Zehao Dou

Aaditya Singh, Adam Fry, Adam Perelman et al. · berkeley, mila

This is the system card published alongside the OpenAI GPT-5 launch, August 2025. GPT-5 is a unified system with a smart and fast model that answers most questions, a deeper reasoning model for harder problems, and a real-time router that quickly decides which model to use based on conversation type, complexity, tool needs, and explicit intent (for example, if you say 'think hard about this' in the prompt). The router is continuously trained on real signals, including when users switch models, preference rates for responses, and measured correctness, improving over time. Once usage limits are reached, a mini version of each model handles remaining queries. This system card focuses primarily on gpt-5-thinking and gpt-5-main, while evaluations for other models are available in the appendix. The GPT-5 system not only outperforms previous models on benchmarks and answers questions more quickly, but -- more importantly -- is more useful for real-world queries. We've made significant advances in reducing hallucinations, improving instruction following, and minimizing sycophancy, and have leveled up GPT-5's performance in three of ChatGPT's most common uses: writing, coding, and health. All of the GPT-5 models additionally feature safe-completions, our latest approach to safety training to prevent disallowed content. Similarly to ChatGPT agent, we have decided to treat gpt-5-thinking as High capability in the Biological and Chemical domain under our Preparedness Framework, activating the associated safeguards. While we do not have definitive evidence that this model could meaningfully help a novice to create severe biological harm -- our defined threshold for High capability -- we have chosen to take a precautionary approach.

Sitan Chen, Zehao Dou, Surbhi Goel et al.

We consider the well-studied problem of learning a linear combination of $k$ ReLU activations with respect to a Gaussian distribution on inputs in $d$ dimensions. We give the first polynomial-time algorithm that succeeds whenever $k$ is a constant. All prior polynomial-time learners require additional assumptions on the network, such as positive combining coefficients or the matrix of hidden weight vectors being well-conditioned. Our approach is based on analyzing random contractions of higher-order moment tensors. We use a multi-scale analysis to argue that sufficiently close neurons can be collapsed together, sidestepping the conditioning issues present in prior work. This allows us to design an iterative procedure to discover individual neurons.

Zehao Dou, Subhodh Kotekal, Zhehao Xu et al.

The recent, impressive advances in algorithmic generation of high-fidelity image, audio, and video are largely due to great successes in score-based diffusion models. A key implementing step is score matching, that is, the estimation of the score function of the forward diffusion process from training data. As shown in earlier literature, the total variation distance between the law of a sample generated from the trained diffusion model and the ground truth distribution can be controlled by the score matching risk. Despite the widespread use of score-based diffusion models, basic theoretical questions concerning exact optimal statistical rates for score estimation and its application to density estimation remain open. We establish the sharp minimax rate of score estimation for smooth, compactly supported densities. Formally, given \(n\) i.i.d. samples from an unknown \(α\)-Hölder density \(f\) supported on \([-1, 1]\), we prove the minimax rate of estimating the score function of the diffused distribution \(f * \mathcal{N}(0, t)\) with respect to the score matching loss is \(\frac{1}{nt^2} \wedge \frac{1}{nt^{3/2}} \wedge (t^{α-1} + n^{-2(α-1)/(2α+1)})\) for all \(α> 0\) and \(t \ge 0\). As a consequence, it is shown the law \(\hat{f}\) of a sample generated from the diffusion model achieves the sharp minimax rate \(\bE(\dTV(\hat{f}, f)^2) \lesssim n^{-2α/(2α+1)}\) for all \(α> 0\) without any extraneous logarithmic terms which are prevalent in the literature, and without the need for early stopping which has been required for all existing procedures to the best of our knowledge.

Yan Luo, Muhammad Osama Khan, Yu Tian et al.

