arXiv subjects

Yingzhen Li

Publications and source records attributed to Yingzhen Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

Compact Memory for Continual Logistic Regression

Despite recent progress, continual learning still does not match the performance of batch training. To avoid catastrophic forgetting, we need to build compact memory of essential past knowledge, but no clear solution has yet emerged, even for shallow neural networks with just one or two layers. In this paper, we present a new method to build compact memory for logistic regression. Our method is based on a result by Khan and Swaroop [2021] who show the existence of optimal memory for such models. We formulate the search for the optimal memory as Hessian-matching and propose a probabilistic PCA method to estimate them. Our approach can drastically improve accuracy compared to Experience Replay. For instance, on Split-ImageNet, we get 60% accuracy compared to 30% obtained by replay with memory-size equivalent to 0.3% of the data size. Increasing the memory size to 2% further boosts the accuracy to 74%, closing the gap to the batch accuracy of 77.6% on this task. Our work opens a new direction for building compact memory that can also be useful in the future for continual deep learning.

cs.LG↗

arXiv2025

Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between arbitrary time points. We introduce Neural Stochastic Flows (NSFs) and their latent variants, which directly learn (latent) SDE transition laws using conditional normalising flows with architectural constraints that preserve properties inherited from stochastic flows. This enables one-shot sampling between arbitrary states and yields up to two orders of magnitude speed-ups at large time gaps. Experiments on synthetic SDE simulations and on real-world tracking and video data show that NSFs maintain distributional accuracy comparable to numerical approaches while dramatically reducing computation for arbitrary time-point sampling.

cs.LG↗

arXiv2025

Discrete Neural Flow Samplers with Locally Equivariant Transformer

Sampling from unnormalised discrete distributions is a fundamental problem across various domains. While Markov chain Monte Carlo offers a principled approach, it often suffers from slow mixing and poor convergence. In this paper, we propose Discrete Neural Flow Samplers (DNFS), a trainable and efficient framework for discrete sampling. DNFS learns the rate matrix of a continuous-time Markov chain such that the resulting dynamics satisfy the Kolmogorov equation. As this objective involves the intractable partition function, we then employ control variates to reduce the variance of its Monte Carlo estimation, leading to a coordinate descent learning algorithm. To further facilitate computational efficiency, we propose locally equivaraint Transformer, a novel parameterisation of the rate matrix that significantly improves training efficiency while preserving powerful network expressiveness. Empirically, we demonstrate the efficacy of DNFS in a wide range of applications, including sampling from unnormalised distributions, training discrete energy-based models, and solving combinatorial optimisation problems.

cs.LG↗

arXiv2025

Bayesian Computation in Deep Learning

Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep neural networks. In generative modeling domain, many widely used deep generative models, such as deep latent variable models, require approximate Bayesian inference to infer their latent variables for the training. In this chapter, we provide an introduction to approximate inference techniques as Bayesian computation methods applied to deep learning models, with a focus on Bayesian neural networks and deep generative models. We review two arguably most popular approximate Bayesian computational methods, stochastic gradient Markov chain Monte Carlo (SG-MCMC) and variational inference (VI), and explain their unique challenges in posterior inference as well as the solutions when applied to deep learning models.

cs.LG↗

arXiv2025

HiBBO: HiPPO-based Space Consistency for High-dimensional Bayesian Optimisation

Bayesian Optimisation (BO) is a powerful tool for optimising expensive blackbox functions but its effectiveness diminishes in highdimensional spaces due to sparse data and poor surrogate model scalability While Variational Autoencoder (VAE) based approaches address this by learning low-dimensional latent representations the reconstructionbased objective function often brings the functional distribution mismatch between the latent space and original space leading to suboptimal optimisation performance In this paper we first analyse the reason why reconstructiononly loss may lead to distribution mismatch and then propose HiBBO a novel BO framework that introduces the space consistency into the latent space construction in VAE using HiPPO - a method for longterm sequence modelling - to reduce the functional distribution mismatch between the latent space and original space Experiments on highdimensional benchmark tasks demonstrate that HiBBO outperforms existing VAEBO methods in convergence speed and solution quality Our work bridges the gap between high-dimensional sequence representation learning and efficient Bayesian Optimisation enabling broader applications in neural architecture search materials science and beyond.

