arXiv subjects

Yuanhang Liu

Publications and source records attributed to Yuanhang Liu.

18 recordsLinked to original sources

arXiv2026

Centering Drives Normalization Gains: Price-Offset Nuisances in Cross-Sectional Return Prediction

Cross-sectional return prediction from raw intraday bars is sensitive to each instrument price level, an additive nuisance under a return-ranking hypothesis. We test whether removing this offset, rather than rescaling amplitudes or changing the encoder, explains gains on a point-in-time CSI 300 five-minute panel. Eight parameter-matched encoders are evaluated with and without RevIN normalization; a parameter-free ladder then separates identity, scale-only, centering, last-value referencing, differencing, and standardization across all fields and restricted channels. Centering drives the reliable effect, while scale-only normalization does not help. All eight paired effects are positive and survive Holm correction on raw rank IC, after style residualization, and after additionally residualizing on short-term reversal. Among six stronger encoders, normalized IC is 0.0830-0.0939 and gains are 0.0376-0.0567. Price-only standardization retains 93-101% of the all-field gain. These results place the main effect in transformed price-channel offset removal rather than amplitude scaling or encoder choice.

cs.CE↗

arXiv2026

A Compact Selective State-Space Model for Cross-Sectional Stock Return Ranking from Raw Intraday Bars

We present STRATA (Staggered-Timescale Residual Architecture), a 244,633-parameter sequence model that maps five trading days of raw five-minute bar and order-book data directly to a next-day cross-sectional return ranking, with no hand-crafted features. The raw-input setting has a structural obstacle: price series are non-stationary and differ across stocks by orders of magnitude, so a model easily latches onto price level rather than dynamics. STRATA addresses it with a stem of five branches--four learnable causal depthwise convolutions whose effective kernels are initialised to sum to zero, plus one cross-field linear contrast--followed by four selective state-space blocks whose decay biases are staggered across the stack and a four-path readout. Because a score that merely tilts toward common style factors scores well on raw rank correlations, every model's scores are residualised against eight price-volume style factors before any metric is computed. Trained on four years of data covering roughly one thousand mid-capitalisation Chinese A-shares and evaluated once on a held-out year, STRATA reaches a style-residualised rank information coefficient of 0.0728 (information ratio 1.128, signal long-short Sharpe 12.85), ahead of six parameter-matched sequence baselines on all four reported metrics; on rank IC the day-level paired gap against every baseline is significant at p < 0.001, and among the arms competitive on predictive power STRATA's scores are the least explained by the controls. The close-to-close target opens before the score exists: measured instead from the first executable price, the decile spread is indistinguishable from zero, while the ordering of the seven architectures is unchanged and STRATA's margin widens.

cs.CE↗

arXiv2026

Enhancing LLM Metacognition via Cognitive Pairwise Training

Reinforcement learning with verifiable rewards (RLVR) has become central to LLM reasoning, but its outcome-level rewards can make models more willing to give confident answers when evidence or reasoning is unreliable. Existing SFT or RL methods mainly teach LLMs to refuse or express uncertainty at the response level, which can overfit abstention behavior rather than improve reasoning reliability. To address this limitation, we propose Cognitive Pairwise Training (CPT), a cognitive mid-training alignment stage that turns pairwise comparisons over reasoning traces into a reusable alignment signal. By learning to distinguish trustworthy from flawed reasoning, CPT encourages the model to internalize a reasoning-quality discrimination boundary rather than memorize surface refusal patterns. Across five model scales and three model families, CPT improves the reasoning--metacognition trade-off. At 14B, CPT+RL outperforms the standard SFT+RL pipeline by +2.2 math-average points and +5.6 abstention-F1 points. Further analyses show that CPT improves trace quality and exhibits strong robustness and scalability across evaluation and training settings. Code and models are released at https://github.com/Tsinghua-dhy/CPT.

cs.LG↗

arXiv2026

RefereeBench: Are Video MLLMs Ready to be Multi-Sport Referees

While Multimodal Large Language Models (MLLMs) excel at generic video understanding, their ability to support specialized, rule-grounded decision-making remains insufficiently explored. In this paper, we introduce RefereeBench, the first large-scale benchmark for evaluating MLLMs as automatic sports referees. Spanning 11 sports with 925 curated videos and 6,475 QA pairs, RefereeBench evaluates five core officiating abilities: foul existence, foul and penalty classification, foul and penalty reasoning, entity perception, and temporal grounding. The benchmark is fully human-annotated to ensure high-quality annotations grounded in authentic officiating logic and multimodal evidence. Extensive evaluations of state-of-the-art MLLMs show that even the strongest models, such as Doubao-Seed-1.8 and Gemini-3-Pro, achieve only around 60% accuracy, while the strongest open-source model, Qwen3-VL, reaches only 47%. These results indicate that current models remain far from being reliable sports referees. Further analysis shows that while models can often identify incidents and involved entities, they struggle with rule application and temporal grounding, and frequently over-call fouls on normal clips. Our benchmark highlights the need for future MLLMs that better integrate domain knowledge and multimodal understanding, advancing trustworthy AI-assisted officiating and broader multimodal decision-making.

