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Optimization · Optimization and Learning under Uncertainty

Dongyan Lucy Huo, Yixuan Zhang, Yudong Chen, Qiaomin Xie

In this work, we investigate stochastic approximation (SA) with Markovian data and nonlinear updates under constant stepsize $\alpha>0$. Existing work has primarily focused on either i.i.d. data or linear update rules. We take a new perspective and carefully examine the simultaneous presence of Markovian dependency of data and nonlinear update rules, delineating how the interplay between these two structures leads to complications that are not captured by prior techniques. By leveraging the smoothness and recurrence properties of the SA updates, we develop a fine-grained analysis of the correlation between the SA iterates $\theta_k$ and Markovian data $x_k$. This enables us to overcome the obstacles in existing analysis and establish for the first time the weak convergence of the joint process $(x_k, \theta_k)$. Furthermore, we present a precise characterization of the asymptotic bias of the SA iterates, given by $\mathbb{E}[\theta_\infty]-\theta^\ast=\alpha(b_\textup{m}+b_\textup{n}+b_\textup{c})+\mathcal{O}(\alpha^{3/2})$. Here, $b_\textup{m}$ is associated with the Markovian noise, $b_\textup{n}$ is tied to the nonlinearity of the SA operator, and notably, $b_\textup{c}$ represents a multiplicative interaction between the Markovian noise and the nonlinearity of the operator, which is absent in previous works. As a by-product of our analysis, we derive finite-time bounds on higher moment $\mathbb{E}[||\theta_k-\theta^\ast||^{2p}]$ and present non-asymptotic geometric convergence rates for the iterates, along with a Central Limit Theorem.

Generative Models · Diffusion models

Nikil Selvam, Amil Merchant, Stefano Ermon

In diffusion models, samples are generated through an iterative refinement process, requiring hundreds of sequential model evaluations. Several recent methods have introduced approximations (fewer discretization steps or distillation) to trade off speed at the cost of sample quality. In contrast, we introduce Self-Refining Diffusion Samplers (SRDS) that retain sample quality and can improve latency at the cost of additional parallel compute. We take inspiration from the Parareal algorithm, a popular numerical method for parallel-in-time integration of differential equations. In SRDS, a quick but rough estimate of a sample is first created and then iteratively refined in parallel through Parareal iterations. SRDS is not only guaranteed to accurately solve the ODE and converge to the serial solution but also benefits from parallelization across the diffusion trajectory, enabling batched inference and pipelining. As we demonstrate for pre-trained diffusion models, the early convergence of this refinement procedure drastically reduces the number of steps required to produce a sample, speeding up generation for instance by up to 1.7x on a 25-step StableDiffusion-v2 benchmark and up to 4.3x on longer trajectories.

Applications

Saehyung Lee, Jisoo Mok, Sangha Park, Yongho Shin, Dahuin Jung, Sungroh Yoon

In our study, we explore methods for detecting unwanted content lurking in visual datasets. We provide a theoretical analysis demonstrating that a model capable of successfully partitioning visual data can be obtained using only textual data. Based on the analysis, we propose Hassle-Free Textual Training (HFTT), a streamlined method capable of acquiring detectors for unwanted visual content, using only textual data in conjunction with pre-trained vision-language models. HFTT features an innovative objective function that significantly reduces the necessity for human involvement in data annotation. Furthermore, HFTT employs a clever textual data synthesis method, effectively emulating the integration of unknown visual data distribution into the training process at no extra cost. The unique characteristics of HFTT extend its utility beyond traditional out-of-distribution detection, making it applicable to tasks that address more abstract concepts. We complement our analyses with experiments in hateful image detection and out-of-distribution detection. Our codes are available at https://github.com/HFTT-anonymous/HFTT.

