GenAI4ELab/papercli-papers huggingface dataset:
Score-based Generative Modeling through Stochastic Evolution Equations in Hilbert Spaces
Authors: Sungbin Lim; Eunbi Yoon; Taehyun Byun; Taewon Kang; Seungwoo Kim; Kyungjae Lee; Sungjoon Choi
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: Continuous-time score-based generative models consist of a pair of stochastic differential equations (SDEs)—a forward SDE that smoothly transitions data into a noise space and a reverse SDE that incrementally eliminates noise from a Gaussian prior distribution to generate data distribution samples—are intrinsically connected by the time-reversal theory on diffusion processes. In this paper, we investigate the use of stochastic evolution equations in Hilbert spaces, which expand the applicability of SDEs in two aspects: sample space and evolution operator, so they enable encompassing recent variations of diffusion models, such as generating functional data or replacing drift coefficients with image transformation. To this end, we derive a generalized time-reversal formula to build a bridge between probabilistic diffusion models and stochastic evolution equations and propose a score-based generative model called Hilbert Diffusion Model (HDM). Combining with Fourier neural operator, we verify the superiority of HDM for sampling functions from functional datasets with a power of kernel two-sample test of 4.2 on Quadratic, 0.2 on Melbourne, and 3.6 on Gridwatch, which outperforms existing diffusion models formulated in function spaces. Furthermore, the proposed method shows its strength in motion synthesis tasks by utilizing the Wiener process with values in Hilbert space. Finally, our empirical results on image datasets also validate a connection between HDM and diffusion models using heat dissipation, revealing the potential for exploring evolution operators and sample spaces.
Global Identifiability of  $\ell_1$-based Dictionary Learning via Matrix Volume Optimization
Authors: Jingzhou Hu; Kejun Huang
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: We propose a novel formulation for dictionary learning that minimizes the determinant of the dictionary matrix, also known as its volume, subject to the constraint that each row of the sparse coefficient matrix has unit $\ell_1$ norm. The main motivation for the proposed formulation is that it provides global identifiability guarantee of the groundtruth dictionary and sparse coefficient matrices, up to the inherent and inconsequential permutation and scaling ambiguity, if a set of vectors obtained from the coefficient matrix lies inside the $\ell_\infty$ norm ball but contains the $\ell_2$ norm ball in their convex hull. Unlike existing work on identifiability of dictionary learning, our result is global, meaning that a globally optimal solution to our proposed formulation has to be a permuted and rescaled version of the groundtruth factors. Another major improvement in our result is that there is no additional assumption on the dictionary matrix other than it is nonsingular, unlike most other work that require the atoms of the dictionary to be mutually incoherent. We also provide a probabilistic analysis and show that if the sparse coefficient matrix is generated from the widely adopted Bernoulli-Gaussian model, then it is globally identifiable if the sample size is bigger than a constant times $k\log k$, where $k$ is the number atoms in the dictionary, with overwhelming probability. The bound is essentially the same as those local identifiability results, but we show that it is also global. Finally, we propose algorithms to solve the new proposed formulation, specifically one based on the linearized-ADMM with efficient per-iteration updates. The proposed algorithms exhibit surprisingly effective performance in correctly and efficiently recovering the dictionary, as demonstrated in the numerical experiments.
Worst-case Performance of Popular Approximate Nearest Neighbor Search Implementations: Guarantees and Limitations
Authors: Piotr Indyk; Haike Xu
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. 
We study the worst-case performance of recent graph-based approximate nearest neighbor search algorithms, such as HNSW, NSG and DiskANN. For DiskANN, we show that its "slow preprocessing'' version provably supports approximate nearest neighbor search query with constant approximation ratio and poly-logarithmic query time, on data sets with bounded "intrinsic'' dimension. 
For the other data structure variants studied, including DiskANN with "fast preprocessing'',  HNSW and NSG,  we present a family of instances on which the empirical query time required to achieve a "reasonable'' accuracy is linear in instance size. For example, for DiskANN, we show that the query procedure can take at least  $0.1 n$ steps on instances of size $n$ before it encounters any of the $5$ nearest neighbors of the query.