cs.CV↗

arXiv2025

AI Mathematician as a Partner in Advancing Mathematical Discovery -- A Case Study in Homogenization Theory

Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system can operate as a research partner rather than a mere problem solver. Focusing on a challenging problem in homogenization theory, we analyze the autonomous reasoning trajectories of AIM and incorporate targeted human interventions to structure the discovery process. Through iterative decomposition of the problem into tractable subgoals, selection of appropriate analytical methods, and validation of intermediate results, we reveal how human intuition and machine computation can complement one another. This collaborative paradigm enhances the reliability, transparency, and interpretability of the resulting proofs, while retaining human oversight for formal rigor and correctness. The approach leads to a complete and verifiable proof, and more broadly, demonstrates how systematic human-AI co-reasoning can advance the frontier of mathematical discovery.

cs.AI↗

arXiv2025

AI Mathematician: Towards Fully Automated Frontier Mathematical Research

Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times. However, these successes have been primarily confined to competition-level problems. In this work, we propose AI Mathematician (AIM) framework, which harnesses the reasoning strength of LRMs to support frontier mathematical research. We have identified two critical challenges of mathematical research compared to competition, the intrinsic complexity of research problems and the requirement of procedural rigor. To address these challenges, AIM incorporates two core strategies: an exploration mechanism to foster longer solution paths, and the pessimistic reasonable verification method to ensure reliability. This early version of AIM already exhibits strong capability in tackling research-level tasks. We conducted extensive experiments across several real-world mathematical topics and obtained promising results. AIM is able to autonomously construct substantial portions of proofs and uncover non-trivial insights within each research area. These findings highlight the potential of LRMs in mathematical discovery and suggest that LRM-based agent systems could significantly accelerate mathematical research in the future.

cs.AI↗

arXiv2024

Assessing Reusability of Deep Learning-Based Monotherapy Drug Response Prediction Models Trained with Omics Data

Cancer drug response prediction (DRP) models present a promising approach towards precision oncology, tailoring treatments to individual patient profiles. While deep learning (DL) methods have shown great potential in this area, models that can be successfully translated into clinical practice and shed light on the molecular mechanisms underlying treatment response will likely emerge from collaborative research efforts. This highlights the need for reusable and adaptable models that can be improved and tested by the wider scientific community. In this study, we present a scoring system for assessing the reusability of prediction DRP models, and apply it to 17 peer-reviewed DL-based DRP models. As part of the IMPROVE (Innovative Methodologies and New Data for Predictive Oncology Model Evaluation) project, which aims to develop methods for systematic evaluation and comparison DL models across scientific domains, we analyzed these 17 DRP models focusing on three key categories: software environment, code modularity, and data availability and preprocessing. While not the primary focus, we also attempted to reproduce key performance metrics to verify model behavior and adaptability. Our assessment of 17 DRP models reveals both strengths and shortcomings in model reusability. To promote rigorous practices and open-source sharing, we offer recommendations for developing and sharing prediction models. Following these recommendations can address many of the issues identified in this study, improving model reusability without adding significant burdens on researchers. This work offers the first comprehensive assessment of reusability and reproducibility across diverse DRP models, providing insights into current model sharing practices and promoting standards within the DRP and broader AI-enabled scientific research community.

q-bio.BM↗

arXiv2024

Carleman estimates for degenerate parabolic equations with single interior point degeneracy and its applications

We study the controllability of a class of $N$-dimensional degenerate parabolic equations with single interior point degeneracy. We employ the Galerkin method to prove the existence of solutions for the equations. The analysis is then divided into two cases based on whether the degenerate point $x=0$ lies within the control region $ω_0$ or not. For each case, we establish specific Carleman estimates. As a result, we achieve null controllability in the first case $0\inω_0$ and unique continuation and approximate controllability in the second case $0\notinω_0$.

math.OC↗

arXiv2024

Variational and Explanatory Neural Networks for Encoding Cancer Profiles and Predicting Drug Responses

