Matching the Statistical Query Lower Bound for k-sparse Parity Problems with Stochastic Gradient Descent

The $k$-parity problem is a classical problem in computational complexity and algorithmic theory, serving as a key benchmark for understanding computational classes. In this paper, we solve the $k$-parity problem with stochastic gradient descent (SGD) on two-layer fully-connected neural networks. We demonstrate that SGD can efficiently solve the $k$-sparse parity problem on a $d$-dimensional hypercube ($k\le O(\sqrt{d})$) with a sample complexity of $\tilde{O}(d^{k-1})$ using $2^{\Theta(k)}$ neurons, thus matching the established $\Omega(d^{k})$ lower bounds of Statistical Query (SQ) models. Our theoretical analysis begins by constructing a good neural network capable of correctly solving the $k$-parity problem. We then demonstrate how a trained neural network with SGD can effectively approximate this good network, solving the $k$-parity problem with small statistical errors. Our theoretical results and findings are supported by empirical evidence, showcasing the efficiency and efficacy of our approach.

Guided Discrete Diffusion for Electronic Health Record Generation

Electronic health records (EHRs) are a pivotal data source that enables numerous applications in computational medicine, e.g., disease progression prediction, clinical trial design, and health economics and outcomes research. Despite wide usability, their sensitive nature raises privacy and confidentially concerns, which limit potential use cases. To tackle these challenges, we explore the use of generative models to synthesize artificial, yet realistic EHRs. While diffusion-based methods have recently demonstrated state-of-the-art performance in generating other data modalities and overcome the training instability and mode collapse issues that plague previous GAN-based approaches, their applications in EHR generation remain underexplored. The discrete nature of tabular medical code data in EHRs poses challenges for high-quality data generation, especially for continuous diffusion models. To this end, we introduce a novel tabular EHR generation method, EHR-D3PM, which enables both unconditional and conditional generation using the discrete diffusion model. Our experiments demonstrate that EHR-D3PM significantly outperforms existing generative baselines on comprehensive fidelity and utility metrics while maintaining less membership vulnerability risks. Furthermore, we show EHR-D3PM is effective as a data augmentation method and enhances performance on downstream tasks when combined with real data.

Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedback

Learning from human feedback plays an important role in aligning generative models, such as large language models (LLM). However, the effectiveness of this approach can be influenced by adversaries, who may intentionally provide misleading preferences to manipulate the output in an undesirable or harmful direction. To tackle this challenge, we study a specific model within this problem domain--contextual dueling bandits with adversarial feedback, where the true preference label can be flipped by an adversary. We propose an algorithm namely robust contextual dueling bandit (\algo), which is based on uncertainty-weighted maximum likelihood estimation. Our algorithm achieves an $\tilde O(d\sqrt{T}+dC)$ regret bound, where $T$ is the number of rounds, $d$ is the dimension of the context, and $ 0 \le C \le T$ is the total number of adversarial feedback. We also prove a lower bound to show that our regret bound is nearly optimal, both in scenarios with and without ($C=0$) adversarial feedback. Additionally, we conduct experiments to evaluate our proposed algorithm against various types of adversarial feedback. Experimental results demonstrate its superiority over the state-of-the-art dueling bandit algorithms in the presence of adversarial feedback.

Settling Constant Regrets in Linear Markov Decision Processes

We study the constant regret guarantees in reinforcement learning (RL). Our objective is to design an algorithm that incurs only finite regret over infinite episodes with high probability. We introduce an algorithm, Cert-LSVI-UCB, for misspecified linear Markov decision processes (MDPs) where both the transition kernel and the reward function can be approximated by some linear function up to misspecification level $\zeta$. At the core of Cert-LSVI-UCB is an innovative certified estimator, which facilitates a fine-grained concentration analysis for multi-phase value-targeted regression, enabling us to establish an instance-dependent regret bound that is constant w.r.t. the number of episodes. Specifically, we demonstrate that for an MDP characterized by a minimal suboptimality gap $\Delta$, Cert-LSVI-UCB has a cumulative regret of $\tilde{\mathcal{O}}(d^3H^5/\Delta)$ with high probability, provided that the misspecification level $\zeta$ is below $\tilde{\mathcal{O}}(\Delta / (\sqrt{d}H^2))$. Remarkably, this regret bound remains constant relative to the number of episodes $K$. To the best of our knowledge, Cert-LSVI-UCB is the first algorithm to achieve a constant, instance-dependent, high-probability regret bound in RL with linear function approximation for infinite runs without relying on prior distribution assumptions. This not only highlights the robustness of Cert-LSVI-UCB to model misspecification but also introduces novel algorithmic designs and analytical techniques of independent interest.

Feel-Good Thompson Sampling for Contextual Dueling Bandits

Contextual dueling bandits, where a learner compares two options based on context and receives feedback indicating which was preferred, extends classic dueling bandits by incorporating contextual information for decision-making and preference learning. Several algorithms based on the upper confidence bound (UCB) have been proposed for linear contextual dueling bandits. However, no algorithm based on posterior sampling has been developed in this setting, despite the empirical success observed in traditional contextual bandits. In this paper, we propose a Thompson sampling algorithm, named FGTS.CDB, for linear contextual dueling bandits. At the core of our algorithm is a new Feel-Good exploration term specifically tailored for dueling bandits. This term leverages the independence of the two selected arms, thereby avoiding a cross term in the analysis. We show that our algorithm achieves nearly minimax-optimal regret, i.e., $\tilde{\mathcal{O}}(d\sqrt T)$, where $d$ is the model dimension and $T$ is the time horizon. Finally, we evaluate our algorithm on synthetic data and observe that FGTS.CDB outperforms existing algorithms by a large margin.

