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Yuhao Zhou

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20 papers
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20

EAAI Journal 2026 Journal Article

Knowledge-based computational deep network for dynamic parameter predication with large language models: A case study on oil transport pipeline network

  • Chengze Du
  • Faming Gong
  • Yuhao Zhou
  • Xiaofeng Ji
  • Yanpu Zhao
  • Jingcheng Gao

In the field of oil industry, Large Language Models (LLMs) are beginning to be applied to the prediction task. In the process of crude oil extraction, the shutdown or startup of wells can disrupt the stability of the existing pipeline network. Artificial intelligence methods cannot accurately mine the change relationship in the data. It has limited ability to dynamically adapt when external conditions change. In this paper, we propose a Knowledge-Based Computational Deep Network (KBCDN) which mainly studies the fusion of mechanistic knowledge and deep learning models to solve the problem of dynamically changing parameter prediction in graph structure. By representing knowledge as both domain-specific mechanistic formulas and task-descriptive texts, the model’s capability to extract features from varying conditions is enhanced. Firstly, by incorporating formulas as attributes of network nodes and edges, the parameter calculations during model training can be informed by domain expert experience. Secondly, task-descriptive texts are used as prompts for LLMs, while time-series data is transformed into textual prototypes. By aligning these texts, LLMs can leverage vast parameter spaces to predict parameters more accurately. The model is applied to three pipeline network systems of offshore oil field. The results show that our model achieves superior performance compared with field expert experience models and state-of-the-art methods. In extreme cases such as prolonged and repeated well shutdowns, KBCDN performs well with error below 5%. KBCDN can also be applied to other graph-based predication tasks, such as electricity distribution, traffic flow and other fields.

AAAI Conference 2026 Conference Paper

Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination

  • Mingqi Wu
  • Zhihao Zhang
  • Qiaole Dong
  • Zhiheng Xi
  • Jun Zhao
  • Senjie Jin
  • Xiaoran Fan
  • Yuhao Zhou

Reasoning in large language models has long been a central research focus, and recent studies employing reinforcement learning (RL) have introduced diverse methods that yield substantial performance gains with minimal or even no external supervision. Surprisingly, some studies even suggest that random or incorrect reward signals can enhance performance. However, these breakthroughs are predominantly observed for the mathematically strong Qwen2.5 series on benchmarks such as MATH-500, AMC, and AIME, and seldom transfer to models like Llama, which warrants a more in-depth investigation. In this work, our empirical analysis reveals that pre-training on massive web-scale corpora leaves Qwen2.5 susceptible to data contamination in widely used benchmarks. Consequently, conclusions derived from contaminated benchmarks on Qwen2.5 series may be unreliable. To obtain trustworthy evaluation results, we introduce a generator that creates fully clean arithmetic problems of arbitrary length and difficulty, dubbed RandomCalculation. Using this leakage-free dataset, we show that only accurate reward signals yield steady improvements that surpass the base model’s performance boundary in mathematical reasoning, whereas random or incorrect rewards do not. Moreover, we conduct more fine-grained analyses to elucidate the factors underlying the different performance observed on the MATH-500 and RandomCalculation benchmarks. Consequently, we recommend that future studies evaluate models on uncontaminated benchmarks and, when feasible, test various model series to ensure trustworthy conclusions about RL and related methods.

FM Conference 2026 Conference Paper

Towards Language Model Guided $$\text {TLA}^{+}$$ Proof Automation

  • Yuhao Zhou
  • Stavros Tripakis

Abstract Formal theorem proving with $$\texttt {TLA}^{+}$$ TLA + provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based theorem provers like Lean, applying these approaches directly to $$\texttt {TLA}^{+}$$ TLA + faces significant challenges due to the hierarchical proof structure of the $$\texttt {TLA}^{+}$$ TLA + proof system. We present a prompt-based approach that leverages LLMs to guide hierarchical decomposition of complex proof obligations into simpler sub-claims, while relying on symbolic provers for verification. Our key insight is to constrain LLMs to generate normalized claim decompositions rather than complete proofs, significantly reducing syntax errors. We also introduce a benchmark suite of 119 theorems adapted from (1) established mathematical collections and (2) inductive proofs of distributed protocols. Our approach consistently outperforms baseline methods across the benchmark suite.

