GenAI4ELab/papercli-papers huggingface dataset:
Escaping saddle points in zeroth-order optimization: the power of two-point estimators
Authors: Zhaolin Ren; Yujie Tang; Na Li
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Two-point zeroth order methods are important in many applications of zeroth-order optimization arising in robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where the problem can be high-dimensional and/or time-varying. Furthermore, such problems may be nonconvex and contain saddle points. While existing works have shown that zeroth-order methods utilizing $\Omega(d)$ function valuations per iteration (with $d$ denoting the problem dimension) can escape saddle points efficiently, it remains an open question if zeroth-order methods based on two-point estimators can escape saddle points. In this paper, we show that by adding an appropriate isotropic perturbation at each iteration, a zeroth-order algorithm based on $2m$ (for any $1 \leq m \leq d$) function evaluations per iteration can not only find $\epsilon$-second order stationary points polynomially fast, but do so using only $\tilde{O}(\frac{d}{m\epsilon^{2}\bar{\psi}})$ function evaluations, where $\bar{\psi} \geq \tilde{\Omega}(\sqrt{\epsilon})$ is a parameter capturing the extent to which the function of interest exhibits the strict saddle property.
SE(3) diffusion model with application to protein backbone generation
Authors: Jason Yim; Brian L. Trippe; Valentin De Bortoli; Emile Mathieu; Arnaud Doucet; Regina Barzilay; Tommi S. Jaakkola
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: The design of novel protein structures remains a challenge in protein engineering for applications across biomedicine and chemistry. In this line of work, a diffusion model over rigid bodies in 3D (referred to as frames) has shown success in generating novel, functional protein backbones that have not been observed in nature. However, there exists no principled methodological framework for diffusion on SE(3), the space of orientation preserving rigid motions in R3, that operates on frames and confers the group invariance. We address these shortcomings by developing theoretical foundations of SE(3) invariant diffusion models on multiple frames followed by a novel framework, FrameDiff, for estimating the SE(3) equivariant score over multiple frames. We apply FrameDiff on monomer backbone generation and find it can generate designable monomers up to 500 amino acids without relying on a pretrained protein structure prediction network that has been integral to previous methods. We find our samples are capable of generalizing beyond any known protein structure.
FeDXL: Provable Federated Learning for Deep X-Risk Optimization
Authors: Zhishuai Guo; Rong Jin; Jiebo Luo; Tianbao Yang
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: In this paper, we tackle a novel federated learning (FL) problem for optimizing a family of X-risks, to which no existing FL algorithms are applicable. In particular, the objective has the form of $\mathbb{E}\_{\mathbf{z}\sim \mathcal{S}\_1} f(\mathbb{E}\_{\mathbf{z}'\sim\mathcal{S}\_2} \ell(\mathbf{w}; \mathbf{z}, \mathbf{z}'))$, where two sets of data $\mathcal S\_1, \mathcal S\_2$ are distributed over multiple machines, $\ell(\cdot; \cdot,\cdot)$ is a pairwise loss that only depends on the prediction outputs of the input data pairs $(\mathbf{z}, \mathbf{z}')$. This problem has important applications in machine learning, e.g., AUROC maximization with a pairwise loss, and partial AUROC maximization with a compositional loss. The challenges for designing an FL algorithm for X-risks lie in the non-decomposability of the objective over multiple machines and the interdependency between different machines. To this end, we propose an active-passive decomposition framework that decouples the gradient's components with two types, namely active parts and passive parts, where the active parts depend on local data that are computed with the local model and the passive parts depend on other machines that are communicated/computed based on historical models and samples. Under this framework, we design two FL algorithms (FeDXL) for handling linear and nonlinear $f$, respectively, based on federated averaging and merging and develop a novel theoretical analysis to combat the latency of the passive parts and the interdependency between the local model parameters and the involved data for computing local gradient estimators. We establish both iteration and communication complexities and show that using the historical samples and models for computing the passive parts do not degrade the complexities. We conduct empirical studies of FeDXL for deep AUROC and partial AUROC maximization, and demonstrate their performance compared with several baselines.
