arXiv subjects

Jiaqi Leng

Publications and source records attributed to Jiaqi Leng.

At least 19 recordsLinked to original sources

arXiv2026

SegDiff: Segmented Trajectory Diffusion for Consistent and Adaptive Robot Manipulation

Imitation learning enables robots to acquire manipulation skills from demonstrations by mapping observations to actions. Existing approaches predict either short-horizon continuous action sequences or discrete keyposes. However, continuous prediction methods suffer from compounding errors due to short prediction horizons and struggle with multi-modal action distributions, whereas keypose-based methods necessitate an external planner, constraining real-time applicability. To address these challenges, we introduce SegDiff, a closed-loop visuomotor policy that integrates the strengths of both paradigms. SegDiff decomposes demonstrations into motion segments between keyposes and learns to predict the continuous trajectory from the current state to the next keypose, enabling long-horizon prediction with real-time refinement. Furthermore, we leverage the capability of diffusion models and DDIM inversion to propose a Dynamic Temporal Ensembling mechanism, which allows the policy to efficiently respond to dynamic environments and mitigate discontinuities caused by inconsistent multi-modal sampling. SegDiff demonstrates significant performance gains over existing approaches across various simulated and real-world scenarios, indicating its strong ability to reason over extended temporal dependencies while maintaining real-time adaptability and control stability.

cs.RO↗

arXiv2026

Unify Robot Actions in Camera Frame

Cross-embodiment robot learning requires a unified action representation with consistent semantics across robot platforms. Existing representations suffer from platform-specific inconsistencies, while current solutions either maintain embodiment-specific action heads or learn latent action spaces, without fundamentally resolving the mismatch. We propose to unify robot actions in the camera frame using camera extrinsics, so that actions share consistent geometric semantics across different robot embodiments, including both single-arm and bimanual robots. However, most existing datasets lack camera extrinsic annotations, and existing offline calibration methods either suffer from local minima or require robot-specific training data. To address this gap, we present CalibAll, a training-free, robot-independent annotation pipeline that estimates camera extrinsics for offline datasets and converts heterogeneous robot actions into standardized camera-frame actions. CalibAll follows a coarse-to-fine calibration strategy: temporal PnP provides a stable initialization, followed by differentiable rendering-based refinement for high precision. Beyond extrinsics, CalibAll produces standardized TCP-pose actions and auxiliary annotations. We apply CalibAll to 16 datasets across 4 robot platforms, producing approximately 97K calibrated data episodes. Downstream simulation and real-robot experiments show that cross-embodiment pretraining with camera-frame actions achieves state-of-the-art performance.

cs.RO↗

arXiv2026

Understanding and Improving Length Generalization in Hierarchical Sparse Attention Models

Effectively processing long contexts is a critical challenge for language models. While standard Transformers are limited by quadratic complexity and poor length extrapolation, alternative architectures like sliding window attention and state space models sacrifice the ability to effectively utilize the full context due to their fixed-size memory. Chunk-based sparse attention has emerged as a promising paradigm for extreme length generalization, yet the key architectural principles underpinning its success are not yet fully understood. In this work, we present a systematic dissection of these models to identify the core components driving their performance. Through a unified framework and comprehensive ablation studies, we demonstrate that a combination of three design principles is critical: (1) an expressive, non-linear Chunk Encoder with a dedicated CLS token to produce representations for retrieval; (2) a Bypassing Residual Path to stably integrate retrieved global information without it being overridden by the local residual stream; and (3) enforced selection sparsity during pre-training to bridge the train-test distribution gap. We provide a theoretical motivation for intra-chunk information processing and landmark generation. By combining these principles, we establish a new state-of-the-art for training-free length extrapolation, successfully generalizing models trained on a 4K context to 32 million tokens on RULER and BABILong. Our findings provide a clear and empirically-grounded set of design principles for developing future, highly-capable long-context language models.