AAAI Conference 2026 Conference Paper

What Makes a Good Speech Tokenizer for LLM-Centric Speech Generation? A Systematic Study

  • Xiaoran Fan
  • Zhichao Sun
  • Yangfan Gao
  • Jingfei Xiong
  • Hang Yan
  • Yifei Cao
  • Jiajun Sun
  • Shuo Li

Speech-language models (SLMs) offer a promising path toward unifying speech and text understanding and generation. However, challenges remain in achieving effective cross-modal alignment and high-quality speech generation. In this work, we systematically investigate the role of speech tokenizer designs in LLM-centric SLMs, augmented by speech heads and speaker modeling. We compare coupled, semi-decoupled, and fully decoupled speech tokenizers under a fair SLM framework and find that decoupled tokenization significantly improves alignment and synthesis quality. To address the information density mismatch between speech and text, we introduce multi-token prediction (MTP) into SLMs, enabling each hidden state to decode multiple speech tokens. This leads to up to 12× faster decoding and a substantial drop in word error rate (from 6.07 to 3.01). Furthermore, we propose a speaker-aware generation paradigm and introduce RoleTriviaQA, a large-scale role-playing knowledge QA benchmark with diverse speaker identities. Experiments demonstrate that our methods enhance both knowledge understanding and speaker consistency.

NeurIPS Conference 2025 Conference Paper

A Regularized Newton Method for Nonconvex Optimization with Global and Local Complexity Guarantees

  • Yuhao Zhou
  • Jintao Xu
  • Bingrui Li
  • Chenglong Bao
  • Chao Ding
  • Jun Zhu

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face a trade‑off between global and local convergence. Whether a parameter-free algorithm of this type can simultaneously achieve optimal global complexity and quadratic local convergence remains an open question. To bridge this long-standing gap, we propose a new class of regularizers constructed from the current and previous gradients, and leverage the conjugate gradient approach with a negative curvature monitor to solve the regularized Newton equation. The proposed algorithm is adaptive, requiring no prior knowledge of the Hessian Lipschitz constant, and achieves a global complexity of $O(\epsilon^{-\frac{3}{2}})$ in terms of the second-order oracle calls, and $\tilde O(\epsilon^{-\frac{7}{4}})$ for Hessian-vector products, respectively. When the iterates converge to a point where the Hessian is positive definite, the method exhibits quadratic local convergence. Preliminary numerical results, including training the physics-informed neural networks, illustrate the competitiveness of our algorithm.

NeurIPS Conference 2025 Conference Paper

Drag-and-Drop LLMs: Zero-Shot Prompt-to-Weights

  • Zhiyuan Liang
  • Dongwen Tang
  • Yuhao Zhou
  • Xuanlei Zhao
  • Mingjia Shi
  • Wangbo Zhao
  • Zekai Li
  • Peihao Wang

Modern Parameter-Efficient Fine-Tuning (PEFT) methods such as low-rank adaptation (LoRA) reduce the cost of customizing large language models (LLMs), yet still require a separate optimization run for every downstream dataset. We introduce \textbf{Drag-and-Drop LLMs (\textit{DnD})}, a prompt-conditioned parameter generator that eliminates per-task training by mapping a handful of unlabeled task prompts directly to LoRA weight updates. A lightweight text encoder distills each prompt batch into condition embeddings, which are then transformed by a cascaded hyper-convolutional decoder into the full set of LoRA matrices. Once trained in a diverse collection of prompt-checkpoint pairs, DnD produces task-specific parameters in seconds, yielding i) up to \textbf{12, 000$\times$} lower overhead than full fine-tuning, ii) average gains up to \textbf{30\%} in performance over the strongest training LoRAs on unseen common-sense reasoning, math, coding, and multimodal benchmarks, and iii) robust cross-domain generalization improving \textbf{40\%} performance without access to the target data or labels. Our results demonstrate that prompt-conditioned parameter generation is a viable alternative to gradient-based adaptation for rapidly specializing LLMs. We open source \href{https: //jerryliang24. github. io/DnD}{our project} in support of future research.

