arXiv subjects

Tianyu Wang

Publications and source records attributed to Tianyu Wang.

At least 91 records · Page 5Linked to original sources

arXiv2026

Agile asymmetric multi-legged locomotion: contact planning via geometric mechanics and spin model duality

Legged robot research is presently focused on bipedal or quadrupedal robots, despite capabilities to build robots with many more legs to potentially improve locomotion performance. This imbalance is not necessarily due to hardware limitations, but rather to the absence of principled control frameworks that explain when and how additional legs improve locomotion performance. In multi-legged systems, coordinating many simultaneous contacts introduces a severe curse of dimensionality that challenges existing modeling and control approaches. As an alternative, multi-legged robots are typically controlled using low-dimensional gaits originally developed for bipeds or quadrupeds. These strategies fail to exploit the new symmetries and control opportunities that emerge in higher-dimensional systems. In this work, we develop a principled framework for discovering new control structures in multi-legged locomotion. We use geometric mechanics to reduce contact-rich locomotion planning to a graph optimization problem, and propose a spin model duality framework from statistical mechanics to exploit symmetry breaking and guide optimal gait reorganization. Using this approach, we identify an asymmetric locomotion strategy for a hexapod robot that achieves a forward speed of 0.61 body lengths per cycle (a 50% improvement over conventional gaits). The resulting asymmetry appears at both the control and hardware levels. At the control level, the body orientation oscillates asymmetrically between fast clockwise and slow counterclockwise turning phases for forward locomotion. At the hardware level, two legs on the same side remain unactuated and can be replaced with rigid parts without degrading performance. Numerical simulations and robophysical experiments validate the framework and reveal novel locomotion behaviors that emerge from symmetry reforming in high-dimensional embodied systems.

cs.RO↗

arXiv2026

Billions-Scale Forecast Reconciliation

The problem of combining multiple forecasts of related quantities that obey expected equality and additivity constraints, often referred to a hierarchical forecast reconciliation, is naturally stated as a simple optimization problem. In this paper we explore optimization-based point forecast reconciliation at scales faced by large retailers. We implement and benchmark several algorithms to solve the forecast reconciliation problem, showing efficacy when the dimension of the problem exceeds four billion forecasted values. To the best of our knowledge, this is the largest forecast reconciliation problem, and perhaps on-par with the largest constrained least-squares-problem ever solved. We also make several theoretical contributions. We show that for a restricted class of problems and when the loss function is weighted appropriately, least-squares forecast reconciliation is equivalent to share-based forecast reconciliation. This formalizes how the optimization based approach can be thought of as a generalization of share-based reconciliation, applicable to multiple, overlapping data hierarchies.

stat.ME↗

arXiv2026

Maximal measures for flows with nonuniform structure

In this paper, we study ergodic optimization of continuous functions for flows by concentrating on the entropy spectrum of their maximizing measures. Precisely, over a wide family of flows with non-uniformly hyperbolic structure, we obtain a picture describing coexistence of continuous functions whose maximizing measures have large and small entropy respectively in $C^0$-topology. Our proof relies on the orbit decomposition technique, originally introduced by Climenhaga and Thompson, for flows with weakened versions of expansiveness and specification property. In particular, our results extend \cite{STY} from non-Markov shift on symbolic spaces to a considerably broad class of continuous flows with nonuniform structure. To illustrate this, we apply our general results to both geodesic flows and frame flows over closed rank one manifolds of nonpositive curvature.

math.DS↗

arXiv2026

OneTrans: Unified Feature Interaction and Sequence Modeling with One Transformer in Industrial Recommender

In recommendation systems, scaling up feature-interaction modules (e.g., Wukong, RankMixer) or user-behavior sequence modules (e.g., LONGER) has achieved notable success. However, these efforts typically proceed on separate tracks, which not only hinders bidirectional information exchange but also prevents unified optimization and scaling. In this paper, we propose OneTrans, a unified Transformer backbone that simultaneously performs user-behavior sequence modeling and feature interaction. OneTrans employs a unified tokenizer to convert both sequential and non-sequential attributes into a single token sequence. The stacked OneTrans blocks share parameters across similar sequential tokens while assigning token-specific parameters to non-sequential tokens. Through causal attention and cross-request KV caching, OneTrans enables precomputation and caching of intermediate representations, significantly reducing computational costs during both training and inference. Experimental results on industrial-scale datasets demonstrate that OneTrans scales efficiently with increasing parameters, consistently outperforms strong baselines, and yields a 5.68% lift in per-user GMV in online A/B tests.

