ICML 2024 论文列表

Both transduction and rejection have emerged as important techniques for defending against adversarial perturbations. A recent work by Goldwasser et. al showed that rejection combined with transduction can give *provable* guarantees (for certain problems) that cannot be achieved otherwise. Nevertheless, under recent strong adversarial attacks (GMSA), Goldwasser et al.'s work was shown to have low performance in a practical deep-learning setting. In this paper, we take a step towards realizing the promise of transduction+rejection in more realistic scenarios. Our key observation is that a novel application of a reduction technique by Tramèr, which was until now only used to demonstrate the vulnerability of certain defenses, can be used to actually construct effective defenses. Theoretically, we show that a careful application of this technique in the transductive setting can give significantly improved sample-complexity for robust generalization. Our theory guides us to design a new transductive algorithm for learning a selective model; extensive experiments using state of the art attacks (AutoAttack, GMSA) show that our approach provides significantly better robust accuracy (81.6% on CIFAR-10 and 57.9% on CIFAR-100 under $l_\infty$ with budget 8/255) than existing techniques. The implementation is available at https://github.com/nilspalumbo/transduction-rejection.

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, such global operations are often prone to over-smoothing and may fail to capture local details. In contrast, convolutional neural networks (CNN) can capture local features but are limited to training and inference at a single resolution. In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels. Specifically, inspired by stencil methods, we prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions. Both these approaches preserve the properties of operator learning and, hence, the ability to predict at any resolution. Adding our layers to FNOs significantly improves their performance, reducing the relative L2-error by 34-72% in our experiments, which include a turbulent 2D Navier-Stokes and the spherical shallow water equations.

Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph $G$ that has $n$ vertices, using the symmetric group $S_n$ as its group of symmetries does not take into account the relations that exist between the vertices. Given that the actual group of symmetries is the automorphism group Aut$(G)$, we show how to construct neural networks that are equivariant to Aut$(G)$ by obtaining a full characterisation of the learnable, linear, Aut$(G)$-equivariant functions between layers that are some tensor power of $\mathbb{R}^{n}$. In particular, we find a spanning set of matrices for these layer functions in the standard basis of $\mathbb{R}^{n}$. This result has important consequences for learning from data whose group of symmetries is a finite group because a theorem by Frucht (1938) showed that any finite group is isomorphic to the automorphism group of a graph.

The generation of initial conditions via accurate data assimilation is crucial for weather forecasting and climate modeling. We propose DiffDA as a denoising diffusion model capable of assimilating atmospheric variables using predicted states and sparse observations. Acknowledging the similarity between a weather forecast model and a denoising diffusion model dedicated to weather applications, we adapt the pretrained GraphCast neural network as the backbone of the diffusion model. Through experiments based on simulated observations from the ERA5 reanalysis dataset, our method can produce assimilated global atmospheric data consistent with observations at 0.25$^\circ$ ($\approx$30km) resolution globally. This marks the highest resolution achieved by ML data assimilation models. The experiments also show that the initial conditions assimilated from sparse observations (less than 0.96% of gridded data) and 48-hour forecast can be used for forecast models with a loss of lead time of at most 24 hours compared to initial conditions from state-of-the-art data assimilation in ERA5. This enables the application of the method to real-world applications, such as creating reanalysis datasets with autoregressive data assimilation.

The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We propose a framework for bridging this gap, by using computational complexity theory to assess local and global perspectives of interpreting ML models. We begin by proposing proofs for two novel insights that are essential for our analysis: (1) a duality between local and global forms of explanations; and (2) the inherent uniqueness of certain global explanation forms. We then use these insights to evaluate the complexity of computing explanations, across three model types representing the extremes of the interpretability spectrum: (1) linear models; (2) decision trees; and (3) neural networks. Our findings offer insights into both the local and global interpretability of these models. For instance, under standard complexity assumptions such as P != NP, we prove that selecting *global* sufficient subsets in linear models is computationally harder than selecting *local* subsets. Interestingly, with neural networks and decision trees, the opposite is true: it is harder to carry out this task locally than globally. We believe that our findings demonstrate how examining explainability through a computational complexity lens can help us develop a more rigorous grasp of the inherent interpretability of ML models.