cs.LG↗

arXiv2025

Memory-Driven Self-Improvement for Decision Making with Large Language Models

Large language models (LLMs) have emerged as effective action policies for sequential decision-making (SDM) tasks due to their extensive prior knowledge. However, this broad yet general knowledge is often insufficient for specific decision-making tasks with limited task-related data, making it challenging to efficiently adapt LLMs to specific SDM tasks. To address this challenge, we propose a memory-driven self-improvement framework that combines LLM general prior knowledge with a compact memory of domain-specific experiences. Memory retains past interactions and associated Q-values, thereby capturing decision-relevant knowledge that facilitates accurate value estimation and informs the LLM prior refinement. The refined LLM prior, in turn, generates higher-reward trajectories that further enrich memory, forming a natural self-improvement framework where memory and LLM prior mutually reinforce each other. Experiments show that our memory-driven approach significantly outperforms both traditional RL and LLM-based baselines, e.g., improving performance by over 40\% on in-distribution tasks and over 75\% when generalized to unseen tasks in ALFWorld.

cs.LG↗

arXiv2025

Recurrent Memory for Online Interdomain Gaussian Processes

We propose a novel online Gaussian process (GP) model that is capable of capturing long-term memory in sequential data in an online learning setting. Our model, Online HiPPO Sparse Variational Gaussian Process (OHSVGP), leverages the HiPPO (High-order Polynomial Projection Operators) framework, which is popularized in the RNN domain due to its long-range memory modeling capabilities. We interpret the HiPPO time-varying orthogonal projections as inducing variables with time-dependent orthogonal polynomial basis functions, which allows the SVGP inducing variables to memorize the process history. We show that the HiPPO framework fits naturally into the interdomain GP framework and demonstrate that the kernel matrices can also be updated online in a recurrence form based on the ODE evolution of HiPPO. We evaluate OHSVGP with online prediction for 1D time series, continual learning in discriminative GP model for data with multidimensional inputs, and deep generative modeling with sparse Gaussian process variational autoencoder, showing that it outperforms existing online GP methods in terms of predictive performance, long-term memory preservation, and computational efficiency.

cs.LG↗

arXiv2025

Your Image is Secretly the Last Frame of a Pseudo Video

Diffusion models, which can be viewed as a special case of hierarchical variational autoencoders (HVAEs), have shown profound success in generating photo-realistic images. In contrast, standard HVAEs often produce images of inferior quality compared to diffusion models. In this paper, we hypothesize that the success of diffusion models can be partly attributed to the additional self-supervision information for their intermediate latent states provided by corrupted images, which along with the original image form a pseudo video. Based on this hypothesis, we explore the possibility of improving other types of generative models with such pseudo videos. Specifically, we first extend a given image generative model to their video generative model counterpart, and then train the video generative model on pseudo videos constructed by applying data augmentation to the original images. Furthermore, we analyze the potential issues of first-order Markov data augmentation methods, which are typically used in diffusion models, and propose to use more expressive data augmentation to construct more useful information in pseudo videos. Our empirical results on the CIFAR10 and CelebA datasets demonstrate that improved image generation quality can be achieved with additional self-supervised information from pseudo videos.

cs.CV↗

arXiv2025

Calibrating Transformers via Sparse Gaussian Processes

Transformer models have achieved profound success in prediction tasks in a wide range of applications in natural language processing, speech recognition and computer vision. Extending Transformer's success to safety-critical domains requires calibrated uncertainty estimation which remains under-explored. To address this, we propose Sparse Gaussian Process attention (SGPA), which performs Bayesian inference directly in the output space of multi-head attention blocks (MHAs) in transformer to calibrate its uncertainty. It replaces the scaled dot-product operation with a valid symmetric kernel and uses sparse Gaussian processes (SGP) techniques to approximate the posterior processes of MHA outputs. Empirically, on a suite of prediction tasks on text, images and graphs, SGPA-based Transformers achieve competitive predictive accuracy, while noticeably improving both in-distribution calibration and out-of-distribution robustness and detection.

cs.LG↗

arXiv2025

On the Challenges and Opportunities in Generative AI

The field of deep generative modeling has grown rapidly in the last few years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models exhibit several fundamental shortcomings that hinder their widespread adoption across domains. In this work, our objective is to identify these issues and highlight key unresolved challenges in modern generative AI paradigms that should be addressed to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with insights for exploring fruitful research directions, thus fostering the development of more robust and accessible generative AI solutions.