NeurIPS Conference 2025 Conference Paper

Pruning-Robust Mamba with Asymmetric Multi-Scale Scanning Paths

  • Jindi Lv
  • Yuhao Zhou
  • Mingjia Shi
  • Zhiyuan Liang
  • Panpan Zhang
  • Xiaojiang Peng
  • Wangbo Zhao
  • Zheng Zhu

Mamba has proven efficient for long-sequence modeling in vision tasks. However, when token reduction techniques are applied to improve efficiency, Mamba-based models exhibit drastic performance degradation compared to Vision Transformers (ViTs). This decline is potentially attributed to Mamba's chain-like scanning mechanism, which we hypothesize not only induces cascading losses in token connectivity but also limits the diversity of spatial receptive fields. In this paper, we propose Asymmetric Multi-scale Vision Mamba (AMVim), a novel architecture designed to enhance pruning robustness. AMVim employs a dual-path structure, integrating a window-aware scanning mechanism into one path while retaining sequential scanning in the other. This asymmetry design promotes token connection diversity and enables multi-scale information flow, reinforcing spatial awareness. Empirical results demonstrate that AMVim achieves state-of-the-art pruning robustness. During token reduction, AMVim-T achieves a substantial 34\% improvement in training-free accuracy with identical model sizes and FLOPs. Meanwhile, AMVim-S exhibits only a 1. 5\% accuracy drop, performing comparably to ViT. Notably, AMVim also delivers superior performance during pruning-free settings, further validating its architectural advantages.

NeurIPS Conference 2025 Conference Paper

REPA Works Until It Doesn’t: Early-Stopped, Holistic Alignment Supercharges Diffusion Training

  • Ziqiao Wang
  • Wangbo Zhao
  • Yuhao Zhou
  • Zekai Li
  • Zhiyuan Liang
  • Mingjia Shi
  • Xuanlei Zhao
  • Pengfei Zhou

Diffusion Transformers (DiTs) deliver state-of-the-art image quality, yet their training remains notoriously slow. A recent remedy---representation alignment (REPA) that matches DiT hidden features to those of a non-generative teacher (e. g. , DINO)---dramatically accelerates the early epochs but plateaus or even degrades performance later. We trace this failure to the capacity mismatch: once the generative student begins modeling the joint data distribution, the teacher's lower-dimensional embeddings and attention patterns become a straitjacket rather than a guide. We then introduce HASTE (Holistic Alignment with Stage-wise Termination for Efficient training), a two-phase schedule that keeps the help and drops the hindrance. Phase I applies a holistic alignment loss that simultaneously distills attention maps (relational priors) and feature projections (semantic anchors) from the teacher into mid-level layers of the DiT, yielding rapid convergence. Phase II then performs one-shot termination that deactivates the alignment loss, once a simple trigger such as a fixed iteration is hit, freeing the DiT to focus on denoising and exploit its generative capacity. HASTE speeds up training of diverse DiTs without architecture changes. On ImageNet 256×256, it reaches the vanilla SiT-XL/2 baseline FID in 50 epochs and matches REPA’s best FID in 500 epochs, amounting to a 28× reduction in optimization steps. HASTE also improves text-to-image DiTs on MS-COCO, proving to be a simple yet principled recipe for efficient diffusion training across various tasks.

