arXiv subjects
Publications and source records attributed to Xiaoyu Huang.
We compute new lower bounds for determinants of $\{\pm 1\}$-matrices of orders $n=51$, $n=107$, $n=111$, $n=115$, and $n=119$, improving previous recorded bounds by $3.1\%$, $0.44\%$, $1.26\%$, $1.68\%$, and $2.12\%$, respectively. We provide the data necessary to construct these matrices.
Researchers studying the inverse Galois problem realized 25 of the 26 sporadic finite simple groups as Galois groups over $\mathbb{Q}$ during 1984--1989. We complete this program by proving that the last remaining sporadic group, the Mathieu group $M_{23}$, occurs as a Galois group over $\mathbb{Q}$. In fact, we produce an explicit degree $23$ polynomial with rational coefficients whose splitting field has Galois group $M_{23}$ over $\mathbb{Q}$. To accomplish this, we use a non-rigid triple of conjugacy classes of $M_{23}$ and compute Belyi maps to construct an explicit regular Galois extension of $\mathbb{Q}(t)$ with Galois group $M_{23}$. Essential for our computation is the numerical Belyi map algorithm developed and implemented by Klug, Musty, Schiavone, Sijsling, and Voight, inspired by ideas of Hejhal and Stark.
Mechanistic interpretability has largely focused on language models and deterministic toy tasks. Much less is known about how sequence models internally represent latent stochastic dynamics under noisy, partially observed observations. We study this question in a controlled multivariate stochastic volatility setting, where models observe only returns while the ground-truth latent volatility state is known to the researcher. This setting provides a useful benchmark for mechanistic interpretability under partial observability: the latent state is hidden from the model but directly available for evaluation. Across architectures, losses, and output heads, we find evidence for a two-stage computation. Hidden representations encode substantial information about the next latent volatility state, and the output head maps this representation to squared return forecasts. Furthermore, in Transformers, latent-state decodability emerges at identifiable architectural stages whose location depends on the volatility period. In long-cycle regimes, this computation simplifies into an explicit latent-state filter consisting of a learned linear projection followed by $\ell^2$ normalization. Output-head replacement further shows that part of the degradation under noisy MSE training arises from readout misalignment rather than representation failure. These results suggest that stochastic volatility models provide a useful benchmark for mechanistic interpretability under noisy latent dynamics and partial observability.
We investigate the extent to which the reduced minimal Weierstrass coefficients of an elliptic curve over $\mathbb{Q}$ may be computed from it's Frobenius traces. Decision tree models reveal that the first two reduced minimal Weierstrass coefficients can be recovered with perfect accuracy from the Frobenius traces at the primes $2$ and $3$, and the third by supplementing these two traces with the conductor parity. We subsequently prove explicit formulae for these coefficients using the Frobenius traces and conductor parity. These formulae appear to be new. In particular, we deduce that the first three reduced minimal Weierstrass coefficients of an elliptic curve are determined by its isogeny class.
Machine learning is increasingly used in mathematical discovery, but in mathematics the desired output is often not a prediction itself, but an explicit construction that can be checked independently. We study this setting through the zeta map on Dyck paths, a classical bijection in the combinatorics of the q,t-Catalan numbers. We train a deliberately small one-layer, one-head encoder-decoder transformer on this map and analyze its learned computation using mechanistic interpretability tools, including decoder cross-attention analysis, linear probing, and causal intervention. The analysis reveals a level-based mechanism: encoder representations make path levels linearly accessible, while the decoder selects and traverses input positions in a structured way. Translating these signals into combinatorics leads to the scaffolding map, an explicit peak-centered traversal algorithm for Dyck paths. We prove that this algorithm agrees with the zeta map, modulo a reversal convention in the labeling. This gives a controlled example of AI-assisted mathematical discovery in which mechanistic interpretability turns model behavior into a precise, human-verifiable combinatorial algorithm.
Digital twins require continuous maintenance to meet the increasing demand for high-precision geospatial data. However, traditional coarse CityGML building models, typically derived from Airborne Laser Scanning (ALS), often exhibit significant geometric deficiencies, particularly regarding facade accuracy due to the nadir perspective of airborne sensors. Integrating these coarse models with high-precision Mobile Laser Scanning (MLS) data is essential to recover detailed facade geometry. Unlike reconstruction-from-scratch approaches that discard existing semantic information and rely heavily on complete data coverage, this work presents an automated refinement framework that utilizes the coarse model as a geometric prior. This method enables targeted updates to facade geometry even in complex urban environments. It integrates surface matching to identify outdated surfaces and employs a binary integer optimization to select optimal faces from candidate data. Crucially, hard constraints are enforced within the optimization to ensure the topological validity of the refined output. Experimental results demonstrate that the proposed approach effectively corrects facade misalignments, reducing the Cloud-to-Mesh RMSE by approximately 36% and achieving centimeter-level alignment. Furthermore, the framework guarantees strictly watertight and manifold geometry, providing a robust solution for upgrading ALS-derived city models.