cs.LG↗

arXiv2025

Neural Flow Samplers with Shortcut Models

Sampling from unnormalized densities presents a fundamental challenge with wide-ranging applications, from posterior inference to molecular dynamics simulations. Continuous flow-based neural samplers offer a promising approach, learning a velocity field that satisfies key principles of marginal density evolution (e.g., the continuity equation) to generate samples. However, this learning procedure requires accurate estimation of intractable terms linked to the computationally challenging partition function, for which existing estimators often suffer from high variance or low accuracy. To overcome this, we introduce an improved estimator for these challenging quantities, employing a velocity-driven Sequential Monte Carlo method enhanced with control variates. Furthermore, we introduce a shortcut consistency model to boost the runtime efficiency of the flow-based neural sampler by minimizing its required sampling steps. Our proposed Neural Flow Shortcut Sampler empirically outperforms existing flow-based neural samplers on both synthetic datasets and complex n-body system targets.

cs.LG↗

arXiv2025

Causal Discovery from Conditionally Stationary Time Series

Causal discovery, i.e., inferring underlying causal relationships from observational data, is highly challenging for AI systems. In a time series modeling context, traditional causal discovery methods mainly consider constrained scenarios with fully observed variables and/or data from stationary time-series. We develop a causal discovery approach to handle a wide class of nonstationary time series that are conditionally stationary, where the nonstationary behaviour is modeled as stationarity conditioned on a set of latent state variables. Named State-Dependent Causal Inference (SDCI), our approach is able to recover the underlying causal dependencies, with provable identifiablity for the state-dependent causal structures. Empirical experiments on nonlinear particle interaction data and gene regulatory networks demonstrate SDCI's superior performance over baseline causal discovery methods. Improved results over non-causal RNNs on modeling NBA player movements demonstrate the potential of our method and motivate the use of causality-driven methods for forecasting.

cs.LG↗

arXiv2025

Unsupervised Accelerated MRI Reconstruction via Ground-Truth-Free Flow Matching

Accelerated magnetic resonance imaging involves reconstructing fully sampled images from undersampled k-space measurements. Current state-of-the-art approaches have mainly focused on either end-to-end supervised training inspired by compressed sensing formulations, or posterior sampling methods built on modern generative models. However, their efficacy heavily relies on large datasets of fully sampled images, which may not always be available in practice. To address this issue, we propose an unsupervised MRI reconstruction method based on ground-truth-free flow matching (GTF$^2$M). Particularly, the GTF$^2$M learns a prior denoising process of fully sampled ground-truth images using only undersampled data. Based on that, an efficient cyclic reconstruction algorithm is further proposed to perform forward and backward integration in the dual space of image-space signal and k-space measurement. We compared our method with state-of-the-art learning-based baselines on the fastMRI database of both single-coil knee and multi-coil brain MRIs. The results show that our proposed unsupervised method can significantly outperform existing unsupervised approaches, and achieve performance comparable to most supervised end-to-end and prior learning baselines trained on fully sampled MRI, while offering greater efficiency than the compared generative model-based approaches.

eess.IV↗

arXiv2025

Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matching

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed covariance moment matching technique and introduce a novel method for learning the diagonal covariance. Unlike traditional data-driven diagonal covariance approximation approaches, our method involves directly regressing the optimal diagonal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency, recall rate and likelihood of commonly used diffusion models.

cs.LG↗

arXiv2024

Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces

Energy-based models (EBMs) offer a flexible framework for probabilistic modelling across various data domains. However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo. We introduce perturbations of the data distribution by simulating a diffusion process on the discrete state space endowed with a graph structure. This allows us to inform the choice of perturbation from the structure of the modelled discrete variable, while the continuous time parameter enables fine-grained control of the perturbation. Empirically, we demonstrate the efficacy of the proposed approaches in a wide range of applications, including the estimation of discrete densities with non-binary vocabulary and binary image modelling. Finally, we train EBMs on tabular data sets with applications in synthetic data generation and calibrated classification.

stat.ML↗

arXiv2024

Mutual Information Multinomial Estimation

Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. This work proposes a new estimator for mutual information. Our main discovery is that a preliminary estimate of the data distribution can dramatically help estimate. This preliminary estimate serves as a bridge between the joint and the marginal distribution, and by comparing with this bridge distribution we can easily obtain the true difference between the joint distributions and the marginal distributions. Experiments on diverse tasks including non-Gaussian synthetic problems with known ground-truth and real-world applications demonstrate the advantages of our method.

cs.LG↗

arXiv2024

Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

cs.LG↗

arXiv2024

Identifying Nonstationary Causal Structures with High-Order Markov Switching Models

Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to nonstationary time series with time-dependent effects or heterogeneous noise. In this work we address nonstationarity via regime-dependent causal structures. We first establish identifiability for high-order Markov Switching Models, which provide the foundations for identifiable regime-dependent causal discovery. Our empirical studies demonstrate the scalability of our proposed approach for high-order regime-dependent structure estimation, and we illustrate its applicability on brain activity data.

stat.ML↗