The distinguishing power of graph transformers is tied to the choice of *positional encoding*: features used to augment the base transformer with information about the graph. There are two primary types of positional encoding: *absolute positional encodings (APEs)* and *relative positional encodings (RPEs)*. APEs assign features to each node and are given as input to the transformer. RPEs instead assign a feature to each *pair of nodes*, e.g., shortest-path distance, and are used to augment the attention block. A priori, it is unclear which method is better for maximizing the power of the resulting graph transformer. In this paper, we aim to understand the relationship between these different types of positional encodings. Interestingly, we show that graph transformers using APEs and RPEs are equivalent in their ability to distinguish non-isomorphic graphs. In particular, we demonstrate how to interchange APEs and RPEs while maintaining their distinguishing power in terms of graph transformers. However, in the case of graphs with node features, we show that RPEs may have an advantage over APEs. Based on our theoretical results, we provide a study of different APEs and RPEs---including the shortest-path and resistance distance and the recently introduced stable and expressive positional encoding (SPE)---and compare their distinguishing power in terms of transformers. We believe our work will help navigate the vast number of positional encoding choices and provide guidance on the future design of positional encodings for graph transformers.

The linear ordering problem consists in finding a linear order $<$ on a finite set $A$ so as to minimize the sum of costs associated with pairs of elements $a, b$ for which $a < b$. The problem is NP-hard and APX-hard. We introduce algorithms for solving the problem *partially* by deciding efficiently for some pairs $(a,b)$ whether $a < b$ is in an optimal solution. To do so, we construct maps from the feasible set of orders to itself and establish efficiently testable conditions on the cost function of the problem for which these maps are improving. We examine the effectiveness and efficiency of these conditions and algorithms empirically, on two data sets.

We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of all possible modern Hopfield models based on the norm of patterns. Specifically, we establish an upper bound criterion for the norm of input query patterns and memory patterns. Only below this criterion, sub-quadratic (efficient) variants of the modern Hopfield model exist, assuming the Strong Exponential Time Hypothesis (SETH). To showcase our theory, we provide a formal example of efficient constructions of modern Hopfield models using low-rank approximation when the efficient criterion holds. This includes a derivation of a lower bound on the computational time, scaling linearly with $\max$\{ \# of stored memory patterns, length of input query sequence\}. In addition, we prove its memory retrieval error bound and exponential memory capacity.

The abundance of free internet data offers unprecedented opportunities for researchers and developers, but it also poses privacy risks. Utilizing data without explicit consent raises critical challenges in protecting personal information.Unlearnable examples have emerged as a feasible protection approach, which renders the data unlearnable, i.e., useless to third parties, by injecting imperceptible perturbations. However, these perturbations only exhibit unlearnable effects on either a particular dataset or label-consistent scenarios, thereby lacking broad applicability. To address both issues concurrently, we propose a universal perturbation generator that harnesses data with concept unlearnability, thereby broadening the scope of unlearnability beyond specific datasets or labels. Specifically, we leverage multi-modal pre-trained models to establish a connection between the data concepts in a shared embedding space. This connection enables the information transformation from image data to text concepts. Consequently, we can align the text embedding using concept-wise discriminant loss, and render the data unlearnable. Extensive experiments conducted on real-world datasets demonstrate the concept unlearnability, i.e., cross-dataset transferability and label-agnostic utility, of our proposed unlearnable examples, as well as their robustness against attacks.

Handling the substantial communication burden in federated learning (FL) still remains a significant challenge. Although recent studies have attempted to compress the local gradients to address this issue, they typically perform compression only within the original parameter space, which may potentially limit the fundamental compression rate of the gradient. In this paper, instead of restricting our scope to a fixed traditional space, we consider an alternative space that provides an improved compressibility of the gradient. To this end, we utilize the structures of input activation and output gradient in designing our mapping function to a new space, which enables *lossless gradient sparsification*, i.e., mapping the gradient to our new space induces a greater number of *near-zero* elements without any loss of information. In light of this attribute, employing sparsification-based compressors in our new space allows for more aggressive compression with minimal information loss than the baselines. More surprisingly, our model even reaches higher accuracies than the full gradient uploading strategy in some cases, an extra benefit for utilizing the new space. We also theoretically confirm that our approach does not alter the existing, best known convergence rate of FL thanks to the orthogonal transformation properties of our mapping.