Learning a 1-layer conditional generative model in total variation
Authors: Ajil Jalal; Justin Kang; Ananya Uppal; Kannan Ramchandran; Eric Price
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: A conditional generative model is a method for sampling from a conditional distribution $p(y \mid x)$.  For example, one may want to sample an image of a cat given the label ``cat''.  A feed-forward conditional generative model is a function $g(x, z)$ that takes the input $x$ and a random seed $z$, and outputs a sample $y$ from $p(y \mid x)$.  Ideally the distribution of outputs $(x, g(x, z))$ would be close in total variation to the ideal distribution $(x, y)$.

Generalization bounds for other learning models require assumptions on the distribution of $x$, even in simple settings like linear regression with Gaussian noise. We show these assumptions are unnecessary in our model, for both linear regression and single-layer ReLU networks.  Given samples $(x, y)$, we show how to learn a 1-layer ReLU conditional generative model in total variation. As our result has no assumption on the distribution of inputs $x$, if we are given access to the internal activations of a deep generative model, we can compose our 1-layer guarantee to progressively learn the deep model using a near-linear number of samples.
Beyond Normal: On the Evaluation of Mutual Information Estimators
Authors: Paweł Czyż; Frederic Grabowski; Julia E Vogt; Niko Beerenwinkel; Alexander Marx
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically evaluated on simple families of probability distributions, namely multivariate normal distribution and selected distributions with one-dimensional random variables. In this paper, we show how to construct a diverse family of distributions with known ground-truth mutual information and propose a language-independent benchmarking platform for mutual information estimators. We discuss the general applicability and limitations of classical and neural estimators in settings involving high dimensions, sparse interactions, long-tailed distributions, and high mutual information. Finally, we provide guidelines for practitioners on how to select appropriate estimator adapted to the difficulty of problem considered and issues one needs to consider when applying an estimator to a new data set.
TaskMet: Task-driven Metric Learning for Model Learning
Authors: Dishank Bansal; Ricky T. Q. Chen; Mustafa Mukadam; Brandon Amos
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Deep learning models are often used with some downstream task. Models solely trained to achieve accurate predictions may struggle to perform well on the desired downstream tasks. We propose using the task loss to learn a metric which parameterizes a loss to train the model. This approach does not alter the optimal prediction model itself, but rather changes the model learning to emphasize the information important for the downstream task. This enables us to achieve the best of both worlds: a prediction model trained in the original prediction space while also being valuable for the desired downstream task. We validate our approach through experiments conducted in two main settings: 1) decision-focused model learning scenarios involving portfolio optimization and budget allocation, and 2) reinforcement learning in noisy environments with distracting states.
High-dimensional Contextual Bandit Problem without Sparsity
Authors: Junpei Komiyama; Masaaki Imaizumi
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: In this research, we investigate the high-dimensional linear contextual bandit problem where the number of features $p$ is greater than the budget $T$, or it may even be infinite. Differing from the majority of previous works in this field, we do not impose sparsity on the regression coefficients. Instead, we rely on recent findings on overparameterized models, which enables us to analyze the performance of the minimum-norm interpolating estimator when data distributions have small effective ranks. We propose an explore-then-commit (EtC) algorithm to address this problem and examine its performance. Through our analysis, we derive the optimal rate of the ETC algorithm in terms of $T$ and show that this rate can be achieved by balancing exploration and exploitation. Moreover, we introduce an adaptive explore-then-commit (AEtC) algorithm that adaptively finds the optimal balance. We assess the performance of the proposed algorithms through a series of simulations.
Uncertainty Quantification over Graph with Conformalized Graph Neural Networks
Authors: Kexin Huang; Ying Jin; Emmanuel Candes; Jure Leskovec
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is significant. We propose conformalized GNN (CF-GNN), extending conformal prediction (CP) to graph-based models for guaranteed uncertainty estimates. Given an entity in the graph, CF-GNN produces a prediction set/interval that provably contains the true label with pre-defined coverage probability (e.g. 90%). We establish a permutation invariance condition that enables the validity of CP on graph data and provide an exact characterization of the test-time coverage. Moreover, besides valid coverage, it is crucial to reduce the prediction set size/interval length for practical use. We observe a key connection between non-conformity scores and network structures, which motivates us to develop a topology-aware output correction model that learns to update the prediction and produces more efficient prediction sets/intervals. Extensive experiments show that CF-GNN achieves any pre-defined target marginal coverage while significantly reducing the prediction set/interval size by up to 74% over the baselines. It also empirically achieves satisfactory conditional coverage over various raw and network features.