cs.CL↗

arXiv2026

Accelerating quantum Gibbs sampling without quantum walks

Szegedy's quantum walk gives a generic quadratic speedup for reversible classical Markov chains, but extending this mechanism to quantum Gibbs sampling has remained challenging beyond special cases. We present a walk-free quantum algorithm for preparing purified Gibbs states with a quadratic improvement in spectral-gap dependence for a broad class of quantum Gibbs samplers that satisfy exact Kubo-Martin-Schwinger detailed balance. Our main structural result is an explicit factorization of the corresponding parent Hamiltonian into noncommutative first-order operators. This turns purified Gibbs-state preparation into a singular-value filtering problem and enables a quantum singular value transformation algorithm with quadratically improved gap dependence under standard coherent-access assumptions. The framework applies to several efficiently implementable Gibbs samplers beyond the Davies setting. We also introduce an auxiliary dissipative dynamics based on the same factorization, which can be used to generate warm starts in the doubled Hilbert space in metastable regimes.

quant-ph↗

arXiv2026

Towards End-to-End Quantum Estimation of Non-Hermitian Pseudospectra

Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts. The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic. For inverse-polynomially small $ε$, we show that deciding whether a point $z\in\mathbb{C}$ is $ε$-close to the spectrum is PSPACE-hard for $5$-local operators, whereas deciding whether $z$ lies in the $ε$-pseudospectrum is QMA-complete for $4$-local operators. This identifies pseudospectrum membership as a natural computational target. We then present a concrete end-to-end quantum framework for deciding pseudospectrum membership, which combines a singular-value estimation step with a dissipative state preparation algorithm. Our Quantum Singular-value Gaussian-filtered Search (QSIGS) combines quantum singular value transformation (QSVT) with classical post-processing to achieve Heisenberg-limited query scaling for singular-value estimation. To prepare suitable input states, we introduce an algorithmic Lindbladian protocol for approximate ground right singular vectors and prove its effectiveness for the Hatano--Nelson model. Finally, we demonstrate the full pipeline on a trapped-ion quantum computer and distinguish points inside and outside the target pseudospectrum near the exceptional point of a minimal non-Hermitian qubit model.

quant-ph↗

arXiv2026

Preference Score Distillation: Leveraging 2D Rewards to Align Text-to-3D Generation with Human Preference

Human preference alignment presents a critical yet underexplored challenge for diffusion models in text-to-3D generation. Existing solutions typically require task-specific fine-tuning, posing significant hurdles in data-scarce 3D domains. To address this, we propose Preference Score Distillation (PSD), an optimization-based framework that leverages pretrained 2D reward models for human-aligned text-to-3D synthesis without 3D training data. Our key insight stems from the incompatibility of pixel-level gradients: due to the absence of noisy samples during reward model training, direct application of 2D reward gradients disturbs the denoising process. Noticing that similar issue occurs in the naive classifier guidance in conditioned diffusion models, we fundamentally rethink preference alignment as a classifier-free guidance (CFG)-style mechanism through our implicit reward model. Furthermore, recognizing that frozen pretrained diffusion models constrain performance, we introduce an adaptive strategy to co-optimize preference scores and negative text embeddings. By incorporating CFG during optimization, online refinement of negative text embeddings dynamically enhances alignment. To our knowledge, we are the first to bridge human preference alignment with CFG theory under score distillation framework. Experiments demonstrate the superiority of PSD in aesthetic metrics, seamless integration with diverse pipelines, and strong extensibility.

cs.CV↗

arXiv2026

Predicting properties of quantum thermal states from a single trajectory

Estimating thermal expectation values of observables is a fundamental task in quantum physics, quantum chemistry, and materials science. While recent quantum algorithms have enabled efficient quantum preparation of thermal states, observable estimation via sampling remains costly: a straightforward implementation separates successive measurements by a full mixing time in order to ensure samples are approximately independent. In this work, we show that the sampling cost can be substantially reduced by using a single Gibbs-sampling trajectory. After a single burn-in period, we interleave coherent measurements that satisfy detailed balance with respect to the target Gibbs state. The efficiency of this approach rests on the fact that, in many settings, the autocorrelation time can be significantly shorter than the mixing time. For energy estimation (and more generally for observables commuting with the Hamiltonian), we implement the required measurements using Gaussian-filtered quantum phase estimation with only logarithmic overhead. We also introduce a weighted operator Fourier transform technique to mitigate measurement-induced disturbance for general observables.