While spatial phonon coherence manifested through band folding is believed to be a key factor governing the anomalous thermal conductivity of periodic structures, we investigate phonon transport from the perspective of temporal coherence. Using mode-resolved analyses, we quantify temporal coherent contributions and elucidate the interplay between phonon coherence time and lifetime in heat conduction of graphene/hexagonal boron nitride superlattices. We find that intrinsic coherence of folded phonon modes dominates the enhancement in ultrashort-period superlattices. In contrast, Wigner transport equation yields only a minor effect of band folding on thermal conductivity. The predictions in temperature dependence of models with and without temporal coherence provide a falsifiable experimental signature of this effect. Temporal coherence therefore constitutes a previously overlooked but fundamental channel for heat conduction, extending the conventional picture of spatially coherent transport and deepening the understanding of phonon dynamics in superlattices.
Realistic highway simulation is critical for scalable safety evaluation of autonomous vehicles, particularly for interactions that are too rare to study from logged data alone. Yet highway traffic generation remains challenging because it requires broad coverage across speeds and maneuvers, controllable generation of rare safety-critical scenarios, and behavioral credibility in multi-agent interactions. We present PHASE, Policy for Heterogeneous Agent Self-play on Expressway, a context-aware self-play framework that addresses these three requirements through explicit per-agent conditioning for controllability, synthetic scenario generation for broad highway coverage, and closed-loop multi-agent training for realistic interaction dynamics. PHASE further supports different vehicle profiles, for example, passenger cars and articulated trailer trucks, within a single policy via vehicle-aware dynamics and context-conditioned actions, and stabilizes self-play with early termination of unrecoverable states, at-fault collision attribution, highway-aware reward shaping, coupled curricula, and robust policy optimization. Despite being trained only on synthetic data, PHASE transfers zero-shot to 512 unseen high-interaction real scenarios in exiD, achieving a 96.3% success rate and reducing ADE/FDE from 6.57/12.07 m to 2.44/5.25 m relative to a prior self-play baseline. In a learned trajectory embedding space, it also improves behavioral realism over IDM, reducing Frechet trajectory distance by 13.1% and energy distance by 20.2%. These results show that synthetic self-play can provide a scalable route to controllable and realistic highway scenario generation without direct imitation of expert logs.
While recent advances in humanoid locomotion have achieved stable walking on varied terrains, capturing the agility and adaptivity of highly dynamic human motions remains an open challenge. In particular, agile parkour in complex environments demands not only low-level robustness, but also human-like motion expressiveness, long-horizon skill composition, and perception-driven decision-making. In this paper, we present Perceptive Humanoid Parkour (PHP), a modular framework that enables humanoid robots to autonomously perform long-horizon, vision-based parkour across challenging obstacle courses. Our approach first leverages motion matching, formulated as nearest-neighbor search in a feature space, to compose retargeted atomic human skills into long-horizon kinematic trajectories. This framework enables the flexible composition and smooth transition of complex skill chains while preserving the elegance and fluidity of dynamic human motions. Next, we train motion-tracking reinforcement learning (RL) expert policies for these composed motions, and distill them into a single depth-based, multi-skill student policy, using a combination of DAgger and RL. Crucially, the combination of perception and skill composition enables autonomous, context-aware decision-making: using only onboard depth sensing and a discrete 2D velocity command, the robot selects and executes whether to step over, climb onto, vault or roll off obstacles of varying geometries and heights. We validate our framework with extensive real-world experiments on a Unitree G1 humanoid robot, demonstrating highly dynamic parkour skills such as climbing tall obstacles up to 1.25m (96% robot height), as well as long-horizon multi-obstacle traversal with closed-loop adaptation to real-time obstacle perturbations.
Likelihood-based policy gradient methods are the dominant approach for training robot control policies from rewards. These methods rely on differentiable action likelihoods, which constrain policy outputs to simple distributions like Gaussians. In this work, we show how flow matching policy gradients -- a recent framework that bypasses likelihood computation -- can be made effective for training and fine-tuning more expressive policies in challenging robot control settings. We introduce an improved objective that enables success in legged locomotion, humanoid motion tracking, and manipulation tasks, as well as robust sim-to-real transfer on two humanoid robots. We then present ablations and analysis on training dynamics. Results show how policies can exploit the flow representation for exploration when training from scratch, as well as improved fine-tuning robustness over baselines.