Learning Theory

Zhan Yu, Qiuhao Chen, Yuling Jiao, Yinan Li, Xiliang Lu, Xin Wang, Jerry Yang

Understanding the power of parameterized quantum circuits (PQCs) in accomplishing machine learning tasks is one of the most important questions in quantum machine learning. In this paper, we focus on the PQC expressivity for general multivariate function classes. Previously established Universal Approximation Theorems for PQCs are either nonconstructive or assisted with parameterized classical data processing, making it hard to justify whether the expressive power comes from the classical or quantum parts. We explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions and establish the first non-asymptotic approximation error bounds for such functions in terms of the number of qubits, the quantum circuit depth and the number of trainable parameters of the PQCs. Notably, we show that for multivariate polynomials and multivariate smooth functions, the quantum circuit size and the number of trainable parameters of our proposed PQCs can be smaller than the deep ReLU neural networks. We further demonstrate the approximation capability of PQCs via numerical experiments. Our results pave the way for designing practical PQCs that can be implemented on near-term quantum devices with limited resources.

Multimodal Models

Divyam Madaan, Taro Makino, Sumit Chopra, Kyunghyun Cho

Supervised multi-modal learning involves mapping multiple modalities to a target label. Previous studies in this field have concentrated on capturing in isolation either the inter-modality dependencies (the relationships between different modalities and the label) or the intra-modality dependencies (the relationships within a single modality and the label). We argue that these conventional approaches that rely solely on either inter- or intra-modality dependencies may not be optimal in general. We view the multi-modal learning problem from the lens of generative models where we consider the target as a source of multiple modalities and the interaction between them. Towards that end, we propose inter- \& intra-modality modeling (I2M2) framework, which captures and integrates both the inter- and intra-modality dependencies, leading to more accurate predictions. We evaluate our approach using real-world healthcare and vision-and-language datasets with state-of-the-art models, demonstrating superior performance over traditional methods focusing only on one type of modality dependency. The code is available at https://github.com/divyam3897/I2M2.

Deep Learning · Algorithms

Rajesh Jayaram, Laxman Dhulipala, Majid Hadian, Jason Lee, Vahab Mirrokni

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding $x \in \mathbb{R}^d$ per data-point, allowing for fast retrieval via highly optimized maximum inner product search (MIPS) algorithms. Recently, beginning with the landmark ColBERT paper, multi-vector models, which produce a set of embedding per data point, have achieved markedly superior performance for IR tasks. Unfortunately, using these models for IR is computationally expensive due to the increased complexity of multi-vector retrieval and scoring. In this paper, we introduce MUVERA (MUlti-VEctor Retrieval Algorithm), a retrieval mechanism which reduces multi-vector similarity search to single-vector similarity search. This enables the usage of off-the-shelf MIPS solvers for multi-vector retrieval. MUVERA asymmetrically generates Fixed Dimensional Encodings (FDEs) of queries and documents, which are vectors whose inner product approximates multi-vector similarity. We prove that FDEs give high-quality $\epsilon$-approximations, thus providing the first single-vector proxy for multi-vector similarity with theoretical guarantees. Empirically, we find that FDEs achieve the same recall as prior state-of-the-art heuristics while retrieving 2-5$\times$ fewer candidates. Compared to prior state of the art implementations, MUVERA achieves consistently good end-to-end recall and latency across a diverse set of the BEIR retrieval datasets, achieving an average of 10% improved recall with 90% lower latency.