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by estimating the time-reversal of this diffusion using score matching ideas. We follow here a similar strategy to sample from unnormalized probability densities and compute their normalizing constants. However, the time-reversed diffusion is here simulated by using an original iterative particle scheme relying on a novel score matching loss. Contrary to standard denoising diffusion models, the resulting Particle Denoising Diffusion Sampler (PDDS) provides asymptotically consistent estimates under mild assumptions. We demonstrate PDDS on multimodal and high dimensional sampling tasks.

Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning. The utility of optimal transport-based distances, such as the Wasserstein distance, for comparing probability measures has spurred active research in developing computationally efficient variations of these distances for spherical probability measures. This paper introduces a high-speed and highly parallelizable distance for comparing spherical measures using the stereographic projection and the generalized Radon transform, which we refer to as the Stereographic Spherical Sliced Wasserstein (S3W) distance. We carefully address the distance distortion caused by the stereographic projection and provide an extensive theoretical analysis of our proposed metric and its rotationally invariant variation. Finally, we evaluate the performance of the proposed metrics and compare them with recent baselines in terms of both speed and accuracy through a wide range of numerical studies, including gradient flows and self-supervised learning. Our code is available at https://github.com/mint-vu/s3wd.

Code provides a general syntactic structure to build complex programs and perform precise computations when paired with a code interpreter – we hypothesize that language models (LMs) can leverage code-writing to improve Chain of Thought reasoning not only for logic and arithmetic tasks, but also for semantic ones (and in particular, those that are a mix of both). For example, consider prompting an LM to write code that counts the number of times it detects sarcasm in an essay: the LM may struggle to write an implementation for "detect_sarcasm(string)" that can be executed by the interpreter (handling the edge cases would be insurmountable). However, LMs may still produce a valid solution if they not only write code, but also selectively "emulate" the interpreter by generating the expected output of "detect_sarcasm(string)". In this work, we propose Chain of Code (CoC), a simple yet surprisingly effective extension that improves LM code-driven reasoning. The key idea is to encourage LMs to format semantic sub-tasks in a program as flexible pseudocode that the interpreter can explicitly catch undefined behaviors and hand off to simulate with an LM (as an "LMulator"). Experiments demonstrate that Chain of Code outperforms Chain of Thought and other baselines across a variety of benchmarks; on BIG-Bench Hard, Chain of Code achieves 84%, a gain of 12% over Chain of Thought. In a nutshell, CoC broadens the scope of reasoning questions that LMs can answer by "thinking in code".

This study introduces a novel transformer model optimized for large-scale point cloud processing in scientific domains such as high-energy physics (HEP) and astrophysics. Addressing the limitations of graph neural networks and standard transformers, our model integrates local inductive bias and achieves near-linear complexity with hardware-friendly regular operations. One contribution of this work is the quantitative analysis of the error-complexity tradeoff of various sparsification techniques for building efficient transformers. Our findings highlight the superiority of using locality-sensitive hashing (LSH), especially OR & AND-construction LSH, in kernel approximation for large-scale point cloud data with local inductive bias. Based on this finding, we propose LSH-based Efficient Point Transformer (**HEPT**), which combines E$^2$LSH with OR & AND constructions and is built upon regular computations. HEPT demonstrates remarkable performance on two critical yet time-consuming HEP tasks, significantly outperforming existing GNNs and transformers in accuracy and computational speed, marking a significant advancement in geometric deep learning and large-scale scientific data processing. Our code is available at https://github.com/Graph-COM/HEPT.