On the Correctness of Automatic Differentiation for Neural Networks with Machine-Representable Parameters
Authors: Wonyeol Lee; Sejun Park; Alex Aiken
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Recent work has shown that forward- and reverse- mode automatic differentiation (AD) over the reals is almost always correct in a mathematically precise sense. However, actual programs work with machine-representable numbers (e.g., floating-point numbers), not reals. In this paper, we study the correctness of AD when the parameter space of a neural network consists solely of machine-representable numbers. In particular, we analyze two sets of parameters on which AD can be incorrect: the incorrect set on which the network is differentiable but AD does not compute its derivative, and the non-differentiable set on which the network is non-differentiable. For a neural network with bias parameters, we first prove that the incorrect set is always empty. We then prove a tight bound on the size of the non-differentiable set, which is linear in the number of non-differentiabilities in activation functions, and give a simple necessary and sufficient condition for a parameter to be in this set. We further prove that AD always computes a Clarke subderivative even on the non-differentiable set. We also extend these results to neural networks possibly without bias parameters.
What can online reinforcement learning with function approximation benefit from general coverage conditions?
Authors: Fanghui Liu; Luca Viano; Volkan Cevher
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: In online reinforcement learning (RL), instead of employing standard structural assumptions on Markov decision processes (MDPs), using a certain coverage condition (original from offline RL) is enough to ensure sample-efficient guarantees (Xie et al. 2023). In this work, we focus on this new direction by digging more possible and general coverage conditions, and study the potential and the utility of them in efficient online RL. We identify more concepts, including the $L^p$ variant of concentrability, the density ratio realizability, and trade-off on the partial/rest coverage condition, that can be also beneficial to sample-efficient online RL, achieving improved regret bound. Furthermore, if exploratory offline data are used, under our coverage conditions, both statistically and computationally efficient guarantees can be achieved for online RL. Besides, even though the MDP structure is given, e.g., linear MDP, we elucidate that, good coverage conditions are still beneficial to obtain faster regret bound beyond $\widetilde{\mathcal{O}}(\sqrt{T})$ and even a logarithmic order regret. These results provide a good justification for the usage of general coverage conditions in efficient online RL.
Graph Mixup with Soft Alignments
Authors: Hongyi Ling; Zhimeng Jiang; Meng Liu; Shuiwang Ji; Na Zou
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: We study graph data augmentation by mixup, which has been used successfully on images. A key operation of mixup is to compute a convex combination of a pair of inputs. This operation is straightforward for grid-like data, such as images, but challenging for graph data. The key difficulty lies in the fact that different graphs typically have different numbers of nodes, and thus there lacks a node-level correspondence between graphs. In this work, we propose S-Mixup, a simple yet effective mixup method for graph classification by soft alignments. Specifically, given a pair of graphs, we explicitly obtain node-level correspondence via computing a soft assignment matrix to match the nodes between two graphs. Based on the soft assignments, we transform the adjacency and node feature matrices of one graph, so that the transformed graph is aligned with the other graph. In this way, any pair of graphs can be mixed directly to generate an augmented graph. We conduct systematic experiments to show that S-Mixup can improve the performance and generalization of graph neural networks (GNNs) on various graph classification tasks. In addition, we show that S-Mixup can increase the robustness of GNNs against noisy labels. Our code is publicly available as part of the DIG package (https://github.com/divelab/DIG).
Transformers Meet Directed Graphs
Authors: Simon Geisler; Yujia Li; Daniel J Mankowitz; Ali Taylan Cemgil; Stephan Günnemann; Cosmin Paduraru
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains, including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian — a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.
Unveiling The Mask of Position-Information Pattern Through the Mist of Image Features
Authors: Chieh Hubert Lin; Hung-Yu Tseng; Hsin-Ying Lee; Maneesh Kumar Singh; Ming-Hsuan Yang
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Recent studies have shown that paddings in convolutional neural networks encode absolute position information which can negatively affect the model performance for certain tasks. However, existing metrics for quantifying the strength of positional information remain unreliable and frequently lead to erroneous results. To address this issue, we propose novel metrics for measuring and visualizing the encoded positional information. We formally define the encoded information as Position-information Pattern from Padding (PPP) and conduct a series of experiments to study its properties as well as its formation. The proposed metrics measure the presence of positional information more reliably than the existing metrics based on PosENet and tests in F-Conv. We also demonstrate that for any extant (and proposed) padding schemes, PPP is primarily a learning artifact and is less dependent on the characteristics of the underlying padding schemes.