Graph Neural Networks

Li Ma, Haoyu Han, Juanhui Li, Harry Shomer, Hui Liu, Xiaofeng Gao, Jiliang Tang

Link prediction, which aims to forecast unseen connections in graphs, is a fundamental task in graph machine learning. Heuristic methods, leveraging a range of different pairwise measures such as common neighbors and shortest paths, often rival the performance of vanilla Graph Neural Networks (GNNs). Therefore, recent advancements in GNNs for link prediction (GNN4LP) have primarily focused on integrating one or a few types of pairwise information. In this work, we reveal that different node pairs within the same dataset necessitate varied pairwise information for accurate prediction and models that only apply the same pairwise information uniformly could achieve suboptimal performance.As a result, we propose a simple mixture of experts model Link-MoE for link prediction. Link-MoE utilizes various GNNs as experts and strategically selects the appropriate expert for each node pair based on various types of pairwise information. Experimental results across diverse real-world datasets demonstrate substantial performance improvement from Link-MoE. Notably, Link-Mo achieves a relative improvement of 18.71% on the MRR metric for the Pubmed dataset and 9.59% on the Hits@100 metric for the ogbl-ppa dataset, compared to the best baselines. The code is available at https://github.com/ml-ml/Link-MoE/.

Probabilistic Methods · Monte Carlo and Sampling Methods

Ye He, Kevin Rojas, Molei Tao

This paper considers the problem of sampling from non-logconcave distribution, based on queries of its unnormalized density. It first describes a framework, Denoising Diffusion Monte Carlo (DDMC), based on the simulation of a denoising diffusion process with its score function approximated by a generic Monte Carlo estimator. DDMC is an oracle-based meta-algorithm, where its oracle is the assumed access to samples that generate a Monte Carlo score estimator. Then we provide an implementation of this oracle, based on rejection sampling, and this turns DDMC into a true algorithm, termed Zeroth-Order Diffusion Monte Carlo (ZOD-MC). We provide convergence analyses by first constructing a general framework, i.e. a performance guarantee for DDMC, without assuming the target distribution to be log-concave or satisfying any isoperimetric inequality. Then we prove that ZOD-MC admits an inverse polynomial dependence on the desired sampling accuracy, albeit still suffering from the curse of dimensionality. Consequently, for low dimensional distributions, ZOD-MC is a very efficient sampler, with performance exceeding latest samplers, including also-denoising-diffusion-based RDMC and RSDMC. Last, we experimentally demonstrate the insensitivity of ZOD-MC to increasingly higher barriers between modes or discontinuity in non-convex potential.

Computer Vision · Image Generation

zheng yu, Yaohua Wang, Siying Cui, Aixi Zhang, Wei-Long Zheng, Senzhang Wang

Facial parts swapping aims to selectively transfer regions of interest from the source image onto the target image while maintaining the rest of the target image unchanged.Most studies on face swapping designed specifically for full-face swapping, are either unable or significantly limited when it comes to swapping individual facial parts, which hinders fine-grained and customized character designs.However, designing such an approach specifically for facial parts swapping is challenged by a reasonable multiple reference feature fusion, which needs to be both efficient and effective.To overcome this challenge, FuseAnyPart is proposed to facilitate the seamless "fuse-any-part" customization of the face.In FuseAnyPart, facial parts from different people are assembled into a complete face in latent space within the Mask-based Fusion Module.Subsequently, the consolidated feature is dispatched to the Addition-based Injection Module forfusion within the UNet of the diffusion model to create novel characters.Extensive experiments qualitatively and quantitatively validate the superiority and robustness of FuseAnyPart.Source codes are available at https://github.com/Thomas-wyh/FuseAnyPart.

Optimization · Bilevel optimization

Ieva Petrulionytė, Julien Mairal, Michael Arbel

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks.