quant-ph↗

arXiv2026

Resource-efficient quantum simulation of transport phenomena via Hamiltonian embedding

Transport phenomena play a key role in a variety of application domains, and efficient simulation of these dynamics remains an outstanding challenge. While quantum computers offer potential for significant speedups, existing algorithms either lack rigorous theoretical guarantees or demand substantial quantum resources, preventing scalable and efficient validation on realistic quantum hardware. To address this gap, we develop a comprehensive framework for simulating classes of transport equations, offering both rigorous theoretical guarantees -- including exponential speedups in specific cases -- and a systematic, hardware-efficient implementation. Central to our approach is the Hamiltonian embedding technique, a white-box approach for end-to-end simulation of sparse Hamiltonians that avoids abstract query models and retains near-optimal asymptotic complexity. Empirical resource estimates indicate that our approach can yield an order-of-magnitude (e.g., $42\times$) reduction in circuit depth given favorable problem structures. We then apply our framework to solve linear and nonlinear transport PDEs, including the first experimental demonstration of a 2D advection equation on a trapped-ion quantum computer.

quant-ph↗

arXiv2026

Distilling Token-Trained Models into Byte-Level Models

Byte Language Models (BLMs) have emerged as a promising direction for scaling language models beyond tokenization. However, existing BLMs typically require training from scratch on trillions of bytes, making them prohibitively expensive. In this paper, we propose an efficient distillation recipe that converts existing token-trained LLMs into BLMs while retaining comparable capabilities. Our recipe follows a two-stage curriculum: (1) Progressive Knowledge Distillation, which aligns byte-level representations with the embeddings of the token-trained teacher model; and (2) Byte-Level Supervised Fine-Tuning, which enables end-to-end generation entirely in the byte space. We validate our approach across multiple model families, including Llama, Qwen, and OLMo, and demonstrate that the distilled BLMs retain most of the teacher models' performance using only approximately 125B bytes.

cs.CL↗

arXiv2026

Operator-Level Quantum Acceleration of Non-Logconcave Sampling

Sampling from probability distributions of the form $σ\propto e^{-βV}$, where $V$ is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when $V$ is non-convex, the resulting distribution becomes non-logconcave, and classical methods such as Langevin dynamics often exhibit poor performance. We introduce the first quantum algorithm that provably accelerates a broad class of continuous-time sampling dynamics. For Langevin dynamics, our method encodes the target Gibbs measure into the amplitudes of a quantum state, identified as the kernel of a block matrix derived from a factorization of the Witten Laplacian operator. This connection enables Gibbs sampling via singular value thresholding and yields up to a quartic quantum speedup over best-known classical Langevin-based methods in the non-logconcave setting. Building on this framework, we further develop the first quantum algorithm that accelerates replica exchange Langevin diffusion, a widely used method for sampling from complex, rugged energy landscapes.

quant-ph↗

arXiv2025

Human2Robot: Learning Robot Actions from Paired Human-Robot Videos

Distilling knowledge from human demonstrations is a promising way for robots to learn and act. Existing methods, which often rely on coarsely-aligned video pairs, are typically constrained to learning global or task-level features. As a result, they tend to neglect the fine-grained frame-level dynamics required for complex manipulation and generalization to novel tasks. We posit that this limitation stems from a vicious circle of inadequate datasets and the methods they inspire. To break this cycle, we propose a paradigm shift that treats fine-grained human-robot alignment as a conditional video generation problem. To this end, we first introduce H&R, a novel third-person dataset containing 2,600 episodes of precisely synchronized human and robot motions, collected using a VR teleoperation system. We then present Human2Robot, a framework designed to leverage this data. Human2Robot employs a Video Prediction Model to learn a rich and implicit representation of robot dynamics by generating robot videos from human input, which in turn guides a decoupled action decoder. Our real-world experiments demonstrate that this approach not only achieves high performance on seen tasks but also exhibits significant one-shot generalization to novel positions, objects, instances, and even new task categories.