Equity in AI for healthcare is crucial due to its direct impact on human well-being. Despite advancements in 2D medical imaging fairness, the fairness of 3D models remains underexplored, hindered by the small sizes of 3D fairness datasets. Since 3D imaging surpasses 2D imaging in SOTA clinical care, it is critical to understand the fairness of these 3D models. To address this research gap, we conduct the first comprehensive study on the fairness of 3D medical imaging models across multiple protected attributes. Our investigation spans both 2D and 3D models and evaluates fairness across five architectures on three common eye diseases, revealing significant biases across race, gender, and ethnicity. To alleviate these biases, we propose a novel fair identity scaling (FIS) method that improves both overall performance and fairness, outperforming various SOTA fairness methods. Moreover, we release Harvard-FairVision, the first large-scale medical fairness dataset with 30,000 subjects featuring both 2D and 3D imaging data and six demographic identity attributes. Harvard-FairVision provides labels for three major eye disorders affecting about 380 million people worldwide, serving as a valuable resource for both 2D and 3D fairness learning. Our code and dataset are publicly accessible at \url{https://ophai.hms.harvard.edu/datasets/harvard-fairvision30k}.

Yaxuan Zhu, Zehao Dou, Haoxin Zheng et al.

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure using Tweedie's formula. Despite the merits of being versatile in solving various inverse problems without re-training, the performance of DPS is hindered by the fact that this posterior approximation can be inaccurate especially for high noise levels. Therefore, we propose \textbf{D}iffusion \textbf{P}osterior \textbf{MC}MC (\textbf{DPMC}), a novel inference algorithm based on Annealed MCMC to solve inverse problems with pretrained diffusion models. We define a series of intermediate distributions inspired by the approximated conditional distributions used by DPS. Through annealed MCMC sampling, we encourage the samples to follow each intermediate distribution more closely before moving to the next distribution at a lower noise level, and therefore reduce the accumulated error along the path. We test our algorithm in various inverse problems, including super resolution, Gaussian deblurring, motion deblurring, inpainting, and phase retrieval. Our algorithm outperforms DPS with less number of evaluations across nearly all tasks, and is competitive among existing approaches.

Hengyu Fu, Zehao Dou, Jiawei Guo et al.

Diffusion Transformer, the backbone of Sora for video generation, successfully scales the capacity of diffusion models, pioneering new avenues for high-fidelity sequential data generation. Unlike static data such as images, sequential data consists of consecutive data frames indexed by time, exhibiting rich spatial and temporal dependencies. These dependencies represent the underlying dynamic model and are critical to validate the generated data. In this paper, we make the first theoretical step towards bridging diffusion transformers for capturing spatial-temporal dependencies. Specifically, we establish score approximation and distribution estimation guarantees of diffusion transformers for learning Gaussian process data with covariance functions of various decay patterns. We highlight how the spatial-temporal dependencies are captured and affect learning efficiency. Our study proposes a novel transformer approximation theory, where the transformer acts to unroll an algorithm. We support our theoretical results by numerical experiments, providing strong evidence that spatial-temporal dependencies are captured within attention layers, aligning with our approximation theory.

Sifan Wang, Zehao Dou, Tong-Rui Liu et al.

Recent advances in generative modeling -- particularly diffusion models and flow matching -- have achieved remarkable success in synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. Here, we introduce $\textbf{FunDiff}$, a novel framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generate continuous functions evaluable at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, showing that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results show that our method generates physically consistent samples with high fidelity to the target distribution and exhibits robustness to noisy and low-resolution data. Code and datasets are publicly available at https://github.com/sifanexisted/fundiff.

Daniel Pfrommer, Zehao Dou, Christopher Scarvelis et al.

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that when these models are queried conditionally, their generations consistently deviate from the idealized "denoising" process upon which diffusion models are formulated, inducing disagreement between popular sampling algorithms (e.g. DDPM, DDIM). We introduce Schedule Deviation, a rigorous measure which captures the rate of deviation from a standard denoising process, and provide a methodology to compute it. Crucially, we demonstrate that the deviation from an idealized denoising process occurs irrespective of the model capacity or amount of training data. We posit that this phenomenon occurs due to the difficulty of bridging distinct denoising flows across different parts of the conditioning space and show theoretically how such a phenomenon can arise through an inductive bias towards smoothness.

