ICLR 2024 Papers

Graph-based semi-supervised learning, particularly in the context of extremely sparse labeled data, often suffers from degenerate solutions where label functions tend to be nearly constant across unlabeled data. In this paper, we introduce Variance-enlarged Poisson Learning (VPL), a simple yet powerful framework tailored to alleviate the issues arising from the presence of degenerate solutions. VPL incorporates a variance-enlarged regularization term, which induces a Poisson equation specifically for unlabeled data. This intuitive approach increases the dispersion of labels from their average mean, effectively reducing the likelihood of degenerate solutions characterized by nearly constant label functions. We subsequently introduce two streamlined algorithms, V-Laplace and V-Poisson, each intricately designed to enhance Laplace and Poisson learning, respectively. Furthermore, we broaden the scope of VPL to encompass graph neural networks, introducing Variance-enlarged Graph Poisson Networks (V-GPN) to facilitate improved label propagation. To achieve a deeper understanding of VPL's behavior, we conduct a comprehensive theoretical exploration in both discrete and variational cases. Our findings elucidate that VPL inherently amplifies the importance of connections within the same class while concurrently tempering those between different classes. We support our claims with extensive experiments, demonstrating the effectiveness of VPL and showcasing its superiority over existing methods. The code is available at https://github.com/hitcszx/VPL.

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer.

Biological cortical neurons are remarkably sophisticated computational devices, temporally integrating their vast synaptic input over an intricate dendritic tree, subject to complex, nonlinearly interacting internal biological processes. A recent study proposed to characterize this complexity by fitting accurate surrogate models to replicate the input-output relationship of a detailed biophysical cortical pyramidal neuron model and discovered it needed temporal convolutional networks (TCN) with millions of parameters. Requiring these many parameters, however, could stem from a misalignment between the inductive biases of the TCN and cortical neuron's computations. In light of this, and to explore the computational implications of leaky memory units and nonlinear dendritic processing, we introduce the Expressive Leaky Memory (ELM) neuron model, a biologically inspired phenomenological model of a cortical neuron. Remarkably, by exploiting such slowly decaying memory-like hidden states and two-layered nonlinear integration of synaptic input, our ELM neuron can accurately match the aforementioned input-output relationship with under ten thousand trainable parameters. To further assess the computational ramifications of our neuron design, we evaluate it on various tasks with demanding temporal structures, including the Long Range Arena (LRA) datasets, as well as a novel neuromorphic dataset based on the Spiking Heidelberg Digits dataset (SHD-Adding). Leveraging a larger number of memory units with sufficiently long timescales, and correspondingly sophisticated synaptic integration, the ELM neuron displays substantial long-range processing capabilities, reliably outperforming the classic Transformer or Chrono-LSTM architectures on LRA, and even solving the Pathfinder-X task with over 70\% accuracy (16k context length). These findings raise further questions about the computational sophistication of individual cortical neurons and their role in extracting complex long-range temporal dependencies.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

The rise in internet usage has led to the generation of massive amounts of data, resulting in the adoption of various supervised and semi-supervised machine learning algorithms, which can effectively utilize the colossal amount of data to train models. However, before deploying these models in the real world, these must be strictly evaluated on performance measures like worst-case recall and satisfy constraints such as fairness. We find that current state-of-the-art empirical techniques offer sub-optimal performance on these practical, non-decomposable performance objectives. On the other hand, the theoretical techniques necessitate training a new model from scratch for each performance objective. To bridge the gap, we propose SelMix, a selective mixup-based inexpensive fine-tuning technique for pre-trained models, to optimize for the desired objective. The core idea of our framework is to determine a sampling distribution to perform a mixup of features between samples from particular classes such that it optimizes the given objective. We comprehensively evaluate our technique against the existing empirical and theoretically principled methods on standard benchmark datasets for imbalanced classification. We find that proposed SelMix fine-tuning significantly improves the performance for various practical non-decomposable objectives across benchmarks.

In Self-Supervised Learning (SSL), models are typically pretrained, fine-tuned, and evaluated on the same domains. However, they tend to perform poorly when evaluated on unseen domains, a challenge that Unsupervised Domain Generalization (UDG) seeks to address. Current UDG methods rely on domain labels, which are often challenging to collect, and domain-specific architectures that lack scalability when confronted with numerous domains, making the current methodology impractical and rigid. Inspired by contrastive-based UDG methods that mitigate spurious correlations by restricting comparisons to examples from the same domain, we hypothesize that eliminating style variability within a batch could provide a more convenient and flexible way to reduce spurious correlations without requiring domain labels. To verify this hypothesis, we introduce Batch Styles Standardization (BSS), a relatively simple yet powerful Fourier-based method to standardize the style of images in a batch specifically designed for integration with SSL methods to tackle UDG. Combining BSS with existing SSL methods offers serious advantages over prior UDG methods: (1) It eliminates the need for domain labels or domain-specific network components to enhance domain-invariance in SSL representations, and (2) offers flexibility as BSS can be seamlessly integrated with diverse contrastive-based but also non-contrastive-based SSL methods. Experiments on several UDG datasets demonstrate that it significantly improves downstream task performances on unseen domains, often outperforming or rivaling UDG methods. Finally, this work clarifies the underlying mechanisms contributing to BSS's effectiveness in improving domain-invariance in SSL representations and performances on unseen domains. Implementations of the extended SSL methods and BSS are provided at this [url](https://gitlab.com/vitadx/articles/towards-domain-invariant-ssl-through-bss).