cs.RO↗

arXiv2025

Hardware-aligned Hierarchical Sparse Attention for Efficient Long-term Memory Access

A key advantage of Recurrent Neural Networks (RNNs) over Transformers is their linear computational and space complexity enables faster training and inference for long sequences. However, RNNs are fundamentally unable to randomly access historical context, and simply integrating attention mechanisms may undermine their efficiency advantages. To overcome this limitation, we propose Hierarchical Sparse Attention (HSA), a novel attention mechanism that enhances RNNs with long-range random access flexibility while preserving their merits in efficiency and length generalization. HSA divides inputs into chunks, selects the top-$k$ chunks and hierarchically aggregates information. The core innovation lies in learning token-to-chunk relevance based on fine-grained token-level information inside each chunk. This approach enhances the precision of chunk selection across both in-domain and out-of-domain context lengths. To make HSA efficient, we further introduce a hardware-aligned kernel design. By combining HSA with Mamba, we introduce RAMba, which achieves perfect accuracy in passkey retrieval across 64 million contexts despite pre-training on only 4K-length contexts, and significant improvements on various downstream tasks, with nearly constant memory footprint. These results show RAMba's huge potential in long-context modeling.

cs.CL↗

arXiv2025

Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding

Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although several theoretically appealing quantum algorithms have been proposed for this task, they typically require a black-box query model of the sparse Hamiltonian, rendering them impractical for near-term implementation on quantum devices. In this paper, we propose a technique named Hamiltonian embedding. This technique simulates a desired sparse Hamiltonian by embedding it into the evolution of a larger and more structured quantum system, allowing for more efficient simulation through hardware-efficient operations. We conduct a systematic study of this new technique and demonstrate significant savings in computational resources for implementing prominent quantum applications. As a result, we can now experimentally realize quantum walks on complicated graphs (e.g., binary trees, glued-tree graphs), quantum spatial search, and the simulation of real-space Schrödinger equations on current trapped-ion and neutral-atom platforms. Given the fundamental role of Hamiltonian evolution in the design of quantum algorithms, our technique markedly expands the horizon of implementable quantum advantages in the NISQ era.

quant-ph↗

arXiv2025

Quantum Optimization via Gradient-Based Hamiltonian Descent

With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between accelerated gradient methods and damped heavy-ball motion, particularly within the framework of Hamiltonian dynamics, has inspired the development of innovative quantum algorithms for continuous optimization. One such algorithm, Quantum Hamiltonian Descent (QHD), leverages quantum tunneling to escape saddle points and local minima, facilitating the discovery of global solutions in complex optimization landscapes. However, QHD faces several challenges, including slower convergence rates compared to classical gradient methods and limited robustness in highly non-convex problems due to the non-local nature of quantum states. Furthermore, the original QHD formulation primarily relies on function value information, which limits its effectiveness. Inspired by insights from high-resolution differential equations that have elucidated the acceleration mechanisms in classical methods, we propose an enhancement to QHD by incorporating gradient information, leading to what we call gradient-based QHD. Gradient-based QHD achieves faster convergence and significantly increases the likelihood of identifying global solutions. Numerical simulations on challenging problem instances demonstrate that gradient-based QHD outperforms existing quantum and classical methods by at least an order of magnitude.

quant-ph↗

arXiv2025

(Sub)Exponential Quantum Speedup for Optimization

We demonstrate provable (sub)exponential quantum speedups in both discrete and continuous optimization, achieved through simple and natural quantum optimization algorithms, namely the quantum adiabatic algorithm for discrete optimization and quantum Hamiltonian descent for continuous optimization. Our result builds on the Gilyén--Hastings--Vazirani (sub)exponential oracle separation for adiabatic quantum computing. With a sequence of perturbative reductions, we compile their construction into two standalone objective functions, whose oracles can be directly leveraged by the plain adiabatic evolution and Schrödinger operator evolution for discrete and continuous optimization, respectively.