cs.IR↗

arXiv2026

DecisionLLM: Large Language Models for Long Sequence Decision Exploration

Long-sequence decision-making, which is usually addressed through reinforcement learning (RL), is a critical component for optimizing strategic operations in dynamic environments, such as real-time bidding in computational advertising. The Decision Transformer (DT) introduced a powerful paradigm by framing RL as an autoregressive sequence modeling problem. Concurrently, Large Language Models (LLMs) have demonstrated remarkable success in complex reasoning and planning tasks. This inspires us whether LLMs, which share the same Transformer foundation, but operate at a much larger scale, can unlock new levels of performance in long-horizon sequential decision-making problem. This work investigates the application of LLMs to offline decision making tasks. A fundamental challenge in this domain is the LLMs' inherent inability to interpret continuous values, as they lack a native understanding of numerical magnitude and order when values are represented as text strings. To address this, we propose treating trajectories as a distinct modality. By learning to align trajectory data with natural language task descriptions, our model can autoregressively predict future decisions within a cohesive framework we term DecisionLLM. We establish a set of scaling laws governing this paradigm, demonstrating that performance hinges on three factors: model scale, data volume, and data quality. In offline experimental benchmarks and bidding scenarios, DecisionLLM achieves strong performance. Specifically, DecisionLLM-3B outperforms the traditional Decision Transformer (DT) by 69.4 on Maze2D umaze-v1 and by 0.085 on AuctionNet. It extends the AIGB paradigm and points to promising directions for future exploration in online bidding.

cs.AI↗

arXiv2026

In-medium nucleon-nucleon cross sections from relativistic ab initio calculations

The in-medium nucleon-nucleon scattering cross section is a pivotal quantity for studying the medium effects of strong interaction, and its precise knowledge is critical for understanding the equation of state for dense matter, intermediate-energy heavy-ion collision dynamics, and related phenomena. In this work, we perform a microscopic investigation of in-medium nucleon-nucleon scattering cross sections, by utilizing the relativistic Brueckner-Hartree-Fock (RBHF) theory with the Bonn potential. The fully incorporation of both positive- and negative-energy states in the RBHF solutions allows us to determine the single-particle potentials, the effective G matrix, and the scattering cross section uniquely. The momentum, density, and isospin dependence of the cross section for pp, nn, and np scattering are studied in detail. Our results provide a solid foundation for future parametrization studies of multiparameter dependency of total scattering cross sections.

nucl-th↗

arXiv2025

OmniVCus: Feedforward Subject-driven Video Customization with Multimodal Control Conditions

Existing feedforward subject-driven video customization methods mainly study single-subject scenarios due to the difficulty of constructing multi-subject training data pairs. Another challenging problem that how to use the signals such as depth, mask, camera, and text prompts to control and edit the subject in the customized video is still less explored. In this paper, we first propose a data construction pipeline, VideoCus-Factory, to produce training data pairs for multi-subject customization from raw videos without labels and control signals such as depth-to-video and mask-to-video pairs. Based on our constructed data, we develop an Image-Video Transfer Mixed (IVTM) training with image editing data to enable instructive editing for the subject in the customized video. Then we propose a diffusion Transformer framework, OmniVCus, with two embedding mechanisms, Lottery Embedding (LE) and Temporally Aligned Embedding (TAE). LE enables inference with more subjects by using the training subjects to activate more frame embeddings. TAE encourages the generation process to extract guidance from temporally aligned control signals by assigning the same frame embeddings to the control and noise tokens. Experiments demonstrate that our method significantly surpasses state-of-the-art methods in both quantitative and qualitative evaluations. Video demos are at our project page: https://caiyuanhao1998.github.io/project/OmniVCus/. Our code, models, data are released at https://github.com/caiyuanhao1998/Open-OmniVCus

cs.CV↗

arXiv2025

Self-Evaluation Unlocks Any-Step Text-to-Image Generation

We introduce the Self-Evaluating Model (Self-E), a novel, from-scratch training approach for text-to-image generation that supports any-step inference. Self-E learns from data similarly to a Flow Matching model, while simultaneously employing a novel self-evaluation mechanism: it evaluates its own generated samples using its current score estimates, effectively serving as a dynamic self-teacher. Unlike traditional diffusion or flow models, it does not rely solely on local supervision, which typically necessitates many inference steps. Unlike distillation-based approaches, it does not require a pretrained teacher. This combination of instantaneous local learning and self-driven global matching bridges the gap between the two paradigms, enabling the training of a high-quality text-to-image model from scratch that excels even at very low step counts. Extensive experiments on large-scale text-to-image benchmarks show that Self-E not only excels in few-step generation, but is also competitive with state-of-the-art Flow Matching models at 50 steps. We further find that its performance improves monotonically as inference steps increase, enabling both ultra-fast few-step generation and high-quality long-trajectory sampling within a single unified model. To our knowledge, Self-E is the first from-scratch, any-step text-to-image model, offering a unified framework for efficient and scalable generation.