The Fast Johnson-Lindenstrauss Transform Is Even Faster
Authors: Ora Nova Fandina; Mikael Møller Høgsgaard; Kasper Green Larsen
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: The Johnson-Lindenstaruss lemma (Johnson & Lindenstrauss, 1984) is a cornerstone result in dimensionality reduction, stating it is possible to embed a set of $n$ points in $d$-dimensional Euclidean space into optimal $k=O(\varepsilon^{-2} \ln n)$ dimensions, while preserving all pairwise distances to within a factor $(1 \pm \varepsilon)$. The seminal Fast Johnson-Lindenstrauss (Fast JL) transform by Ailon and Chazelle (SICOMP'09) supports computing the embedding of a data point in $O(d \ln d +k \ln^2 n)$ time, where the $d \ln d$ term comes from multiplication with a $d \times d$ Hadamard matrix and the $k \ln^2 n$ term comes from multiplication with a sparse $k \times d$ matrix. Despite the Fast JL transform being more than a decade old, it is one of the fastest dimensionality reduction techniques for many tradeoffs between $\varepsilon, d$ and $n$. In this work, we give a surprising new analysis of the Fast JL transform, showing that the $k \ln^2 n$ term in the embedding time can be improved to $(k \ln^2 n)/\alpha$ for an $\alpha = \Omega(\min\{\varepsilon^{-1}\ln(1/\varepsilon), \ln n\})$. The improvement follows by using an even sparser matrix. We complement our improved analysis with a lower bound showing that our new analysis is in fact tight.
Perturbation Analysis of Neural Collapse
Authors: Tom Tirer; Haoxiang Huang; Jonathan Niles-Weed
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.
Stabilizing Transformer Training by Preventing Attention Entropy Collapse
Authors: Shuangfei Zhai; Tatiana Likhomanenko; Etai Littwin; Dan Busbridge; Jason Ramapuram; Yizhe Zhang; Jiatao Gu; Joshua M. Susskind
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Training stability is of great importance to Transformers. In this work, we investigate the training dynamics of Transformers by examining the evolution of the attention layers. In particular, we track the attention entropy for each attention head during the course of training, which is a proxy for model sharpness. We identify a common pattern across different architectures and tasks, where low attention entropy is accompanied by high training instability, which can take the form of oscillating loss or divergence. We denote the pathologically low attention entropy, corresponding to highly concentrated attention scores, as $\textit{entropy collapse}$. As a remedy, we propose $\sigma$Reparam, a simple and efficient solution where we reparametrize all linear layers with spectral normalization and an additional learned scalar. We demonstrate that $\sigma$Reparam successfully prevents entropy collapse in the attention layers, promoting more stable training. Additionally, we prove a tight lower bound of the attention entropy, which decreases exponentially fast with the spectral norm of the attention logits, providing additional motivation for our approach. We conduct experiments with $\sigma$Reparam on image classification, image self-supervised learning, machine translation, speech recognition, and language modeling tasks. We show that $\sigma$Reparam provides stability and robustness with respect to the choice of hyperparameters, going so far as enabling training (a) a Vision Transformer to competitive performance without warmup, weight decay, layer normalization or adaptive optimizers; (b) deep architectures in machine translation and (c) speech recognition to competitive performance without warmup and adaptive optimizers. Code is available at https://github.com/apple/ml-sigma-reparam.
Normalizing Flows for Interventional Density Estimation
Authors: Valentyn Melnychuk; Dennis Frauen; Stefan Feuerriegel
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the distribution of potential outcomes. In this work, we estimate the density of potential outcomes after interventions from observational data. For this, we propose a novel, fully-parametric deep learning method called Interventional Normalizing Flows. Specifically, we combine two normalizing flows, namely (i) a nuisance flow for estimating nuisance parameters and (ii) a target flow for parametric estimation of the density of potential outcomes. We further develop a tractable optimization objective based on a one-step bias correction for efficient and doubly robust estimation of the target flow parameters. As a result, our Interventional Normalizing Flows offer a properly normalized density estimator. Across various experiments, we demonstrate that our Interventional Normalizing Flows are expressive and highly effective, and scale well with both sample size and high-dimensional confounding. To the best of our knowledge, our Interventional Normalizing Flows are the first proper fully-parametric, deep learning method for density estimation of potential outcomes.
