arXiv subjects

Yuxin Tao

Publications and source records attributed to Yuxin Tao.

4 recordsLinked to original sources

arXiv2026

Scheduling Recursive Reasoning in Looped Transformers

Recurrent reasoning models have attracted growing attention for scaling test-time computation, typically by iteratively refining latent states with shared parameters. However, these models apply each learned update with a fixed unit scale, which can be conservative when updates make persistent progress and overly aggressive when they fluctuate, limiting the benefit of additional loops. To understand how the scale should vary along the trajectory, we first analyze the sensitivity of terminal loss to recurrent update scale. We show that its temporal average admits an exact decomposition into persistent-progress and centered-fluctuation contributions. Based on this, we introduce the Trajectory Adaptive Progress-Fluctuation Scheduler (TAPS), which tracks their balance across recurrent updates and adapts the step size online. Theoretically, we establish sufficient conditions under which TAPS reduces expected terminal loss and reaches a target quality in fewer recurrent loops. Empirically, we show that TAPS improves terminal accuracy across structured reasoning tasks without retraining. By further incorporating the progress-fluctuation principle into training, TAPS yields additional accuracy gains with up to 1.56 times wall-clock speedup at matched baseline accuracy. The broad applicability of TAPS is supported by its effectiveness across diverse recurrent architectures and inference strategies. Together, these results establish update scale as complementary control axis of recurrent inference alongside architecture and depth.

cs.LG↗

arXiv2026

Asymmetric GARCH modelling without moment conditions

Heavy tails and stability are two persistent challenges in modelling financial time series, yet most existing approaches rely on finite-moment assumptions and pay insufficient attention to stability issues. To bridge this gap, we propose an asymmetric GARCH model with standardized non-Gaussian stable innovations (sAGARCH), which accommodates infinite variance and even infinite mean. We establish a comprehensive inference framework for both stationary and explosive cases, proving the strong consistency and asymptotic normality of the maximum likelihood estimator, including the tail index parameter. We also discuss multiple estimators for the asymptotic variance. Additionally, we propose a modified Kolmogorov-type test statistic for diagnostic checking, along with tests for strict stationarity and asymmetry. Through Monte Carlo simulations with heavy-tailed innovations, we provide further insight into the finite-sample performance of the intercept estimator. Empirical applications to stock returns further highlight the usefulness and merits of the proposed sAGARCH model.

stat.ME↗

arXiv2026

Generalized Spectral Testing with Sample Splitting

Residual-based goodness-of-fit tests for parametric time-series models are often complicated by parameter-estimation effects, which can alter the limiting behavior of diagnostic statistics. We propose a sample-splitting generalized spectral test (in the spirit of Escanciano(2006)) for assessing conditional mean specification in linear and nonlinear time-series models. The procedure estimates the model parameter on a fitting subsample and constructs a generalized spectral Cramer-von Mises statistic from residuals computed on a checking/testing subsample. The statistic aggregates pairwise conditional mean restrictions over all lags and is therefore bandwidth-free and free of truncation-lag selection. Under mild regularity conditions and a score-alignment condition, the residual-based process has the same limiting null distribution as the infeasible oracle process based on the true errors. Although the resulting limiting law is still non-pivotal, it can be consistently approximated by a simple multiplier bootstrap that does not require generating bootstrap time series or re-estimating parameters. Such an oracle-equivalence property is in sharp contrast to the original full-sample test, for which parameter estimation contributes an additional first-order term to the limiting process, and requires re-estimating parameters in each bootstrapped sample. We further establish consistency of the proposed test against fixed alternatives and nontrivial power against local alternatives. Extensive simulations and real data analyses show that the proposed test controls size well, has comparable power, and delivers substantial computational savings in models where repeated estimation is costly.

econ.EM↗

arXiv2026

Harnesses for Inference-Time Alignment over Execution Trajectories

Harness engineering has emerged as an important inference-time technique for large language model (LLM) agents, aiming to improve long-term performance through task decomposition and guided execution. However, more elaborate harnesses are not uniformly better: increasing decomposition or guidance can sometimes improve execution, but can also reduce final task success. We study harness design through the lens of inference-time trajectory alignment. This perspective separates harness into two mechanisms: task decomposition, which structures a task into sub-goals, and guided execution, which reshapes local action distributions during execution. This decomposition allows us to quantify how workflow granularity, retry budgets, and guidance-induced action reweighting shape the performance limits of harness design. It further reveals concrete failure modes, including over-decomposition, over-pruning, and hallucinated execution. We validate these predictions through controlled synthetic experiments and real terminal agent benchmarks. Inspired by the theory, we further show that effective harnesses can be partial: specifying only the initial steps and leaving the remaining execution to agent can achieve higher pass rate than fully structured workflows.

cs.LG↗