cs.CV↗

arXiv2025

A Proof of Talagrand's Creating Large Sets Conjecture

Talagrand conjectured that if a family of sets $\mathcal{F}$ over $X = \{ 1,2,\cdots, N \}$ is of large measure, then constant times of unions of sets in $\mathcal{F}$ will cover a large portion of the power set of $X$. This conjecture is a central open problem at the intersection of combinatorics and probability theory, and was described by Talagrand as a personal favorite. This paper provides a proof confirming this conjecture.

math.CO↗

arXiv2025

Conformal Correction for Efficiency May be at Odds with Entropy

Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or wrap the base model with an extra module using a conformal-aware inefficiency loss. In this work, we empirically and theoretically identify a trade-off between the CP efficiency and the entropy of model prediction. We then propose an entropy-constrained conformal correction method, exploring a better Pareto optimum between efficiency and entropy. Extensive experimental results on both computer vision and graph datasets demonstrate the efficacy of the proposed method. For instance, it can significantly improve the efficiency of state-of-the-art CP methods by up to 34.4%, given an entropy threshold.

cs.LG↗

arXiv2025

Head Stabilization for Wheeled Bipedal Robots via Force-Estimation-Based Admittance Control

Wheeled bipedal robots are emerging as flexible platforms for field exploration. However, head instability induced by uneven terrain can degrade the accuracy of onboard sensors or damage fragile payloads. Existing research primarily focuses on stabilizing the mobile platform but overlooks active stabilization of the head in the world frame, resulting in vertical oscillations that undermine overall stability. To address this challenge, we developed a model-based ground force estimation method for our 6-degree-of-freedom wheeled bipedal robot. Leveraging these force estimates, we implemented an admittance control algorithm to enhance terrain adaptability. Simulation experiments validated the real-time performance of the force estimator and the robot's robustness when traversing uneven terrain.

cs.RO↗

arXiv2025

The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence

This paper studies the Nesterov-Spokoiny Acceleration (NSA), a variant of the accelerated gradient method by Nesterov and Spokoiny. For smooth convex optimization, NSA achieves a strict $o(1/k^2)$ convergence rate in function value and an $o(1/(k^3 \log k))$ rate in squared gradient norm, while ensuring monotonic descent of the objective. We further study a zeroth-order version of NSA that handles inexact gradients, and extends NSA to composite optimization problems, in each case establishing $o(1/k^2)$ convergence in function value. A continuous-time analysis reveals connections to high-resolution ODEs known to underlie acceleration phenomena.

math.OC↗

arXiv2025

Whole-Body Control With Terrain Estimation of A 6-DoF Wheeled Bipedal Robot

Wheeled bipedal robots have garnered increasing attention in exploration and inspection. However, most research simplifies calculations by ignoring leg dynamics, thereby restricting the robot's full motion potential. Additionally, robots face challenges when traversing uneven terrain. To address the aforementioned issue, we develop a complete dynamics model and design a whole-body control framework with terrain estimation for a novel 6 degrees of freedom wheeled bipedal robot. This model incorporates the closed-loop dynamics of the robot and a ground contact model based on the estimated ground normal vector. We use a LiDAR inertial odometry framework and improved Principal Component Analysis for terrain estimation. Task controllers, including PD control law and LQR, are employed for pose control and centroidal dynamics-based balance control, respectively. Furthermore, a hierarchical optimization approach is used to solve the whole-body control problem. We validate the performance of the terrain estimation algorithm and demonstrate the algorithm's robustness and ability to traverse uneven terrain through both simulation and real-world experiments.