BEATs: Audio Pre-Training with Acoustic Tokenizers
Authors: Sanyuan Chen; Yu Wu; Chengyi Wang; Shujie LIU; Daniel Tompkins; Zhuo Chen; Wanxiang Che; Xiangzhan Yu; Furu Wei
Venue: ICML 2023 (ICML 2023 OralPoster)

Abstract: We introduce a self-supervised learning (SSL) framework BEATs for general audio representation pre-training, where we optimize an acoustic tokenizer and an audio SSL model by iterations. Unlike the previous audio SSL models that employ reconstruction loss for pre-training, our audio SSL model is trained with the discrete label prediction task, where the labels are generated by a semantic-rich acoustic tokenizer. We propose an iterative pipeline to jointly optimize the tokenizer and the pre-trained model, aiming to abstract high-level semantics and discard the redundant details for audio. The experimental results demonstrate our acoustic tokenizers can generate discrete labels with rich audio semantics and our audio SSL models achieve state-of-the-art (SOTA) results across various audio classification benchmarks, even outperforming previous models that use more training data and model parameters significantly. Specifically, we set a new SOTA mAP 50.6% on AudioSet-2M without using any external data, and 98.1% accuracy on ESC-50. The code and pre-trained models are available at https://aka.ms/beats.
IncDSI: Incrementally Updatable Document Retrieval
Authors: Varsha Kishore; Chao Wan; Justin Lovelace; Yoav Artzi; Kilian Q Weinberger
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: Differentiable Search Index is a recently proposed paradigm for document retrieval, that encodes information about a corpus of documents within the parameters of a neural network and directly maps queries to corresponding documents. These models have achieved state-of-the-art performances for document retrieval across many benchmarks. These kinds of models have a significant limitation: it is not easy to add new documents after a model is trained. We propose IncDSI, a method to add documents in real time (about 20-50ms per document), without retraining the model on the entire dataset (or even parts thereof). Instead we formulate the addition of documents as a constrained optimization problem that makes minimal changes to the network parameters. Although orders of magnitude faster, our approach is competitive with re-training the model on the whole dataset and enables the development of document retrieval systems that can be updated with new information in real-time. Our code for IncDSI is available at https://github.com/varshakishore/IncDSI.
Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction
Authors: Yuchao Lin; Keqiang Yan; Youzhi Luo; Yi Liu; Xiaoning Qian; Shuiwang Ji
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: We study property prediction for crystal materials. A crystal structure consists of a minimal unit cell that is repeated infinitely in 3D space. How to accurately represent such repetitive structures in machine learning models remains unresolved. Current methods construct graphs by establishing edges only between nearby nodes, thereby failing to faithfully capture infinite repeating patterns and distant interatomic interactions. In this work, we propose several innovations to overcome these limitations. First, we propose to model physics-principled interatomic potentials directly instead of only using distances as in many existing methods. These potentials include the Coulomb potential, London dispersion potential, and Pauli repulsion potential. Second, we model the complete set of potentials among all atoms, instead of only between nearby atoms as in existing methods. This is enabled by our approximations of infinite potential summations with provable error bounds. We further develop efficient algorithms to compute the approximations. Finally, we propose to incorporate our computations of complete interatomic potentials into message passing neural networks for representation learning. We perform experiments on the JARVIS and Materials Project benchmarks for evaluation. Results show that the use of interatomic potentials and complete interatomic potentials leads to consistent performance improvements with reasonable computational costs. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).
The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing
Authors: Xingyu Xu; Yandi Shen; Yuejie Chi; Cong Ma
Venue: ICML 2023 (ICML 2023 Poster)

Abstract: We propose $\textsf{ScaledGD($\lambda$)}$, a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, $\textsf{ScaledGD($\lambda$)}$ starts from a small random initialization, and proceeds by gradient descent with a specific form of preconditioning with a fixed damping term to combat overparameterization. At the expense of light computational overhead incurred by preconditioners, $\textsf{ScaledGD($\lambda$)}$ is remarkably robust to ill-conditioning compared to vanilla gradient descent ($\mathsf{GD}$). Specifically, we show that, under the Gaussian design, $\textsf{ScaledGD($\lambda$)}$ converges to the true low-rank matrix at a constant linear rate that is independent of the condition number (apart from a short nearly dimension-free burdening period), with near-optimal sample complexity. This significantly improves upon the convergence rate of vanilla $\mathsf{GD}$ which suffers from a polynomial dependency with the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.