Recent text-to-image generative models have demonstrated remarkable abilities in generating realistic images. Despite their great success, these models struggle to generate high-fidelity images with prompts oriented toward human-object interaction (HOI). The difficulty in HOI generation arises from two aspects. Firstly, the complexity and diversity of human poses challenge plausible human generation. Furthermore, untrustworthy generation of interaction boundary regions may lead to deficiency in HOI semantics. To tackle the problems, we propose a Semantic-Aware HOI generation framework SA-HOI . It utilizes human pose quality and interaction boundary region information as guidance for denoising process, thereby encouraging refinement in these regions to produce more reasonable HOI images. Based on it, we establish an iterative inversion and image refinement pipeline to continually enhance generation quality. Further, we introduce a comprehensive benchmark for HOI generation, which comprises a dataset involving diverse and fine-grained HOI categories, along with multiple custom-tailored evaluation metrics for HOI generation. Experiments demonstrate that our method significantly improves generation quality under both HOI-specific and conventional image evaluation metrics. The code is available at https://github.com/XZPKU/SA-HOI.git

We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. Posterior samples are obtained by interpolating the predicted quantiles using monotonic cubic Hermite spline, with specific treatment for the tail behavior and multi-modal distributions. We introduce an alternative definition for the Bayesian credible region using the local Cumulative Density Function (CDF), offering substantially faster evaluation than the traditional Highest Posterior Density Region (HPDR). In case of limited simulation budget and/or known model misspecification, a post-processing calibration step can be integrated into NQE to ensure the unbiasedness of the posterior estimation with negligible additional computational cost. We demonstrate that NQE achieves state-of-the-art performance on a variety of benchmark problems.

We study nonconvex zeroth-order optimization (ZOO) in a high-dimensional space $\mathbb R^d$ for functions with approximately $s$-sparse gradients. To reduce the dependence on the dimensionality $d$ in the query complexity, high-dimensional ZOO methods seek to leverage gradient sparsity to design gradient estimators. The previous best method needs $O\big(s\log\frac ds\big)$ queries per step to achieve $O\big(\frac1T\big)$ rate of convergence w.r.t. the number T of steps. In this paper, we propose *Gradient Compressed Sensing* (GraCe), a query-efficient and accurate estimator for sparse gradients that uses only $O\big(s\log\log\frac ds\big)$ queries per step and still achieves $O\big(\frac1T\big)$ rate of convergence. To our best knowledge, we are the first to achieve a *double-logarithmic* dependence on $d$ in the query complexity under weaker assumptions. Our proposed GraCe generalizes the Indyk–Price–Woodruff (IPW) algorithm in compressed sensing from linear measurements to nonlinear functions. Furthermore, since the IPW algorithm is purely theoretical due to its impractically large constant, we improve the IPW algorithm via our *dependent random partition* technique together with our corresponding novel analysis and successfully reduce the constant by a factor of nearly $4300$. Our GraCe is not only theoretically query-efficient but also achieves strong empirical performance. We benchmark our GraCe against $12$ existing ZOO methods with $10000$-dimensional functions and demonstrate that GraCe significantly outperforms existing methods. Our code is publicly available at https://github.com/q-rz/ICML24-GraCe.

Latent representations are extensively used for tasks like visualization, interpolation, or feature extraction in deep learning models. This paper demonstrates the importance of considering the inductive bias imposed by an equivariant model when using latent representations as neglecting these biases can lead to decreased performance in downstream tasks. We propose principles for choosing invariant projections of latent representations and show their effectiveness in two examples: A permutation equivariant variational auto-encoder for molecular graph generation, where an invariant projection can be designed to maintain information without loss, and for a rotation-equivariant representation in image classification, where random invariant projections proves to retain a high degree of information. In both cases, the analysis of invariant latent representations proves superior to their equivariant counterparts. Finally, we illustrate that the phenomena documented here for equivariant neural networks have counterparts in standard neural networks where invariance is encouraged via augmentation.

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and exhibits sub-optimal efficiency for certain PDE formulations, while data-driven neural methods typically lack mathematical guarantee of convergence and correctness. This paper articulates a mathematically rigorous neural solver for linear PDEs. The proposed UGrid solver, built upon the principled integration of U-Net and MultiGrid, manifests a mathematically rigorous proof of both convergence and correctness, and showcases high numerical accuracy, as well as strong generalization power to various input geometry/values and multiple PDE formulations. In addition, we devise a new residual loss metric, which enables unsupervised training and affords more stability and a larger solution space over the legacy losses.