NeurIPS Conference 2025 Conference Paper

Scientists' First Exam: Probing Cognitive Abilities of MLLM via Perception, Understanding, and Reasoning

  • Yuhao Zhou
  • Yiheng Wang
  • Xuming He
  • Ruoyao Xiao
  • Zhiwei Li
  • Qiantai Feng
  • Zijie Guo
  • Yuejin Yang

Scientific discoveries increasingly rely on complex multimodal reasoning based on information-intensive scientific data and domain-specific expertise. Empowered by expert-level scientific benchmarks, scientific Multimodal Large Language Models (MLLMs) hold the potential to significantly enhance this discovery process in realistic workflows. However, current scientific benchmarks mostly focus on evaluating the knowledge understanding capabilities of MLLMs, leading to an inadequate assessment of their perception and reasoning abilities. To address this gap, we present the Scientists’ First Exam (SFE) benchmark, designed to evaluate the scientific cognitive capacities of MLLMs through three interconnected levels: scientific signal perception, scientific attribute understanding, scientific comparative reasoning. Specifically, SFE comprises 830 expert-verified VQA pairs across three question types, spanning 66 multimodal tasks across five high-value disciplines. Extensive experiments reveal that current state-of-the-art GPT-o3 and InternVL-3 achieve only 34. 08% and 26. 52% on SFE, highlighting significant room for MLLMs to improve in scientific realms. We hope the insights obtained in SFE will facilitate further developments in AI-enhanced scientific discoveries.

IROS Conference 2024 Conference Paper

In-Hand Singulation and Scooping Manipulation with a 5 DOF Tactile Gripper

  • Yuhao Zhou
  • Pokuang Zhou
  • Shaoxiong Wang
  • Yu She

Manipulation tasks often require a high degree of dexterity, typically necessitating grippers with multiple degrees of freedom (DoF). While a robotic hand equipped with multiple fingers can execute precise and intricate manipulation tasks, the inherent redundancy stemming from its extensive DoF often adds unnecessary complexity. In this paper, we introduce the design of a tactile sensor-equipped gripper with two fingers and five DoF. We present a novel design integrating a GelSight tactile sensor, enhancing sensing capabilities and enabling finer control during specific manipulation tasks. To evaluate the gripper’s performance, we conduct experiments involving two challenging tasks: 1) retrieving, singularizing, and classification of various objects embedded in granular media, and 2) executing scooping manipulations of credit cards in confined environments to achieve precise insertion. Our results demonstrate the efficiency of the proposed approach, with a high success rate for singulation and classification tasks, particularly for spherical objects at high as 94. 3%, and a 100% success rate for scooping and inserting credit cards.

ICLR Conference 2024 Conference Paper

The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editing

  • Shen Nie
  • Hanzhong Allan Guo
  • Cheng Lu 0011
  • Yuhao Zhou
  • Chenyu Zheng
  • Chongxuan Li

We present a unified probabilistic formulation for diffusion-based image editing, where a latent variable is edited in a task-specific manner and generally deviates from the corresponding marginal distribution induced by the original stochastic or ordinary differential equation (SDE or ODE). Instead, it defines a corresponding SDE or ODE for editing. In the formulation, we prove that the Kullback-Leibler divergence between the marginal distributions of the two SDEs gradually decreases while that for the ODEs remains as the time approaches zero, which shows the promise of SDE in image editing. Inspired by it, we provide the SDE counterparts for widely used ODE baselines in various tasks including inpainting and image-to-image translation, where SDE shows a consistent and substantial improvement. Moreover, we propose \emph{SDE-Drag} -- a simple yet effective method built upon the SDE formulation for point-based content dragging. We build a challenging benchmark (termed \emph{DragBench}) with open-set natural, art, and AI-generated images for evaluation. A user study on DragBench indicates that SDE-Drag significantly outperforms our ODE baseline, existing diffusion-based methods, and the renowned DragGAN. Our results demonstrate the superiority and versatility of SDE in image editing and push the boundary of diffusion-based editing methods. See the project page \url{https://ml-gsai.github.io/SDE-Drag-demo/} for the code and DragBench dataset.