Optimization

Aleksandros Sobczyk, Marko Mladenovic, Mathieu Luisier

Approximating invariant subspaces of generalized eigenvalue problems (GEPs) is a fundamental computational problem at the core of machine learning and scientific computing. It is, for example, the root of Principal Component Analysis (PCA) for dimensionality reduction, data visualization, and noise filtering, and of Density Functional Theory (DFT), arguably the most popular method to calculate the electronic structure of materials. Given Hermitian $H,S\in\mathbb{C}^{n\times n}$, where $S$ is positive-definite, let $\Pi_k$ be the true spectral projector on the invariant subspace that is associated with the $k$ smallest (or largest) eigenvalues of the GEP $HC=SC\Lambda$, for some $k\in[n]$. We show that we can compute a matrix $\widetilde\Pi_k$ such that $\lVert\Pi_k-\widetilde\Pi_k\rVert_2\leq \epsilon$, in $O\left( n^{\omega+\eta}\mathrm{polylog}(n,\epsilon^{-1},\kappa(S),\mathrm{gap}_k^{-1}) \right)$ bit operations in the floating point model, for some $\epsilon\in(0,1)$, with probability $1-1/n$. Here, $\eta>0$ is arbitrarily small, $\omega\lesssim 2.372$ is the matrix multiplication exponent, $\kappa(S)=\lVert S\rVert_2\lVert S^{-1}\rVert_2$, and $\mathrm{gap}_k$ is the gap between eigenvalues $k$ and $k+1$. To achieve such provable "forward-error" guarantees, our methods rely on a new $O(n^{\omega+\eta})$ stability analysis for the Cholesky factorization, and a smoothed analysis for computing spectral gaps, which can be of independent interest.Ultimately, we obtain new matrix multiplication-type bit complexity upper bounds for PCA problems, including classical PCA and (randomized) low-rank approximation.

ZAIXI ZHANG, Marinka Zitnik, Qi Liu

Designing ligand-binding proteins, such as enzymes and biosensors, is essential in bioengineering and protein biology. One critical step in this process involves designing protein pockets, the protein interface binding with the ligand. Current approaches to pocket generation often suffer from time-intensive physical computations or template-based methods, as well as compromised generation quality due to the overlooking of domain knowledge. To tackle these challenges, we propose PocketFlow, a generative model that incorporates protein-ligand interaction priors based on flow matching. During training, PocketFlow learns to model key types of protein-ligand interactions, such as hydrogen bonds. In the sampling, PocketFlow leverages multi-granularity guidance (overall binding affinity and interaction geometry constraints) to facilitate generating high-affinity and valid pockets. Extensive experiments show that PocketFlow outperforms baselines on multiple benchmarks, e.g., achieving an average improvement of 1.29 in Vina Score and 0.05 in scRMSD. Moreover, modeling interactions make PocketFlow a generalized generative model across multiple ligand modalities, including small molecules, peptides, and RNA.

Reinforcement Learning · Planning

Dillon Chen, Sylvie Thiebaux

Graph learning is naturally well suited for use in symbolic, object-centric planning due to its ability to exploit relational structures exhibited in planning domains and to take as input planning instances with arbitrary number of objects. Numeric planning is an extension of symbolic planning in which states may now also exhibit numeric variables. In this work, we propose data-efficient and interpretable machine learning models for learning to solve numeric planning tasks. This involves constructing a new graph kernel for graphs with both continuous and categorical attributes, as well as new optimisation methods for learning heuristic functions for numeric planning. Experiments show that our graph kernels are vastly more efficient and generalise better than graph neural networks for numeric planning, and also yield competitive coverage performance over domain-independent numeric planners.

Language · Dialogue

Dingkang Yang, Jinjie Wei, Dongling Xiao, Shunli Wang, Tong Wu, Gang Li, Mingcheng Li, Shuaibing Wang, Jiawei Chen, Yue Jiang 等

Developing intelligent pediatric consultation systems offers promising prospects for improving diagnostic efficiency, especially in China, where healthcare resources are scarce. Despite recent advances in Large Language Models (LLMs) for Chinese medicine, their performance is sub-optimal in pediatric applications due to inadequate instruction data and vulnerable training procedures.To address the above issues, this paper builds PedCorpus, a high-quality dataset of over 300,000 multi-task instructions from pediatric textbooks, guidelines, and knowledge graph resources to fulfil diverse diagnostic demands. Upon well-designed PedCorpus, we propose PediatricsGPT, the first Chinese pediatric LLM assistant built on a systematic and robust training pipeline.In the continuous pre-training phase, we introduce a hybrid instruction pre-training mechanism to mitigate the internal-injected knowledge inconsistency of LLMs for medical domain adaptation. Immediately, the full-parameter Supervised Fine-Tuning (SFT) is utilized to incorporate the general medical knowledge schema into the models. After that, we devise a direct following preference optimization to enhance the generation of pediatrician-like humanistic responses. In the parameter-efficient secondary SFT phase,a mixture of universal-specific experts strategy is presented to resolve the competency conflict between medical generalist and pediatric expertise mastery. Extensive results based on the metrics, GPT-4, and doctor evaluations on distinct downstream tasks show that PediatricsGPT consistently outperforms previous Chinese medical LLMs. The project and data will be released at https://github.com/ydk122024/PediatricsGPT.