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey \& Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at https://github.com/mandt-lab/PSLD

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse ––– also known as the "underfilling" phenomenon ––– is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called *local dimensionality regularization (LDReg)*. Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such problems. Amongst such priors, score-based generative models (SGM) have recently been successfully applied to several different inverse problems. In this study, we exploit the particular structure of the prior defined by the SGM to define a sequence of intermediate linear inverse problems. As the noise level decreases, the posteriors of these inverse problems get closer to the target posterior of the original inverse problem. To sample from this sequence of posteriors, we propose the use of Sequential Monte Carlo (SMC) methods. The proposed algorithm, \algo, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems in a Bayesian setting.

In critical applications, it is vital for classifiers to defer decision-making to humans. We propose a post-hoc method that makes existing classifiers selectively abstain from predicting certain samples. Our abstaining classifier is incentivized to maintain the original accuracy for each sub-population (i.e. no harm) while achieving a set of group fairness definitions to a user specified degree. To this end, we design an Integer Programming (IP) procedure that assigns abstention decisions for each training sample to satisfy a set of constraints. To generalize the abstaining decisions to test samples, we then train a surrogate model to learn the abstaining decisions based on the IP solutions in an end-to-end manner. We analyze the feasibility of the IP procedure to determine the possible abstention rate for different levels of unfairness tolerance and accuracy constraint for achieving no harm. To the best of our knowledge, this work is the first to identify the theoretical relationships between the constraint parameters and the required abstention rate. Our theoretical results are important since a high abstention rate is often infeasible in practice due to a lack of human resources. Our framework outperforms existing methods in terms of fairness disparity without sacrificing accuracy at similar abstention rates.

Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory and corresponding assumptions on the form of data. We propose Neural Fourier Transform (NFT), a general framework of learning the latent linear action of the group without assuming explicit knowledge of how the group acts on data. We present the theoretical foundations of NFT and show that the existence of a linear equivariant feature, which has been assumed ubiquitously in equivariance learning, is equivalent to the existence of a group invariant kernel on the dataspace. We also provide experimental results to demonstrate the application of NFT in typical scenarios with varying levels of knowledge about the acting group.

Semi-supervised learning (SSL) has witnessed great progress with various improvements in the self-training framework with pseudo labeling. The main challenge is how to distinguish high-quality pseudo labels against the confirmation bias. However, existing pseudo-label selection strategies are limited to pre-defined schemes or complex hand-crafted policies specially designed for classification, failing to achieve high-quality labels, fast convergence, and task versatility simultaneously. To these ends, we propose a Semi-supervised Reward framework (SemiReward) that predicts reward scores to evaluate and filter out high-quality pseudo labels, which is pluggable to mainstream SSL methods in wide task types and scenarios. To mitigate confirmation bias, SemiReward is trained online in two stages with a generator model and subsampling strategy. With classification and regression tasks on 13 standard SSL benchmarks across three modalities, extensive experiments verify that SemiReward achieves significant performance gains and faster convergence speeds upon Pseudo Label, FlexMatch, and Free/SoftMatch. Code and models are available at https://github.com/Westlake-AI/SemiReward.

Large Language Models (LLMs) exhibit emerging in-context learning abilities through prompt engineering. The recent progress in large-scale generative models has further expanded their use in real-world language applications. However, the critical challenge of improving the generalizability and factuality of LLMs in natural language understanding and question answering remains under-explored. While previous in-context learning research has focused on enhancing models to adhere to users' specific instructions and quality expectations, and to avoid undesired outputs, little to no work has explored the use of task-specific fine-tuned Language Models (SLMs) to improve LLMs' in-context learning during the inference stage. Our primary contribution is the establishment of a simple yet effective framework that enhances the reliability of LLMs as it: 1) generalizes out-of-distribution data, 2) elucidates how LLMs benefit from discriminative models, and 3) minimizes hallucinations in generative tasks. Using our proposed plug-in method, enhanced versions of Llama 2 and ChatGPT surpass their original versions regarding generalizability and factuality. We offer a comprehensive suite of resources, including 16 curated datasets, prompts, model checkpoints, and LLM outputs across 9 distinct tasks. Our empirical analysis sheds light on the advantages of incorporating discriminative models into LLMs and highlights the potential of our methodology in fostering more reliable LLMs.

