Extracting Training Data from Unconditional Diffusion Models

As diffusion probabilistic models (DPMs) are being employed as mainstream models for generative artificial intelligence (AI), the study of their memorization of the raw training data has attracted growing attention. Existing works in this direction aim to establish an understanding of whether or to what extent DPMs learn by memorization. Such an understanding is crucial for identifying potential risks of data leakage and copyright infringement in diffusion models and, more importantly, for more controllable generation and trustworthy application of Artificial Intelligence Generated Content (AIGC). While previous works have made important observations of when DPMs are prone to memorization, these findings are mostly empirical, and the developed data extraction methods only work for conditional diffusion models. In this work, we aim to establish a theoretical understanding of memorization in DPMs with 1) a memorization metric for theoretical analysis, 2) an analysis of conditional memorization with informative and random labels, and 3) two better evaluation metrics for measuring memorization. Based on the theoretical analysis, we further propose a novel data extraction method called \textbf{Surrogate condItional Data Extraction (SIDE)} that leverages a classifier trained on generated data as a surrogate condition to extract training data directly from unconditional diffusion models. Our empirical results demonstrate that SIDE can extract training data from diffusion models where previous methods fail, and it is on average over 50\% more effective across different scales of the CelebA dataset.

Explainable Bayesian Recurrent Neural Smoother to Capture Global State Evolutionary Correlations

Through integrating the evolutionary correlations across global states in the bidirectional recursion, an explainable Bayesian recurrent neural smoother (EBRNS) is proposed for offline data-assisted fixed-interval state smoothing. At first, the proposed model, containing global states in the evolutionary interval, is transformed into an equivalent model with bidirectional memory. This transformation incorporates crucial global state information with support for bi-directional recursive computation. For the transformed model, the joint state-memory-trend Bayesian filtering and smoothing frameworks are derived by introducing the bidirectional memory iteration mechanism and offline data into Bayesian estimation theory. The derived frameworks are implemented using the Gaussian approximation to ensure analytical properties and computational efficiency. Finally, the neural network modules within EBRNS and its two-stage training scheme are designed. Unlike most existing approaches that artificially combine deep learning and model-based estimation, the bidirectional recursion and internal gated structures of EBRNS are naturally derived from Bayesian estimation theory, explainably integrating prior model knowledge, online measurement, and offline data. Experiments on representative real-world datasets demonstrate that the high smoothing accuracy of EBRNS is accompanied by data efficiency and a lightweight parameter scale.

The Implicit Bias of Adam on Separable Data

Adam has become one of the most favored optimizers in deep learning problems. Despite its success in practice, numerous mysteries persist regarding its theoretical understanding. In this paper, we study the implicit bias of Adam in linear logistic regression. Specifically, we show that when the training data are linearly separable, Adam converges towards a linear classifier that achieves the maximum $\ell_\infty$-margin. Notably, for a general class of diminishing learning rates, this convergence occurs within polynomial time. Our result shed light on the difference between Adam and (stochastic) gradient descent from a theoretical perspective.

Self-Control of LLM Behaviors by Compressing Suffix Gradient into Prefix Controller

We propose Self-Control, a novel method utilizing suffix gradients to control the behavior of large language models (LLMs) without explicit human annotations. Given a guideline expressed in suffix string and the model's self-assessment of adherence, Self-Control computes the gradient of this self-judgment concerning the model's hidden states, directly influencing the auto-regressive generation process towards desired behaviors. To enhance efficiency, we introduce Self-Control_{prefix}, a compact module that encapsulates the learned representations from suffix gradients into a Prefix Controller, facilitating inference-time control for various LLM behaviors. Our experiments demonstrate Self-Control's efficacy across multiple domains, including emotional modulation, ensuring harmlessness, and enhancing complex reasoning. Especially, Self-Control_{prefix} enables a plug-and-play control and jointly controls multiple attributes, improving model outputs without altering model parameters or increasing inference-time costs.

Slight Corruption in Pre-training Data Makes Better Diffusion Models

Diffusion models (DMs) have shown remarkable capabilities in generating realistic high-quality images, audios, and videos. They benefit significantly from extensive pre-training on large-scale datasets, including web-crawled data with paired data and conditions, such as image-text and image-class pairs. Despite rigorous filtering, these pre-training datasets often inevitably contain corrupted pairs where conditions do not accurately describe the data. This paper presents the first comprehensive study on the impact of such corruption in pre-training data of DMs. We synthetically corrupt ImageNet-1K and CC3M to pre-train and evaluate over 50 conditional DMs. Our empirical findings reveal that various types of slight corruption in pre-training can significantly enhance the quality, diversity, and fidelity of the generated images across different DMs, both during pre-training and downstream adaptation stages. Theoretically, we consider a Gaussian mixture model and prove that slight corruption in the condition leads to higher entropy and a reduced 2-Wasserstein distance to the ground truth of the data distribution generated by the corruptly trained DMs. Inspired by our analysis, we propose a simple method to improve the training of DMs on practical datasets by adding condition embedding perturbations (CEP). CEP significantly improves the performance of various DMs in both pre-training and downstream tasks. We hope that our study provides new insights into understanding the data and pre-training processes of DMs.