Antigen-Specific Antibody Design via Direct Energy-based Preference Optimization

Antibody design, a crucial task with significant implications across various disciplines such as therapeutics and biology, presents considerable challenges due to its intricate nature. In this paper, we tackle antigen-specific antibody design as a protein sequence-structure co-design problem, considering both rationality and functionality. Leveraging a pre-trained conditional diffusion model that jointly models sequences and structures of complementarity-determining regions (CDR) in antibodies with equivariant neural networks, we propose direct energy-based preference optimization to guide the generation of antibodies with both rational structures and considerable binding affinities to given antigens. Our method involves fine-tuning the pre-trained diffusion model using a residue-level decomposed energy preference. Additionally, we employ gradient surgery to address conflicts between various types of energy, such as attraction and repulsion. Experiments on RAbD benchmark show that our approach effectively optimizes the energy of generated antibodies and achieves state-of-the-art performance in designing high-quality antibodies with low total energy and high binding affinity, demonstrating the superiority of our approach.

Protein Conformation Generation via Force-Guided SE(3) Diffusion Models

The conformational landscape of proteins is crucial to understanding their functionality in complex biological processes. Traditional physics-based computational methods, such as molecular dynamics (MD) simulations, suffer from rare event sampling and long equilibration time problems, hindering their applications in general protein systems. Recently, deep generative modeling techniques, especially diffusion models, have been employed to generate novel protein conformations. However, existing score-based diffusion methods cannot properly incorporate important physical prior knowledge to guide the generation process, causing large deviations in the sampled protein conformations from the equilibrium distribution. In this paper, to overcome these limitations, we propose a force-guided SE(3) diffusion model, ConfDiff, for protein conformation generation. By incorporating a force-guided network with a mixture of data-based score models, ConfDiff can can generate protein conformations with rich diversity while preserving high fidelity. Experiments on a variety of protein conformation prediction tasks, including 12 fast-folding proteins and the Bovine Pancreatic Trypsin Inhibitor (BPTI), demonstrate that our method surpasses the state-of-the-art method.

Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systems

Real-world multi-agent systems are often dynamic and continuous, where the agents co-evolve and undergo changes in their trajectories and interactions over time. For example, the COVID-19 transmission in the U.S. can be viewed as a multi-agent system, where states act as agents and daily population movements between them are interactions. Estimating the counterfactual outcomes in such systems enables accurate future predictions and effective decision-making, such as formulating COVID-19 policies. However, existing methods fail to model the continuous dynamic effects of treatments on the outcome, especially when multiple treatments (e.g., "stay-at-home" and "get-vaccine" policies) are applied simultaneously. To tackle this challenge, we propose Causal Graph Ordinary Differential Equations (CAG-ODE), a novel model that captures the continuous interaction among agents using a Graph Neural Network (GNN) as the ODE function. The key innovation of our model is to learn time-dependent representations of treatments and incorporate them into the ODE function, enabling precise predictions of potential outcomes. To mitigate confounding bias, we further propose two domain adversarial learning-based objectives, which enable our model to learn balanced continuous representations that are not affected by treatments or interference. Experiments on two datasets (i.e., COVID-19 and tumor growth) demonstrate the superior performance of our proposed model.

Diffusion Language Models Are Versatile Protein Learners

This paper introduces diffusion protein language model (DPLM), a versatile protein language model that demonstrates strong generative and predictive capabilities for protein sequences. We first pre-train scalable DPLMs from evolutionary-scale protein sequences within a generative self-supervised discrete diffusion probabilistic framework, which generalizes language modeling for proteins in a principled way. After pre-training, DPLM exhibits the ability to generate structurally plausible, novel, and diverse protein sequences for unconditional generation. We further demonstrate the proposed diffusion generative pre-training makes DPLM possess a better understanding of proteins, making it a superior representation learner, which can be fine-tuned for various predictive tasks, comparing favorably to ESM2 (Lin et al., 2022). Moreover, DPLM can be tailored for various needs, which showcases its prowess of conditional generation in several ways: (1) conditioning on partial peptide sequences, e.g., generating scaffolds for functional motifs with high success rate; (2) incorporating other modalities as conditioner, e.g., structure-conditioned generation for inverse folding; and (3) steering sequence generation towards desired properties, e.g., satisfying specified secondary structures, through a plug-and-play classifier guidance.

Self-Play Fine-Tuning of Diffusion Models for Text-to-Image Generation

Fine-tuning Diffusion Models remains an underexplored frontier in generative artificial intelligence (GenAI), especially when compared with the remarkable progress made in fine-tuning Large Language Models (LLMs). While cutting-edge diffusion models such as Stable Diffusion (SD) and SDXL rely on supervised fine-tuning, their performance inevitably plateaus after seeing a certain volume of data. Recently, reinforcement learning (RL) has been employed to fine-tune diffusion models with human preference data, but it requires at least two images ("winner" and "loser" images) for each text prompt. In this paper, we introduce an innovative technique called self-play fine-tuning for diffusion models (SPIN-Diffusion), where the diffusion model engages in competition with its earlier versions, facilitating an iterative self-improvement process. Our approach offers an alternative to conventional supervised fine-tuning and RL strategies, significantly improving both model performance and alignment. Our experiments on the Pick-a-Pic dataset reveal that SPIN-Diffusion outperforms the existing supervised fine-tuning method in aspects of human preference alignment and visual appeal right from its first iteration. By the second iteration, it exceeds the performance of RLHF-based methods across all metrics, achieving these results with less data.