Recent work of Burungale-Skinner-Tian-Wan established the first infinite families of quadratic twists of non-CM elliptic curves over $\mathbb{Q}$ for which the strong Birch-Swinnerton-Dyer (BSD) conjecture holds. Building on their results, we encode the required hypotheses into an explicit algorithm and apply it to the database of elliptic curves in the $L$-functions and Modular Forms Database (LMFDB), identifying all elliptic curves $E$ of conductor at most $500{,}000$ that admit infinitely many quadratic twists satisfying the strong BSD conjecture. Our computations provide certain numerical evidence for a conjecture of Radziwi{\l}{\l} and Soundararajan predicting Gaussian behavior in the analytic order of the Shafarevich-Tate group, while also observing a systematic positive bias within the BSD-satisfying subfamily.
There is a large class of problems in algebraic combinatorics which can be distilled into the same challenge: construct an explicit combinatorial bijection. Traditionally, researchers have solved challenges like these by visually inspecting the data for patterns, formulating conjectures, and then proving them. But what is to be done if patterns fail to emerge until the data grows beyond human scale? In this paper, we propose a new workflow for discovering combinatorial bijections via machine learning. As a proof of concept, we train a transformer on paired Dyck paths and use its learned attention patterns to derive a new algorithmic description of the zeta map, which we call the \textit{Scaffolding Map}.
A dominant paradigm for teaching humanoid robots complex skills is to retarget human motions as kinematic references to train reinforcement learning (RL) policies. However, existing retargeting pipelines often struggle with the significant embodiment gap between humans and robots, producing physically implausible artifacts like foot-skating and penetration. More importantly, common retargeting methods neglect the rich human-object and human-environment interactions essential for expressive locomotion and loco-manipulation. To address this, we introduce OmniRetarget, an interaction-preserving data generation engine based on an interaction mesh that explicitly models and preserves the crucial spatial and contact relationships between an agent, the terrain, and manipulated objects. By minimizing the Laplacian deformation between the human and robot meshes while enforcing kinematic constraints, OmniRetarget generates kinematically feasible trajectories. Moreover, preserving task-relevant interactions enables efficient data augmentation, from a single demonstration to different robot embodiments, terrains, and object configurations. We comprehensively evaluate OmniRetarget by retargeting motions from OMOMO, LAFAN1, and our in-house MoCap datasets, generating over 8-hour trajectories that achieve better kinematic constraint satisfaction and contact preservation than widely used baselines. Such high-quality data enables proprioceptive RL policies to successfully execute long-horizon (up to 30 seconds) parkour and loco-manipulation skills on a Unitree G1 humanoid, trained with only 5 reward terms and simple domain randomization shared by all tasks, without any learning curriculum.
Recent advances in organoid models have revolutionized the study of human kidney disease mechanisms and drug discovery by enabling scalable, cost-effective research without the need for animal sacrifice. Here, we present a kidney organoid platform optimized for efficient screening in polycystic kidney disease (PKD). While these systems generate rich spatial-temporal microscopy video datasets, current manual approaches to analysis remain limited to coarse classifications (e.g., hit vs. non-hit), often missing valuable pixel-level and longitudinal information. To help overcome this bottleneck, we developed Organoid Tracker, a graphical user interface (GUI) platform designed with a modular plugin architecture, which empowers researchers to extract detailed, quantitative metrics without programming expertise. Built on the cutting-edge vision foundation model Segment Anything Model 2 (SAM2), Organoid Tracker enables zero-shot segmentation and automated analysis of spatial-temporal microscopy videos. It quantifies key metrics such as cyst formation rate, growth velocity, and morphological changes, while generating comprehensive reports. By providing an extensible, open-source framework, Organoid Tracker offers a powerful solution for improving and accelerating research in kidney development, PKD modeling, and therapeutic discovery. The platform is publicly available as open-source software at https://github.com/hrlblab/OrganoidTracker.