quant-ph↗

arXiv2025

WLPCM Approach for Great Lakes Regulation

This study develops a water-level management model for the Great Lakes using a predictive control framework. Requirement 1: Historical data (pre-2019) revealed consistent monthly water-level patterns. A simulated annealing algorithm optimized flow control via the Moses-Saunders Dam and Compensating Works to align levels with multi-year benchmarks. Requirement 2: A Water Level Predictive Control Model (WLPCM) integrated delayed differential equations (DDEs) and model predictive control (MPC) to account for inflow/outflow dynamics and upstream time lags. Natural variables (e.g., precipitation) were modeled via linear regression, while dam flow rates were optimized over 6-month horizons with feedback adjustments for robustness. Requirement 3: Testing WLPCM on 2017 data successfully mitigated Ottawa River flooding, outperforming historical records. Sensitivity analysis via the Sobol method confirmed model resilience to parameter variations. Requirement 4: Ice-clogging was identified as the most impactful natural variable (via RMSE-based sensitivity tests), followed by snowpack and precipitation. Requirement 5: Stakeholder demands (e.g., flood prevention, ecological balance) were incorporated into a fitness function. Compared to Plan 2014, WLPCM reduced catastrophic high levels in Lake Ontario and excessive St. Lawrence River flows by prioritizing long-term optimization. Key innovations include DDE-based predictive regulation, real-time feedback loops, and adaptive control under extreme conditions. The framework balances hydrological dynamics, stakeholder needs, and uncertainty management, offering a scalable solution for large freshwater systems.

math.OC↗

arXiv2025

Quantum Hamiltonian Descent for Non-smooth Optimization

Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed, scalability, and parameter tuning, particularly in high-dimensional and non-convex settings. In this paper, we explore how quantum mechanics can be leveraged to overcome these limitations. Specifically, we investigate the theoretical properties of the Quantum Hamiltonian Descent (QHD) algorithm for non-smooth optimization in both continuous and discrete time. First, we propose continuous-time variants of the general QHD algorithm and establish their global convergence and convergence rate for non-smooth convex and strongly convex problems through a novel Lyapunov function design. Furthermore, we prove the finite-time global convergence of continuous-time QHD for non-smooth non-convex problems under mild conditions (i.e., locally Lipschitz). In addition, we propose discrete-time QHD, a fully digitized implementation of QHD via operator splitting (i.e., product formula). We find that discrete-time QHD exhibits similar convergence properties even with large time steps. Finally, numerical experiments validate our theoretical findings and demonstrate the computational advantages of QHD over classical non-smooth non-convex optimization algorithms.

math.OC↗

arXiv2025

FNIN: A Fourier Neural Operator-based Numerical Integration Network for Surface-form-gradients

Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients. Traditional methods encounter significant challenges in achieving high accuracy and handling high-resolution inputs, particularly facing the complex nature of discontinuities and the inefficiencies associated with large-scale linear solvers. Although recent advances in deep learning, such as photometric stereo, have enhanced normal estimation accuracy, they do not fully address the intricacies of gradient-based surface reconstruction. To overcome these limitations, we propose a Fourier neural operator-based Numerical Integration Network (FNIN) within a two-stage optimization framework. In the first stage, our approach employs an iterative architecture for numerical integration, harnessing an advanced Fourier neural operator to approximate the solution operator in Fourier space. Additionally, a self-learning attention mechanism is incorporated to effectively detect and handle discontinuities. In the second stage, we refine the surface reconstruction by formulating a weighted least squares problem, addressing the identified discontinuities rationally. Extensive experiments demonstrate that our method achieves significant improvements in both accuracy and efficiency compared to current state-of-the-art solvers. This is particularly evident in handling high-resolution images with complex data, achieving errors of fewer than 0.1 mm on tested objects.

cs.CV↗