Fairness

Zhuoping Zhou, Davoud Ataee Tarzanagh, Bojian Hou, Qi Long, Li Shen

This paper examines the issue of fairness in the estimation of graphical models (GMs), particularly Gaussian, Covariance, and Ising models. These models play a vital role in understanding complex relationships in high-dimensional data. However, standard GMs can result in biased outcomes, especially when the underlying data involves sensitive characteristics or protected groups. To address this, we introduce a comprehensive framework designed to reduce bias in the estimation of GMs related to protected attributes. Our approach involves the integration of the pairwise graph disparity error and a tailored loss function into a nonsmooth multi-objective optimization problem, striving to achieve fairness across different sensitive groups while maintaining the effectiveness of the GMs. Experimental evaluations on synthetic and real-world datasets demonstrate that our framework effectively mitigates bias without undermining GMs' performance.

Reinforcement Learning · Everything Else

Deqian Kong, Dehong Xu, Minglu Zhao, Bo Pang, Jianwen Xie, Andrew Lizarraga, Yuhao Huang, Sirui Xie, Ying Nian Wu

In tasks aiming for long-term returns, planning becomes essential. We study generative modeling for planning with datasets repurposed from offline reinforcement learning. Specifically, we identify temporal consistency in the absence of step-wise rewards as one key technical challenge. We introduce the Latent Plan Transformer (LPT), a novel model that leverages a latent variable to connect a Transformer- based trajectory generator and the final return. LPT can be learned with maximum likelihood estimation on trajectory-return pairs. In learning, posterior sampling of the latent variable naturally integrates sub-trajectories to form a consistent abstrac- tion despite the finite context. At test time, the latent variable is inferred from an expected return before policy execution, realizing the idea of planning as inference. Our experiments demonstrate that LPT can discover improved decisions from sub- optimal trajectories, achieving competitive performance across several benchmarks, including Gym-Mujoco, Franka Kitchen, Maze2D, and Connect Four. It exhibits capabilities in nuanced credit assignments, trajectory stitching, and adaptation to environmental contingencies. These results validate that latent variable inference can be a strong alternative to step-wise reward prompting.

Miscellaneous Aspects of Machine Learning · Representation Learning

Connor Mclaughlin, Lili Su

Federated learning (FL) is a distributed learning framework that leverages commonalities between distributed client datasets to train a global model. Under heterogeneous clients, however, FL can fail to produce stable training results. Personalized federated learning (PFL) seeks to address this by learning individual models tailored to each client. One approach is to decompose model training into shared representation learning and personalized classifier training. Nonetheless, previous works struggle to navigate the bias-variance trade-off in classifier learning, relying solely on limited local datasets or introducing costly techniques to improve generalization.In this work, we frame representation learning as a generative modeling task, where representations are trained with a classifier based on the global feature distribution. We then propose an algorithm, pFedFDA, that efficiently generates personalized models by adapting global generative classifiers to their local feature distributions. Through extensive computer vision benchmarks, we demonstrate that our method can adjust to complex distribution shifts with significant improvements over current state-of-the-art in data-scarce settings.