ICML Conference 2024 Conference Paper

Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations

  • Kaiwen Xue
  • Yuhao Zhou
  • Shen Nie
  • Xu Min
  • Xiaolu Zhang
  • Jun Zhou 0011
  • Chongxuan Li

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising in modeling both continuous and discrete data, while simultaneously maintaining fast sampling capabilities. This paper aims to understand and enhance BFNs by connecting them with DMs through stochastic differential equations (SDEs). We identify the linear SDEs corresponding to the noise-addition processes in BFNs, demonstrate that BFN’s regression losses are aligned with denoise score matching, and validate the sampler in BFN as a first-order solver for the respective reverse-time SDE. Based on these findings and existing recipes of fast sampling in DMs, we propose specialized solvers for BFNs that markedly surpass the original BFN sampler in terms of sample quality with a limited number of function evaluations (e. g. , 10) on both image and text datasets. Notably, our best sampler achieves an increase in speed of $5\sim20$ times for free.

NeurIPS Conference 2023 Conference Paper

PRIOR: Personalized Prior for Reactivating the Information Overlooked in Federated Learning.

  • Mingjia Shi
  • Yuhao Zhou
  • Kai Wang
  • Huaizheng Zhang
  • Shudong Huang
  • Qing Ye
  • Jiancheng Lv

Classical federated learning (FL) enables training machine learning models without sharing data for privacy preservation, but heterogeneous data characteristic degrades the performance of the localized model. Personalized FL (PFL) addresses this by synthesizing personalized models from a global model via training on local data. Such a global model may overlook the specific information that the clients have been sampled. In this paper, we propose a novel scheme to inject personalized prior knowledge into the global model in each client, which attempts to mitigate the introduced incomplete information problem in PFL. At the heart of our proposed approach is a framework, the $\textit{PFL with Bregman Divergence}$ (pFedBreD), decoupling the personalized prior from the local objective function regularized by Bregman divergence for greater adaptability in personalized scenarios. We also relax the mirror descent (RMD) to extract the prior explicitly to provide optional strategies. Additionally, our pFedBreD is backed up by a convergence analysis. Sufficient experiments demonstrate that our method reaches the $\textit{state-of-the-art}$ performances on 5 datasets and outperforms other methods by up to 3. 5% across 8 benchmarks. Extensive analyses verify the robustness and necessity of proposed designs. The code will be made public.

NeurIPS Conference 2022 Conference Paper

DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps

  • Cheng Lu
  • Yuhao Zhou
  • Fan Bao
  • Jianfei Chen
  • Chongxuan Li
  • Jun Zhu

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4. 70 FID in 10 function evaluations and 2. 87 FID in 20 function evaluations on the CIFAR10 dataset, and a 4~16x speedup compared with previous state-of-the-art training-free samplers on various datasets.

NeurIPS Conference 2022 Conference Paper

Fast Instrument Learning with Faster Rates

  • Ziyu Wang
  • Yuhao Zhou
  • Jun Zhu

We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box. Our algorithm enjoys faster-rate convergence and adapts to the dimensionality of informative latent features, while avoiding an expensive minimax optimization procedure, which has been necessary to establish similar guarantees. It further brings the benefit of flexible machine learning models to quasi-Bayesian uncertainty quantification, likelihood-based model selection, and model averaging. Simulation studies demonstrate the competitive performance of our method.