Bowen Baker, Joost Huizinga, Leo Gao et al.

Mitigating reward hacking--where AI systems misbehave due to flaws or misspecifications in their learning objectives--remains a key challenge in constructing capable and aligned models. We show that we can monitor a frontier reasoning model, such as OpenAI o3-mini, for reward hacking in agentic coding environments by using another LLM that observes the model's chain-of-thought (CoT) reasoning. CoT monitoring can be far more effective than monitoring agent actions and outputs alone, and we further found that a LLM weaker than o3-mini, namely GPT-4o, can effectively monitor a stronger model. Because CoT monitors can be effective at detecting exploits, it is natural to ask whether those exploits can be suppressed by incorporating a CoT monitor directly into the agent's training objective. While we show that integrating CoT monitors into the reinforcement learning reward can indeed produce more capable and more aligned agents in the low optimization regime, we find that with too much optimization, agents learn obfuscated reward hacking, hiding their intent within the CoT while still exhibiting a significant rate of reward hacking. Because it is difficult to tell when CoTs have become obfuscated, it may be necessary to pay a monitorability tax by not applying strong optimization pressures directly to the chain-of-thought, ensuring that CoTs remain monitorable and useful for detecting misaligned behavior.

Zehao Dou, Minshuo Chen, Mengdi Wang et al.

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive number of steps involved. In response, consistency models have been developed to merge multiple steps in the sampling process, thereby significantly boosting the speed of sample generation without compromising quality. This paper contributes towards the first statistical theory for consistency models, formulating their training as a distribution discrepancy minimization problem. Our analysis yields statistical estimation rates based on the Wasserstein distance for consistency models, matching those of vanilla diffusion models. Additionally, our results encompass the training of consistency models through both distillation and isolation methods, demystifying their underlying advantage.

Zehao Dou, Jakub Grudzien Kuba, Yaodong Yang

Value function decomposition is becoming a popular rule of thumb for scaling up multi-agent reinforcement learning (MARL) in cooperative games. For such a decomposition rule to hold, the assumption of the individual-global max (IGM) principle must be made; that is, the local maxima on the decomposed value function per every agent must amount to the global maximum on the joint value function. This principle, however, does not have to hold in general. As a result, the applicability of value decomposition algorithms is concealed and their corresponding convergence properties remain unknown. In this paper, we make the first effort to answer these questions. Specifically, we introduce the set of cooperative games in which the value decomposition methods find their validity, which is referred as decomposable games. In decomposable games, we theoretically prove that applying the multi-agent fitted Q-Iteration algorithm (MA-FQI) will lead to an optimal Q-function. In non-decomposable games, the estimated Q-function by MA-FQI can still converge to the optimum under the circumstance that the Q-function needs projecting into the decomposable function space at each iteration. In both settings, we consider value function representations by practical deep neural networks and derive their corresponding convergence rates. To summarize, our results, for the first time, offer theoretical insights for MARL practitioners in terms of when value decomposition algorithms converge and why they perform well.

Zehao Dou, Yuanzhi Li

Adam-type methods, the extension of adaptive gradient methods, have shown great performance in the training of both supervised and unsupervised machine learning models. In particular, Adam-type optimizers have been widely used empirically as the default tool for training generative adversarial networks (GANs). On the theory side, however, despite the existence of theoretical results showing the efficiency of Adam-type methods in minimization problems, the reason of their wonderful performance still remains absent in GAN's training. In existing works, the fast convergence has long been considered as one of the most important reasons and multiple works have been proposed to give a theoretical guarantee of the convergence to a critical point of min-max optimization algorithms under certain assumptions. In this paper, we firstly argue empirically that in GAN's training, Adam does not converge to a critical point even upon successful training: Only the generator is converging while the discriminator's gradient norm remains high throughout the training. We name this one-sided convergence. Then we bridge the gap between experiments and theory by showing that Adam-type algorithms provably converge to a one-sided first order stationary points in min-max optimization problems under the one-sided MVI condition. We also empirically verify that such one-sided MVI condition is satisfied for standard GANs after trained over standard data sets. To the best of our knowledge, this is the very first result which provides an empirical observation and a strict theoretical guarantee on the one-sided convergence of Adam-type algorithms in min-max optimization.