A Human-Like Reasoning Framework for Multi-Phases Planning Task with Large Language Models

Recent studies have highlighted their proficiency in some simple tasks like writing and coding through various reasoning strategies. However, LLM agents still struggle with tasks that require comprehensive planning, a process that challenges current models and remains a critical research issue. In this study, we concentrate on travel planning, a Multi-Phases planning problem, that involves multiple interconnected stages, such as outlining, information gathering, and planning, often characterized by the need to manage various constraints and uncertainties. Existing reasoning approaches have struggled to effectively address this complex task. Our research aims to address this challenge by developing a human-like planning framework for LLM agents, i.e., guiding the LLM agent to simulate various steps that humans take when solving Multi-Phases problems. Specifically, we implement several strategies to enable LLM agents to generate a coherent outline for each travel query, mirroring human planning patterns. Additionally, we integrate Strategy Block and Knowledge Block into our framework: Strategy Block facilitates information collection, while Knowledge Block provides essential information for detailed planning. Through our extensive experiments, we demonstrate that our framework significantly improves the planning capabilities of LLM agents, enabling them to tackle the travel planning task with improved efficiency and effectiveness. Our experimental results showcase the exceptional performance of the proposed framework; when combined with GPT-4-Turbo, it attains $10\times$ the performance gains in comparison to the baseline framework deployed on GPT-4-Turbo.

Faster Sampling via Stochastic Gradient Proximal Sampler

Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than Langevin-based algorithms in the deterministic setting Lee et al. (2021), has yet to be explored in its stochastic variants. In this paper, we study the Stochastic Proximal Samplers (SPS) for sampling from non-log-concave distributions. We first establish a general framework for implementing stochastic proximal samplers and establish the convergence theory accordingly. We show that the convergence to the target distribution can be guaranteed as long as the second moment of the algorithm trajectory is bounded and restricted Gaussian oracles can be well approximated. We then provide two implementable variants based on Stochastic gradient Langevin dynamics (SGLD) and Metropolis-adjusted Langevin algorithm (MALA), giving rise to SPS-SGLD and SPS-MALA. We further show that SPS-SGLD and SPS-MALA can achieve $\epsilon$-sampling error in total variation (TV) distance within $\tilde{\mathcal{O}}(d\epsilon^{-2})$ and $\tilde{\mathcal{O}}(d^{1/2}\epsilon^{-2})$ gradient complexities, which outperform the best-known result by at least an $\tilde{\mathcal{O}}(d^{1/3})$ factor. This enhancement in performance is corroborated by our empirical studies on synthetic data with various dimensions, demonstrating the efficiency of our proposed algorithm.

Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference

To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the entire denoising diffusion process into several segments, each corresponding to a reverse transition kernel (RTK) sampling subproblem. Specifically, DDPM uses a Gaussian approximation for the RTK, resulting in low per-subproblem complexity but requiring a large number of segments (i.e., subproblems), which is conjectured to be inefficient. To address this, we develop a general RTK framework that enables a more balanced subproblem decomposition, resulting in $\tilde O(1)$ subproblems, each with strongly log-concave targets. We then propose leveraging two fast sampling algorithms, the Metropolis-Adjusted Langevin Algorithm (MALA) and Underdamped Langevin Dynamics (ULD), for solving these strongly log-concave subproblems. This gives rise to the RTK-MALA and RTK-ULD algorithms for diffusion inference. In theory, we further develop the convergence guarantees for RTK-MALA and RTK-ULD in total variation (TV) distance: RTK-ULD can achieve $\epsilon$ target error within $\tilde{\mathcal O}(d^{1/2}\epsilon^{-1})$ under mild conditions, and RTK-MALA enjoys a $\mathcal{O}(d^{2}\log(d/\epsilon))$ convergence rate under slightly stricter conditions. These theoretical results surpass the state-of-the-art convergence rates for diffusion inference and are well supported by numerical experiments.

Improving Group Robustness on Spurious Correlation Requires Preciser Group Inference

Standard empirical risk minimization (ERM) models may prioritize learning spurious correlations between spurious features and true labels, leading to poor accuracy on groups where these correlations do not hold. Mitigating this issue often requires expensive spurious attribute (group) labels or relies on trained ERM models to infer group labels when group information is unavailable. However, the significant performance gap in worst-group accuracy between using pseudo group labels and using oracle group labels inspires us to consider further improving group robustness through preciser group inference. Therefore, we propose GIC, a novel method that accurately infers group labels, resulting in improved worst-group performance. GIC trains a spurious attribute classifier based on two key properties of spurious correlations: (1) high correlation between spurious attributes and true labels, and (2) variability in this correlation between datasets with different group distributions. Empirical studies on multiple datasets demonstrate the effectiveness of GIC in inferring group labels, and combining GIC with various downstream invariant learning methods improves worst-group accuracy, showcasing its powerful flexibility. Additionally, through analyzing the misclassifications in GIC, we identify an interesting phenomenon called semantic consistency, which may contribute to better decoupling the association between spurious attributes and labels, thereby mitigating spurious correlation.

The Dog Walking Theory: Rethinking Convergence in Federated Learning

Federated learning (FL) is a collaborative learning paradigm that allows different clients to train one powerful global model without sharing their private data. Although FL has demonstrated promising results in various applications, it is known to suffer from convergence issues caused by the data distribution shift across different clients, especially on non-independent and identically distributed (non-IID) data. In this paper, we study the convergence of FL on non-IID data and propose a novel \emph{Dog Walking Theory} to formulate and identify the missing element in existing research. The Dog Walking Theory describes the process of a dog walker leash walking multiple dogs from one side of the park to the other. The goal of the dog walker is to arrive at the right destination while giving the dogs enough exercise (i.e., space exploration). In FL, the server is analogous to the dog walker while the clients are analogous to the dogs. This analogy allows us to identify one crucial yet missing element in existing FL algorithms: the leash that guides the exploration of the clients. To address this gap, we propose a novel FL algorithm \emph{FedWalk} that leverages an external easy-to-converge task at the server side as a \emph{leash task} to guide the local training of the clients. We theoretically analyze the convergence of FedWalk with respect to data heterogeneity (between server and clients) and task discrepancy (between the leash and the original tasks). Experiments on multiple benchmark datasets demonstrate the superiority of FedWalk over state-of-the-art FL methods under both IID and non-IID settings.