NeurIPS Conference 2022 Conference Paper

Gradient Estimation with Discrete Stein Operators

  • Jiaxin Shi
  • Yuhao Zhou
  • Jessica Hwang
  • Michalis Titsias
  • Lester Mackey

Gradient estimation---approximating the gradient of an expectation with respect to the parameters of a distribution---is central to the solution of many machine learning problems. However, when the distribution is discrete, most common gradient estimators suffer from excessive variance. To improve the quality of gradient estimation, we introduce a variance reduction technique based on Stein operators for discrete distributions. We then use this technique to build flexible control variates for the REINFORCE leave-one-out estimator. Our control variates can be adapted online to minimize variance and do not require extra evaluations of the target function. In benchmark generative modeling tasks such as training binary variational autoencoders, our gradient estimator achieves substantially lower variance than state-of-the-art estimators with the same number of function evaluations.

ICRA Conference 2021 Conference Paper

Retrieval and Localization with Observation Constraints

  • Yuhao Zhou
  • Huanhuan Fan
  • Shuang Gao
  • Yuchen Yang
  • Xudong Zhang
  • Jijunnan Li
  • Yandong Guo

Accurate visual re-localization is very critical to many artificial intelligence applications, such as augmented reality, virtual reality, robotics and autonomous driving. To accomplish this task, we propose an integrated visual re-localization method called RLOCS by combining image retrieval, semantic consistency and geometry verification to achieve accurate estimations. The localization pipeline is designed as a coarse-to-fine paradigm. In the retrieval part, we cascade the architecture of ResNet101-GeM-ArcFace and employ DBSCAN followed by spatial verification to obtain a better initial coarse pose. We design a module called observation constraints, which combines geometry information and semantic consistency for filtering outliers. Comprehensive experiments are conducted on open datasets, including retrieval on R-Oxford5k and R-Paris6k, semantic segmentation on Cityscapes, localization on Aachen Day-Night and InLoc. By creatively modifying separate modules in the total pipeline, our method achieves many performance improvements on the challenging localization benchmarks.

NeurIPS Conference 2021 Conference Paper

Scalable Quasi-Bayesian Inference for Instrumental Variable Regression

  • Ziyu Wang
  • Yuhao Zhou
  • Tongzheng Ren
  • Jun Zhu

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we present a scalable quasi-Bayesian procedure for IV regression, building upon the recently developed kernelized IV models. Contrary to Bayesian modeling for IV, our approach does not require additional assumptions on the data generating process, and leads to a scalable approximate inference algorithm with time cost comparable to the corresponding point estimation methods. Our algorithm can be further extended to work with neural network models. We analyze the theoretical properties of the proposed quasi-posterior, and demonstrate through empirical evaluation the competitive performance of our method.

ICML Conference 2020 Conference Paper

Nonparametric Score Estimators

  • Yuhao Zhou
  • Jiaxin Shi
  • Jun Zhu 0001

Estimating the score, i. e. , the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable densities. Kernel estimators based on Stein’s methods or score matching have shown promise, however their theoretical properties and relationships have not been fully-understood. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. It allows us to analyse existing estimators and construct new ones with desirable properties by choosing different hypothesis spaces and regularizers. A unified convergence analysis is provided for such estimators. Finally, we propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.

NeurIPS Conference 2020 Conference Paper

wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations

  • Alexei Baevski
  • Yuhao Zhou
  • Abdelrahman Mohamed
  • Michael Auli

We show for the first time that learning powerful representations from speech audio alone followed by fine-tuning on transcribed speech can outperform the best semi-supervised methods while being conceptually simpler. wav2vec 2. 0 masks the speech input in the latent space and solves a contrastive task defined over a quantization of the latent representations which are jointly learned. Experiments using all labeled data of Librispeech achieve 1. 8/3. 3 WER on the clean/other test sets. When lowering the amount of labeled data to one hour, wav2vec 2. 0 outperforms the previous state of the art on the 100 hour subset while using 100 times less labeled data. Using just ten minutes of labeled data and pre-training on 53k hours of unlabeled data still achieves 4. 8/8. 2 WER. This demonstrates the feasibility of speech recognition with limited amounts of labeled data.

v2026.09.13