data cause ratio concentration, while retaining a nonzero learning signal on high-ratio tokens. Experiments across a wide range of settings show that our method matches or exceeds tuned baselines, introducing no new objective hyper-parameters and removing several existing ones. The code is available at https://github.com/FeynRL-project/FeynRL.

cs.LG↗

arXiv2025

An adaptive delaminating Levin method in two dimensions

We present an adaptive delaminating Levin method for evaluating bivariate oscillatory integrals over rectangular domains. Whereas previous analyses of Levin methods impose non-resonance conditions that exclude stationary and resonance points, we rigorously establish the existence of a slowly-varying, approximate solution to the Levin PDE across all frequency regimes, even when the non-resonance condition is violated. This allows us to derive error estimates for the numerical solution of the Levin PDE via the Chebyshev spectral collocation method, and for the evaluation of the corresponding oscillatory integrals, showing that high accuracy can be achieved regardless of whether or not stationary and resonance points are present. We then present a Levin method incorporating adaptive subdivision in both two and one dimensions, as well as delaminating Chebyshev spectral collocation, which is effective in both the presence and absence of stationary and resonance points. We demonstrate the effectiveness of our algorithm with a number of numerical experiments.

math.NA↗

arXiv2025

Transformer Block Coupling and its Correlation with Generalization in LLMs

Large Language Models (LLMs) have made significant strides in natural language processing, and a precise understanding of the internal mechanisms driving their success is essential. In this work, we analyze the trajectories of token embeddings as they pass through transformer blocks, linearizing the system along these trajectories through their Jacobian matrices. By examining the relationships between these block Jacobians, we uncover the phenomenon of \textbf{transformer block coupling} in a multitude of LLMs, characterized by the coupling of their top singular vectors across tokens and depth. Our findings reveal that coupling \textit{positively correlates} with model performance, and that this relationship is stronger than with other hyperparameters such as parameter count, model depth, and embedding dimension. We further investigate how these properties emerge during training, observing a progressive development of coupling, increased linearity, and layer-wise exponential growth in token trajectories. Additionally, experiments with Vision Transformers (ViTs) corroborate the emergence of coupling and its relationship with generalization, reinforcing our findings in LLMs. Collectively, these insights offer a novel perspective on token interactions in transformers, opening new directions for studying their mechanisms as well as improving training and generalization.

cs.LG↗

arXiv2023

A solver for linear scalar ordinary differential equations whose running time is bounded independent of frequency

When the eigenvalues of the coefficient matrix for a linear scalar ordinary differential equation are of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing such solutions using standard techniques grows with the magnitudes of the eigenvalues. As a consequence, the running times of most solvers for ordinary differential equations also grow with these eigenvalues. However, a large class of scalar ordinary differential equations with slowly-varying coefficients admit slowly-varying phase functions that can be represented at a cost which is bounded independent of the magnitudes of the eigenvalues of the corresponding coefficient matrix. Here, we introduce a numerical algorithm for constructing slowly-varying phase functions which represent the solutions of a linear scalar ordinary differential equation. Our method's running time depends on the complexity of the equation's coefficients, but is bounded independent of the magnitudes of the equation's eigenvalues. Once the phase functions have been constructed, essentially any reasonable initial or boundary value problem for the scalar equation can be easily solved. We present the results of numerical experiments showing that, despite its greater generality, our algorithm is competitive with state-of-the-art methods for solving highly-oscillatory second order differential equations. We also compare our method with Magnus-type exponential integrators and find that our approach is orders of magnitude faster in the high-frequency regime.

math.NA↗

arXiv2023

The Levin approach to the numerical calculation of phase functions

The solutions of scalar ordinary differential equations become more complex as their coefficients increase in magnitude. As a consequence, when a standard solver is applied to such an equation, its running time grows with the magnitudes of the equation's coefficients. It is well known, however, that scalar ordinary differential equations with slowly-varying coefficients admit slowly-varying phase functions whose cost to represent via standard techniques is largely independent of the magnitude of the equation's coefficients. This observation is the basis of most methods for the asymptotic approximation of the solutions of ordinary differential equations, including the WKB method. Here, we introduce two numerical algorithms for constructing phase functions for scalar ordinary differential equations inspired by the classical Levin method for the calculation of oscillatory integrals. In the case of a large class of scalar ordinary differential equations with slowly-varying coefficients, their running times are independent of the magnitude of the equation's coefficients. The results of extensive numerical experiments demonstrating the properties of our algorithms are presented.

math.NA↗