The human-like form of humanoid robots positions them uniquely to achieve the agility and versatility in motor skills that humans possess. Learning from human demonstrations offers a scalable approach to acquiring these capabilities. However, prior works either produce unnatural motions or rely on motion-specific tuning to achieve satisfactory naturalness. Furthermore, these methods are often motion- or goal-specific, lacking the versatility to compose diverse skills, especially when solving unseen tasks. We present BeyondMimic, a framework that scales to diverse motions and carries the versatility to compose them seamlessly in tackling unseen downstream tasks. At heart, a compact motion-tracking formulation enables mastering a wide range of radically agile behaviors, including aerial cartwheels, spin-kicks, flip-kicks, and sprinting, with a single setup and shared hyperparameters, all while achieving state-of-the-art human-like performance. Moving beyond the mere imitation of existing motions, we propose a unified latent diffusion model that empowers versatile goal specification, seamless task switching, and dynamic composition of these agile behaviors. Leveraging classifier guidance, a diffusion-specific technique for test-time optimization toward novel objectives, our model extends its capability to solve downstream tasks never encountered during training, including motion inpainting, joystick teleoperation, and obstacle avoidance, and transfers these skills zero-shot to real hardware. This work opens new frontiers for humanoid robots by pushing the limits of scalable human-like motor skill acquisition from human motion and advancing seamless motion synthesis that achieves generalization and versatility beyond training setups.
Vision-language-action (VLA) models have demonstrated strong semantic understanding and zero-shot generalization, yet most existing systems assume an accurate low-level controller with hand-crafted action "vocabulary" such as end-effector pose or root velocity. This assumption confines prior work to quasi-static tasks and precludes the agile, whole-body behaviors required by humanoid whole-body control (WBC) tasks. To capture this gap in the literature, we start by introducing the first sim-to-real-ready, vision-language, closed-loop benchmark for humanoid WBC, comprising over 150 tasks from 10 categories. We then propose LeVERB: Latent Vision-Language-Encoded Robot Behavior, a hierarchical latent instruction-following framework for humanoid vision-language WBC, the first of its kind. At the top level, a vision-language policy learns a latent action vocabulary from synthetically rendered kinematic demonstrations; at the low level, a reinforcement-learned WBC policy consumes these latent verbs to generate dynamics-level commands. In our benchmark, LeVERB can zero-shot attain a 80% success rate on simple visual navigation tasks, and 58.5% success rate overall, outperforming naive hierarchical whole-body VLA implementation by 7.8 times.
General-purpose humanoid robots are expected to interact intuitively with humans, enabling seamless integration into daily life. Natural language provides the most accessible medium for this purpose. However, translating language into humanoid whole-body motion remains a significant challenge, primarily due to the gap between linguistic understanding and physical actions. In this work, we present an end-to-end, language-directed policy for real-world humanoid whole-body control. Our approach combines reinforcement learning with policy distillation, allowing a single neural network to interpret language commands and execute corresponding physical actions directly. To enhance motion diversity and compositionality, we incorporate a Conditional Variational Autoencoder (CVAE) structure. The resulting policy achieves agile and versatile whole-body behaviors conditioned on language inputs, with smooth transitions between various motions, enabling adaptation to linguistic variations and the emergence of novel motions. We validate the efficacy and generalizability of our method through extensive simulations and real-world experiments, demonstrating robust whole-body control. Please see our website at LangWBC.github.io for more information.
Despite significant interest and advancements in humanoid robotics, most existing commercially available hardware remains high-cost, closed-source, and non-transparent within the robotics community. This lack of accessibility and customization hinders the growth of the field and the broader development of humanoid technologies. To address these challenges and promote democratization in humanoid robotics, we demonstrate Berkeley Humanoid Lite, an open-source humanoid robot designed to be accessible, customizable, and beneficial for the entire community. The core of this design is a modular 3D-printed gearbox for the actuators and robot body. All components can be sourced from widely available e-commerce platforms and fabricated using standard desktop 3D printers, keeping the total hardware cost under $5,000 (based on U.S. market prices). The design emphasizes modularity and ease of fabrication. To address the inherent limitations of 3D-printed gearboxes, such as reduced strength and durability compared to metal alternatives, we adopted a cycloidal gear design, which provides an optimal form factor in this context. Extensive testing was conducted on the 3D-printed actuators to validate their durability and alleviate concerns about the reliability of plastic components. To demonstrate the capabilities of Berkeley Humanoid Lite, we conducted a series of experiments, including the development of a locomotion controller using reinforcement learning. These experiments successfully showcased zero-shot policy transfer from simulation to hardware, highlighting the platform's suitability for research validation. By fully open-sourcing the hardware design, embedded code, and training and deployment frameworks, we aim for Berkeley Humanoid Lite to serve as a pivotal step toward democratizing the development of humanoid robotics. All resources are available at https://lite.berkeley-humanoid.org.