Bayesian Learning via Q-Exponential Process
Authors: Shuyi Li; Michael O'Connor; Shiwei Lan
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Regularization is one of the most fundamental topics in optimization, statistics and machine learning. To get sparsity in estimating a parameter $u\in\mathbb{R}^d$, an $\ell_q$ penalty term, $\Vert u\Vert_q$, is usually added to the objective function. What is the probabilistic distribution corresponding to such $\ell_q$ penalty? What is the \emph{correct} stochastic process corresponding to $\Vert u\Vert_q$ when we model functions $u\in L^q$? This is important for statistically modeling high-dimensional objects such as images, with penalty to preserve certainty properties, e.g. edges in the image.
In this work, we generalize the $q$-exponential distribution (with density proportional to) $\exp{(- \frac{1}{2}|u|^q)}$ to a stochastic process named \emph{$Q$-exponential (Q-EP) process} that corresponds to the $L_q$ regularization of functions. The key step is to specify consistent multivariate $q$-exponential distributions by choosing from a large family of elliptic contour distributions. The work is closely related to Besov process which is usually defined in terms of series. Q-EP can be regarded as a definition of Besov process with explicit probabilistic formulation, direct control on the correlation strength, and tractable prediction formula. From the Bayesian perspective, Q-EP provides a flexible prior on functions with sharper penalty ($q<2$) than the commonly used Gaussian process (GP, $q=2$).
We compare GP, Besov and Q-EP in modeling functional data, reconstructing images and solving inverse problems and demonstrate the advantage of our proposed methodology.
The Double-Edged Sword of Implicit Bias: Generalization vs. Robustness in ReLU Networks
Authors: Spencer Frei; Gal Vardi; Peter Bartlett; Nathan Srebro
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: In this work, we study the implications of the implicit bias of gradient flow on generalization and adversarial robustness in ReLU networks.  We focus on a setting where the data consists of clusters and the correlations between cluster means are small, and show that in two-layer ReLU networks gradient flow is biased towards solutions that generalize well, but are vulnerable to adversarial examples. Our results hold even in cases where the network is highly overparameterized.  Despite the potential for harmful overfitting in such settings, we prove that the implicit bias of gradient flow prevents it.  However, the implicit bias also leads to non-robust solutions (susceptible to small adversarial $\ell_2$-perturbations), even though robust networks that fit the data exist.
Deep Reinforcement Learning with Plasticity Injection
Authors: Evgenii Nikishin; Junhyuk Oh; Georg Ostrovski; Clare Lyle; Razvan Pascanu; Will Dabney; Andre Barreto
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: A growing body of evidence suggests that neural networks employed in deep reinforcement learning (RL) gradually lose their plasticity, the ability to learn from new data; however, the analysis and mitigation of this phenomenon is hampered by the complex relationship between plasticity, exploration, and performance in RL. This paper introduces plasticity injection, a minimalistic intervention that increases the network plasticity without changing the number of trainable parameters or biasing the predictions. The applications of this intervention are two-fold: first, as a diagnostic tool — if injection increases the performance, we may conclude that an agent's network was losing its plasticity. This tool allows us to identify a subset of Atari environments where the lack of plasticity causes performance plateaus, motivating future studies on understanding and combating plasticity loss. Second, plasticity injection can be used to improve the computational efficiency of RL training if the agent has to re-learn from scratch due to exhausted plasticity or by growing the agent's network dynamically without compromising performance. The results on Atari show that plasticity injection attains stronger performance compared to alternative methods while being computationally efficient.
Learning Energy-based Model via Dual-MCMC Teaching
Authors: Jiali Cui; Tian Han
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: This paper studies the fundamental learning problem of the energy-based model (EBM). Learning the EBM can be achieved using the maximum likelihood estimation (MLE), which typically involves the Markov Chain Monte Carlo (MCMC) sampling, such as the Langevin dynamics. However, the noise-initialized Langevin dynamics can be challenging in practice and hard to mix. This motivates the exploration of joint training with the generator model where the generator model serves as a complementary model to bypass MCMC sampling. However, such a method can be less accurate than the MCMC and result in biased EBM learning. While the generator can also serve as an initializer model for better MCMC sampling, its learning can be biased since it only matches the EBM and has no access to empirical training examples. Such biased generator learning may limit the potential of learning the EBM. To address this issue, we present a joint learning framework that interweaves the maximum likelihood learning algorithm for both the EBM and the complementary generator model. In particular, the generator model is learned by MLE to match both the EBM and the empirical data distribution, making it a more informative initializer for MCMC sampling of EBM. Learning generator with observed examples typically requires inference of the generator posterior. To ensure accurate and efficient inference, we adopt the MCMC posterior sampling and introduce a complementary inference model to initialize such latent MCMC sampling. We show that three separate models can be seamlessly integrated into our joint framework through two (dual-) MCMC teaching, enabling effective and efficient EBM learning.
Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting
Authors: Marcel Kollovieh; Abdul Fatir Ansari; Michael Bohlke-Schneider; Jasper Zschiegner; Hao Wang; Bernie Wang
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (*predict*). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (*refine*). Notably, the generative performance of the model remains intact — downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (*synthesize*).

Our code is available at https://github.com/amazon-science/unconditional-time-series-diffusion
Uncertainty Quantification via Neural Posterior Principal Components
Authors: Elias Nehme; Omer Yair; Tomer Michaeli
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Uncertainty quantification is crucial for the deployment of image restoration models in safety-critical domains, like autonomous driving and biological imaging. To date, methods for uncertainty visualization have mainly focused on per-pixel estimates. Yet, a heatmap of per-pixel variances is typically of little practical use, as it does not capture the strong correlations between pixels. A more natural measure of uncertainty corresponds to the variances along the principal components (PCs) of the posterior distribution. Theoretically, the PCs can be computed by applying PCA on samples generated from a conditional generative model for the input image. However, this requires generating a very large number of samples at test time, which is painfully slow with the current state-of-the-art (diffusion) models. In this work, we present a method for predicting the PCs of the posterior distribution for any input image, in a single forward pass of a neural network. Our method can either wrap around a pre-trained model that was trained to minimize the mean square error (MSE), or can be trained from scratch to output both a predicted image and the posterior PCs. We showcase our method on multiple inverse problems in imaging, including denoising, inpainting, super-resolution, and biological image-to-image translation. Our method reliably conveys instance-adaptive uncertainty directions, achieving uncertainty quantification comparable with posterior samplers while being orders of magnitude faster. Code and examples are available on our [webpage](https://eliasnehme.github.io/NPPC/).
FedGCN: Convergence-Communication Tradeoffs in Federated Training of Graph Convolutional Networks
Authors: Yuhang Yao; Weizhao Jin; Srivatsan Ravi; Carlee Joe-Wong
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Methods for training models on graphs distributed across multiple clients have recently grown in popularity, due to the size of these graphs as well as regulations on keeping data where it is generated. However, the cross-client edges naturally exist among clients. Thus, distributed methods for training a model on a single graph incur either significant communication overhead between clients or a loss of available information to the training. We introduce the Federated Graph Convolutional Network (FedGCN) algorithm, which uses federated learning to train GCN models for semi-supervised node classification with fast convergence and little communication. Compared to prior methods that require extra communication among clients at each training round, FedGCN clients only communicate with the central server in one pre-training step, greatly reducing communication costs and allowing the use of homomorphic encryption to further enhance privacy. We theoretically analyze the tradeoff between FedGCN's convergence rate and communication cost under different data distributions. Experimental results show that our FedGCN algorithm achieves better model accuracy with 51.7\% faster convergence on average and at least 100$\times$ less communication compared to prior work.
Contextual Stochastic Bilevel Optimization
Authors: Yifan Hu; Jie Wang; Yao Xie; Andreas Krause; Daniel Kuhn
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework extends classical stochastic bilevel optimization when the lower-level decision maker responds optimally not only to the decision of the upper-level decision maker but also to some side information and when there are multiple or even infinite many followers. It captures important applications such as meta-learning, personalized federated learning, end-to-end learning, and Wasserstein distributionally robust optimization with side information (WDRO-SI). Due to the presence of contextual information, existing single-loop methods for classical stochastic bilevel optimization are unable to converge. To overcome this challenge, we introduce an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities. When specialized to stochastic nonconvex optimization, our method matches  existing lower bounds. For meta-learning, the complexity of our method does not depend on the number of tasks. Numerical experiments further validate our theoretical results.