Human cancers present a significant public health challenge and require the discovery of novel drugs through translational research. Transcriptomics profiling data that describes molecular activities in tumors and cancer cell lines are widely utilized for predicting anti-cancer drug responses. However, existing AI models face challenges due to noise in transcriptomics data and lack of biological interpretability. To overcome these limitations, we introduce VETE (Variational and Explanatory Transcriptomics Encoder), a novel neural network framework that incorporates a variational component to mitigate noise effects and integrates traceable gene ontology into the neural network architecture for encoding cancer transcriptomics data. Key innovations include a local interpretability-guided method for identifying ontology paths, a visualization tool to elucidate biological mechanisms of drug responses, and the application of centralized large scale hyperparameter optimization. VETE demonstrated robust accuracy in cancer cell line classification and drug response prediction. Additionally, it provided traceable biological explanations for both tasks and offers insights into the mechanisms underlying its predictions. VETE bridges the gap between AI-driven predictions and biologically meaningful insights in cancer research, which represents a promising advancement in the field.

q-bio.QM↗

arXiv2024

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space

In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.

math.AP↗

arXiv2024

Impulse approximate controllability for stochastic evolution equations and its applications

This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm problem seeks to identify an optimal impulse control characterized by the minimum norm among all feasible controls, guiding the system's solutions from an initial state within a fixed time interval toward a predetermined target while the minimal time problem is to find an optimal impulse control (among certain control constraint set), which steers the solution of the stochastic equation from a given initial state to a given target set as soon as possible. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case.

math.OC↗

arXiv2023

The solvability and a Stackelberg-Nash game problem for degenerate elliptic equations

This study aims to investigate the functional properties of weak solution spaces and their compact embedding properties in relation to the Dirichlet problem associated with a specific class of degenerate elliptic equations. To expand the scope of analysis for degenerate elliptic problems, we employ weighted Sobolev inequalities and compact embedding techniques within the framework of weighted Sobolev spaces. Additionally, we apply these findings to examine a Stackelberg-Nash game problem and obtain the existence of the Stackelberg-Nash equilibrium.

math.AP↗

arXiv2023

Observability inequalities for the backward stochastic evolution equations and their applications

The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination of spectral inequalities, interpolation inequalities, and the telegraph series method as our primary tools to directly establish observability inequalities. Furthermore, we explore three specific equations as application examples: a stochastic degenerate equation, a stochastic fourth order parabolic equation and a stochastic heat equation. It is noteworthy that these equations can be rendered null controllability with only one control in the drift term to each system.

math.OC↗

arXiv2023

Observability inequality, the interpolation inequality and the spectral inequality for the degenerate parabolic equation in R

This paper investigates the interrelationships between the observability inequality, the Hölder-type interpolation inequality, and the spectral inequality for the degenerate parabolic equation in $\mathbb{R}$. We elucidate the distinctive properties of observable sets pertaining to the degenerate parabolic equation. Specifically, we establish that a measurable set in $\mathbb{R}$ fulfills the observability inequality when it exhibits $γ$-thickness at a scale $L$, where $γ>0$ and $L>0$.

math.AP↗

arXiv2023

Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations

This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equations. We propose a formulation of the optimization problem that encompasses both the actuator location and its associated minimum norm control. Specifically, we transform the problem into a two-person zero-sum game problem, resulting in the development of four equivalent formulations. Finally, we establish the crucial result that the solution to the relaxed optimization problem serves as an optimal actuator location for the classical problem.

math.OC↗

arXiv2023

Null controllability of two kinds of coupled parabolic systems with switching control

The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in time for such coupled system, and then by the HUM method to obtain the null controllability. Next, we investigate the null controllability of such coupled system for segmented time intervals. Notably, these results are obtained through spectral inequalities rather than using the method of Carleman estimates. Such coupled systems with switching control, to the best of our knowledge, are among the first to discuss.

math.OC↗

arXiv2023

Norm and time optimal control problems of stochastic heat equations

This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by a discussion of its properties. We then explore the equivalence between the norm optimal control and time optimal control, and subsequently establish the bang-bang property of the time optimal control. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case.

math.OC↗

arXiv2023

Observability Inequality from Measurable Sets and the Stackelberg-Nash Game Problem for Degenerate Parabolic Equations

In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping series method, to establish an observability inequality for the degenerate parabolic equation over measurable subsets in the time-space domain. As a direct application, we formulate a captivating Stackelberg-Nash game problem and provide a proof of the existence of its equilibrium. Additionally, we characterize the set of Stackelberg-Nash equilibria and delve into the analysis of a norm optimal control problem.

math.OC↗