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state—something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

We characterize the statistical efficiency of knowledge transfer through $n$ samples from a teacher to a probabilistic student classifier with input space $\mathcal{S}$ over labels $\mathcal{A}$. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate $\sqrt{{|\mathcal{S}||\mathcal{A}|}/{n}}$. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to ${{|\mathcal{S}||\mathcal{A}|}/{n}}$. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on $\mathcal{A}$ given every sampled input, thereby provably enables the student to enjoy a rate ${|\mathcal{S}|}/{n}$ free of $|\mathcal{A}|$. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

Self-supervised learning through contrastive representations is an emergent and promising avenue, aiming at alleviating the availability of labeled data. Recent research in the field also demonstrates its viability for several downstream tasks, henceforth leading to works that implement the contrastive principle through innovative loss functions and methods. However, despite achieving impressive progress, most methods depend on prohibitively large batch sizes and compute requirements for good performance. In this work, we propose the $\textbf{AUC}$-$\textbf{C}$ontrastive $\textbf{L}$earning, a new approach to contrastive learning that demonstrates robust and competitive performance in compute-limited regimes. We propose to incorporate the contrastive objective within the AUC-maximization framework, by noting that the AUC metric is maximized upon enhancing the probability of the network's binary prediction difference between positive and negative samples which inspires adequate embedding space arrangements in representation learning. Unlike standard contrastive methods, when performing stochastic optimization, our method maintains unbiased stochastic gradients and thus is more robust to batchsizes as opposed to standard stochastic optimization problems. Remarkably, our method with a batch size of 256, outperforms several state-of-the-art methods that may need much larger batch sizes (e.g., 4096), on ImageNet and other standard datasets. Experiments on transfer learning, few-shot learning, and other downstream tasks also demonstrate the viability of our method.

Dense Self-Supervised Learning (SSL) creates positive pairs by building positive paired regions or points, thereby aiming to preserve local features, for example of individual objects. However, existing approaches tend to couple objects by leaking information from the neighboring contextual regions when the pairs have a limited overlap. In this paper, we first quantitatively identify and confirm the existence of such a coupling phenomenon. We then address it by developing a remarkably simple yet highly effective solution comprising a novel augmentation method, Region Collaborative Cutout (RCC), and a corresponding decoupling branch. Importantly, our design is versatile and can be seamlessly integrated into existing SSL frameworks, whether based on Convolutional Neural Networks (CNNs) or Vision Transformers (ViTs). We conduct extensive experiments, incorporating our solution into two CNN-based and two ViT-based methods, with results confirming the effectiveness of our approach. Moreover, we provide empirical evidence that our method significantly contributes to the disentanglement of feature representations among objects, both in quantitative and qualitative terms.

Adversarial attacks have been a looming and unaddressed threat in the industry. However, through a decade-long history of the robustness evaluation literature, we have learned that mounting a strong or optimal attack is challenging. It requires both machine learning and domain expertise. In other words, the white-box threat model, religiously assumed by a large majority of the past literature, is unrealistic. In this paper, we propose a new practical threat model where the adversary relies on transfer attacks through publicly available surrogate models. We argue that this setting will become the most prevalent for security-sensitive applications in the future. We evaluate the transfer attacks in this setting and propose a specialized defense method based on a game-theoretic perspective. The defenses are evaluated under 24 public models and 11 attack algorithms across three datasets (CIFAR-10, CIFAR-100, and ImageNet). Under this threat model, our defense, PubDef, outperforms the state-of-the-art white-box adversarial training by a large margin with almost no loss in the normal accuracy. For instance, on ImageNet, our defense achieves 62% accuracy under the strongest transfer attack vs only 36% of the best adversarially trained model. Its accuracy when not under attack is only 2% lower than that of an undefended model (78% vs 80%). We release our code at https://github.com/wagner-group/pubdef.

A powerful concept behind much of the recent progress in machine learning is the extraction of common features across data from heterogeneous sources or tasks. Intuitively, using all of one's data to learn a common representation function benefits both computational effort and statistical generalization by leaving a smaller number of parameters to fine-tune on a given task. Toward theoretically grounding these merits, we propose a general setting of recovering linear operators $M$ from noisy vector measurements $y = Mx + w$, where the covariates $x$ may be both non-i.i.d. and non-isotropic. We demonstrate that existing isotropy-agnostic meta-learning approaches incur biases on the representation update, which causes the scaling of the noise terms to lose favorable dependence on the number of source tasks. This in turn can cause the sample complexity of representation learning to be bottlenecked by the single-task data size. We introduce an adaptation, $\texttt{De-bias}$ & $\texttt{Feature-Whiten}$ ($\texttt{DFW}$), of the popular alternating minimization-descent (AMD) scheme proposed in Collins et al., (2021), and establish linear convergence to the optimal representation with noise level scaling down with the $\textit{total}$ source data size. This leads to generalization bounds on the same order as an oracle empirical risk minimizer. We verify the vital importance of $\texttt{DFW}$ on various numerical simulations. In particular, we show that vanilla alternating-minimization descent fails catastrophically even for iid, but mildly non-isotropic data. Our analysis unifies and generalizes prior work, and provides a flexible framework for a wider range of applications, such as in controls and dynamical systems.