Zehao Dou, Zhuoran Yang, Zhaoran Wang et al.

As one of the most popular methods in the field of reinforcement learning, Q-learning has received increasing attention. Recently, there have been more theoretical works on the regret bound of algorithms that belong to the Q-learning class in different settings. In this paper, we analyze the cumulative regret when conducting Nash Q-learning algorithm on 2-player turn-based stochastic Markov games (2-TBSG), and propose the very first gap dependent logarithmic upper bounds in the episodic tabular setting. This bound matches the theoretical lower bound only up to a logarithmic term. Furthermore, we extend the conclusion to the discounted game setting with infinite horizon and propose a similar gap dependent logarithmic regret bound. Also, under the linear MDP assumption, we obtain another logarithmic regret for 2-TBSG, in both centralized and independent settings.

Tangjun Wang, Zehao Dou, Chenglong Bao et al.

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points and is a critical component for achieving high classification accuracy. Many existing deep learning approaches directly impose the fusion loss when training neural networks. In this work, inspired by the convection-diffusion ordinary differential equations (ODEs), we propose a novel diffusion residual network (Diff-ResNet), internally introduces diffusion into the architectures of neural networks. Under the structured data assumption, it is proved that the proposed diffusion block can increase the distance-diameter ratio that improves the separability of inter-class points and reduces the distance among local intra-class points. Moreover, this property can be easily adopted by the residual networks for constructing the separable hyperplanes. Extensive experiments of synthetic binary classification, semi-supervised graph node classification and few-shot image classification in various datasets validate the effectiveness of the proposed method.

Yuanzhi Li, Zehao Dou

Generative Adversarial Networks (GANs) are widely used models to learn complex real-world distributions. In GANs, the training of the generator usually stops when the discriminator can no longer distinguish the generator's output from the set of training examples. A central question of GANs is that when the training stops, whether the generated distribution is actually close to the target distribution, and how the training process reaches to such configurations efficiently? In this paper, we established a theoretical results towards understanding this generator-discriminator training process. We empirically observe that during the earlier stage of the GANs training, the discriminator is trying to force the generator to match the low degree moments between the generator's output and the target distribution. Moreover, only by matching these empirical moments over polynomially many training examples, we prove that the generator can already learn notable class of distributions, including those that can be generated by two-layer neural networks.

Zehao Dou, Stanley J. Osher, Bao Wang

In this paper, we analyze efficacy of the fast gradient sign method (FGSM) and the Carlini-Wagner's L2 (CW-L2) attack. We prove that, within a certain regime, the untargeted FGSM can fool any convolutional neural nets (CNNs) with ReLU activation; the targeted FGSM can mislead any CNNs with ReLU activation to classify any given image into any prescribed class. For a special two-layer neural network: a linear layer followed by the softmax output activation, we show that the CW-L2 attack increases the ratio of the classification probability between the target and ground truth classes. Moreover, we provide numerical results to verify all our theoretical results.

Zehao Dou, Zhihua Zhang

Attention mechanisms in sequence to sequence models have shown great ability and wonderful performance in various natural language processing (NLP) tasks, such as sentence embedding, text generation, machine translation, machine reading comprehension, etc. Unfortunately, existing attention mechanisms only learn either high-level or low-level features. In this paper, we think that the lack of hierarchical mechanisms is a bottleneck in improving the performance of the attention mechanisms, and propose a novel Hierarchical Attention Mechanism (Ham) based on the weighted sum of different layers of a multi-level attention. Ham achieves a state-of-the-art BLEU score of 0.26 on Chinese poem generation task and a nearly 6.5% averaged improvement compared with the existing machine reading comprehension models such as BIDAF and Match-LSTM. Furthermore, our experiments and theorems reveal that Ham has greater generalization and representation ability than existing attention mechanisms.