Michael Crawshaw, Mingrui Liu

In federated learning, it is common to assume that clients are always available to participate in training, which may not be feasible with user devices in practice. Recent works analyze federated learning under more realistic participation patterns, such as cyclic client availability or arbitrary participation. However, all such works either require strong assumptions (e.g., all clients participate almost surely within a bounded window), do not achieve linear speedup and reduced communication rounds, or are not applicable in the general non-convex setting. In this work, we focus on nonconvex optimization and consider participation patterns in which the chance of participation over a fixed window of rounds is equal among all clients, which includes cyclic client availability as a special case. Under this setting, we propose a new algorithm, named Amplified SCAFFOLD, and prove that it achieves linear speedup, reduced communication, and resilience to data heterogeneity simultaneously. In particular, for cyclic participation, our algorithm is proved to enjoy $\mathcal{O}(\epsilon^{-2})$ communication rounds to find an $\epsilon$-stationary point in the non-convex stochastic setting. In contrast, the prior work under the same setting requires $\mathcal{O}(\kappa^2 \epsilon^{-4})$ communication rounds, where $\kappa$ denotes the data heterogeneity. Therefore, our algorithm significantly reduces communication rounds due to better dependency in terms of $\epsilon$ and $\kappa$. Our analysis relies on a fine-grained treatment of the nested dependence between client participation and errors in the control variates, which results in tighter guarantees than previous work. We also provide experimental results with (1) synthetic data and (2) real-world data with a large number of clients $(N = 250)$, demonstrating the effectiveness of our algorithm under periodic client participation.

Reinforcement Learning · Deep RL

David Yunis, Justin Jung, Falcon Dai, Matthew Walter

Exploration in sparse-reward reinforcement learning (RL) is difficult due to the need for long, coordinated sequences of actions in order to achieve any reward. Skill learning, from demonstrations or interaction, is a promising approach to address this, but skill extraction and inference are expensive for current methods. We present a novel method to extract skills from demonstrations for use in sparse-reward RL, inspired by the popular Byte-Pair Encoding (BPE) algorithm in natural language processing. With these skills, we show strong performance in a variety of tasks, 1000$\times$ acceleration for skill-extraction and 100$\times$ acceleration for policy inference. Given the simplicity of our method, skills extracted from 1\% of the demonstrations in one task can be transferred to a new loosely related task. We also note that such a method yields a finite set of interpretable behaviors. Our code is available at https://github.com/dyunis/subwords_as_skills.

Computer Vision

Yuhang Wen, Mengyuan Liu, Songtao Wu, Beichen Ding

Skeleton-based multi-entity action recognition is a challenging task aiming to identify interactive actions or group activities involving multiple diverse entities. Existing models for individuals often fall short in this task due to the inherent distribution discrepancies among entity skeletons, leading to suboptimal backbone optimization. To this end, we introduce a Convex Hull Adaptive Shift based multi-Entity action recognition method (CHASE), which mitigates inter-entity distribution gaps and unbiases subsequent backbones. Specifically, CHASE comprises a learnable parameterized network and an auxiliary objective. The parameterized network achieves plausible, sample-adaptive repositioning of skeleton sequences through two key components. First, the Implicit Convex Hull Constrained Adaptive Shift ensures that the new origin of the coordinate system is within the skeleton convex hull. Second, the Coefficient Learning Block provides a lightweight parameterization of the mapping from skeleton sequences to their specific coefficients in convex combinations. Moreover, to guide the optimization of this network for discrepancy minimization, we propose the Mini-batch Pair-wise Maximum Mean Discrepancy as the additional objective. CHASE operates as a sample-adaptive normalization method to mitigate inter-entity distribution discrepancies, thereby reducing data bias and improving the subsequent classifier's multi-entity action recognition performance. Extensive experiments on six datasets, including NTU Mutual 11/26, H2O, Assembly101, Collective Activity and Volleyball, consistently verify our approach by seamlessly adapting to single-entity backbones and boosting their performance in multi-entity scenarios. Our code is publicly available at https://github.com/Necolizer/CHASE .