cs.RO↗

arXiv2025

Optimal swimming with body compliance in an overdamped medium

Elongate animals and robots use undulatory body waves to locomote through diverse environments. Geometric mechanics provides a framework to model and optimize such systems in highly damped environments, connecting a prescribed shape change pattern (gait) with locomotion displacement. However, the practical applicability of controlling compliant physical robots remains to be demonstrated. In this work, we develop a framework based on geometric mechanics to predict locomotor performance and search for optimal swimming strategies of compliant swimmers. We introduce a compliant extension of Purcell's three-link swimmer by incorporating series-connected springs at the joints. Body dynamics are derived using resistive force theory. Geometric mechanics is incorporated into movement prediction and into an optimization framework that identifies strategies for controlling compliant swimmers to achieve maximal displacement. We validate our framework on a physical cable-driven three-link limbless robot and demonstrate accurate prediction and optimization of locomotor performance under varied programmed, state-dependent compliance in a granular medium. Our results establish a systematic, physics-based approach for modeling and controlling compliant swimming locomotion, highlighting compliance as a design feature that can be exploited for robust movement in both homogeneous and heterogeneous environments.

cs.RO↗

arXiv2025

Revisit First-order Methods for Geodesically Convex Optimization

In a seminal work of Zhang and Sra, gradient descent methods for geodesically convex optimization were comprehensively studied. In particular, Zhang and Sra derived a comparison inequality that relates the iterative points in the optimization process. Since their seminal work, numerous follow-ups have studied different downstream usages of their comparison lemma. In this work, we introduce the concept of quasilinearization to optimization, presenting a novel framework for analyzing geodesically convex optimization. By leveraging this technique, we establish state-of-the-art convergence rates -- for both deterministic and stochastic settings -- under weaker assumptions than previously required. The technique of quasilinearization may prove valuable for other non-Euclidean optimization problems.

math.OC↗

arXiv2025

The Omega Turn: A General Turning Template for Elongate Robots

Elongate limbless robots have the potential to locomote through tightly packed spaces for applications such as search-and-rescue and industrial inspections. The capability to effectively and robustly maneuver elongate limbless robots is crucial to realize such potential. However, there has been limited research on turning strategies for such systems. To achieve effective and robust turning performance in cluttered spaces, we take inspiration from a microscopic nematode, C. elegans, which exhibits remarkable maneuverability in rheologically complex environments partially because of its ability to perform omega turns. Despite recent efforts to analyze omega turn kinematics, it remains unknown if there exists a wave equation sufficient to prescribe an omega turn, let alone its reconstruction on robot platforms. Here, using a comparative theory-biology approach, we prescribe the omega turn as a superposition of two traveling waves. With wave equations as a guideline, we design a controller for limbless robots enabling robust and effective turning behaviors in lab and cluttered field environments. Finally, we show that such omega turn controllers can also generalize to elongate multi-legged robots, demonstrating an alternative effective body-driven turning strategy for elongate robots, with and without limbs.

cs.RO↗

arXiv2025

Taming Variability: Randomized and Bootstrapped Conformal Risk Control for LLMs

We transform the randomness of LLMs into precise assurances using an actuator at the API interface that applies a user-defined risk constraint in finite samples via Conformal Risk Control (CRC). This label-free and model-agnostic actuator manages ship/abstain/escalate actions based solely on a scalar score from opaque outputs. We enhance CRC's computational efficiency and robustness through Batched Bootstrap CRC (BB-CRC) and Randomized Batched Weighted-Average CRC (RBWA-CRC), reducing calibration calls and stabilizing thresholds while maintaining statistical validity. Additionally, we present a semantic quantification method grounded in gram matrix geometry, resulting in interpretable signal and metric design. Together these pieces deliver principled randomness control for LLM hallucination mitigation and LLM-as-judge reliability. Our framework is assessed using four datasets, demonstrating its efficacy in enhancing factual accuracy and measuring LLM-as-judge performance, yielding a simplified and computationally efficient control layer that converts variability into statistical validity.

stat.ME↗

arXiv2025

Unsupervised Conformal Inference: Bootstrapping and Alignment to Control LLM Uncertainty

Deploying black-box LLMs requires managing uncertainty in the absence of token-level probability or true labels. We propose introducing an unsupervised conformal inference framework for generation, which integrates: generative models, incorporating: (i) an LLM-compatible atypical score derived from response-embedding Gram matrix, (ii) UCP combined with a bootstrapping variant (BB-UCP) that aggregates residuals to refine quantile precision while maintaining distribution-free, finite-sample coverage, and (iii) conformal alignment, which calibrates a single strictness parameter $τ$ so a user predicate (e.g., factuality lift) holds on unseen batches with probability $\ge 1-α$. Across different benchmark datasets, our gates achieve close-to-nominal coverage and provide tighter, more stable thresholds than split UCP, while consistently reducing the severity of hallucination, outperforming lightweight per-response detectors with similar computational demands. The result is a label-free, API-compatible gate for test-time filtering that turns geometric signals into calibrated, goal-aligned decisions.

stat.ML↗