NeurIPS 2023 Papers

Inductive Conformal Prediction (ICP) provides a practical and effective approach for equipping deep learning models with uncertainty estimates in the form of set-valued predictions which are guaranteed to contain the ground truth with high probability. Despite the appeal of this coverage guarantee, these sets may not be efficient: the size and contents of the prediction sets are not directly controlled, and instead depend on the underlying model and choice of score function. To remedy this, recent work has proposed learning model and score function parameters using data to directly optimize the efficiency of the ICP prediction sets. While appealing, the generalization theory for such an approach is lacking: direct optimization of empirical efficiency may yield prediction sets that are either no longer efficient on test data, or no longer obtain the required coverage on test data. In this work, we use PAC-Bayes theory to obtain generalization bounds on both the coverage and the efficiency of set-valued predictors which can be directly optimized to maximize efficiency while satisfying a desired test coverage. In contrast to prior work, our framework allows us to utilize the entire calibration dataset to learn the parameters of the model and score function, instead of requiring a separate hold-out set for obtaining test-time coverage guarantees. We leverage these theoretical results to provide a practical algorithm for using calibration data to simultaneously fine-tune the parameters of a model and score function while guaranteeing test-time coverage and efficiency of the resulting prediction sets. We evaluate the approach on regression and classification tasks, and outperform baselines calibrated using a Hoeffding bound-based PAC guarantee on ICP, especially in the low-data regime.

Real-world datasets are typically imbalanced in the sense that only a few classes have numerous samples, while many classes are associated with only a few samples. As a result, a naive ERM learning process will be biased towards the majority classes, making it difficult to generalize to the minority classes. To address this issue, one simple but effective approach is to modify the loss function to emphasize the learning on minority classes, such as re-weighting the losses or adjusting the logits via class-dependent terms. However, existing generalization analysis of such losses is still coarse-grained and fragmented, failing to explain some empirical results. To bridge this gap between theory and practice, we propose a novel technique named data-dependent contraction to capture how these modified losses handle different classes. On top of this technique, a fine-grained generalization bound is established for imbalanced learning, which helps reveal the mystery of re-weighting and logit-adjustment in a unified manner. Furthermore, a principled learning algorithm is developed based on the theoretical insights. Finally, the empirical results on benchmark datasets not only validate the theoretical results but also demonstrate the effectiveness of the proposed method.

Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the famous $k$-median and $k$-means objectives. One may also choose centers to be $j$ dimensional subspaces, which gives rise to subspace clustering. In this paper, we consider learning bounds for these problems. That is, given a set of $n$ samples $P$ drawn independently from some unknown, but fixed distribution $\mathcal{D}$, how quickly does a solution computed on $P$ converge to the optimal clustering of $\mathcal{D}$? We give several near optimal results. In particular, 1. For center-based objectives, we show a convergence rate of $\tilde{O}\left(\sqrt{{k}/{n}}\right)$. This matches the known optimal bounds of [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] and [Bartlett, Linder, and Lugosi, IEEE Trans. Inf. Theory 1998] for $k$-means and extends it to other important objectives such as $k$-median. 2. For subspace clustering with $j$-dimensional subspaces, we show a convergence rate of $\tilde{O}\left(\sqrt{{(kj^2)}/{n}}\right)$. These are the first provable bounds for most of these problems. For the specific case of projective clustering, which generalizes $k$-means, we show a converge rate of $\Omega\left(\sqrt{{(kj)}/{n}}\right)$ is necessary, thereby proving that the bounds from [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] are essentially optimal.

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle cases involving distribution shifts in the spectral domain. In this paper, we discover that there exist cases with distribution shifts unobservable in the time domain while observable in the spectral domain, and propose to study distribution shifts on dynamic graphs in the spectral domain for the first time. However, this investigation poses two key challenges: i) it is non-trivial to capture different graph patterns that are driven by various frequency components entangled in the spectral domain; and ii) it remains unclear how to handle distribution shifts with the discovered spectral patterns. To address these challenges, we propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), which can handle distribution shifts on dynamic graphs by capturing and utilizing invariant and variant spectral patterns. Specifically, we first design a DyGNN with Fourier transform to obtain the ego-graph trajectory spectrums, allowing the mixed dynamic graph patterns to be transformed into separate frequency components. We then develop a disentangled spectrum mask to filter graph dynamics from various frequency components and discover the invariant and variant spectral patterns. Finally, we propose invariant spectral filtering, which encourages the model to rely on invariant patterns for generalization under distribution shifts. Experimental results on synthetic and real-world dynamic graph datasets demonstrate the superiority of our method for both node classification and link prediction tasks under distribution shifts.

Deep deraining networks consistently encounter substantial generalization issues when deployed in real-world applications, although they are successful in laboratory benchmarks. A prevailing perspective in deep learning encourages using highly complex data for training, with the expectation that richer image background content will facilitate overcoming the generalization problem. However, through comprehensive and systematic experimentation, we discover that this strategy does not enhance the generalization capability of these networks. On the contrary, it exacerbates the tendency of networks to overfit specific degradations. Our experiments reveal that better generalization in a deraining network can be achieved by simplifying the complexity of the training background images. This is because that the networks are ``slacking off'' during training, that is, learning the least complex elements in the image background and degradation to minimize training loss. When the background images are less complex than the rain streaks, the network will prioritize the background reconstruction, thereby suppressing overfitting the rain patterns and leading to improved generalization performance. Our research offers a valuable perspective and methodology for better understanding the generalization problem in low-level vision tasks and displays promising potential for practical application.

We generalize the notion of average Lipschitz smoothness proposed by Ashlagi et al. (COLT 2021) by extending it to Hölder smoothness. This measure of the "effective smoothness" of a function is sensitive to the underlying distribution and can be dramatically smaller than its classic "worst-case" Hölder constant. We consider both the realizable and the agnostic (noisy) regression settings, proving upper and lower risk bounds in terms of the average Hölder smoothness; these rates improve upon both previously known rates even in the special case of average Lipschitz smoothness. Moreover, our lower bound is tight in the realizable setting up to log factors, thus we establish the minimax rate. From an algorithmic perspective, since our notion of average smoothness is defined with respect to the unknown underlying distribution, the learner does not have an explicit representation of the function class, hence is unable to execute ERM. Nevertheless, we provide distinct learning algorithms that achieve both (nearly) optimal learning rates. Our results hold in any totally bounded metric space, and are stated in terms of its intrinsic geometry. Overall, our results show that the classic worst-case notion of Hölder smoothness can be essentially replaced by its average, yielding considerably sharper guarantees.

Deep learning models have been widely used to assist doctors with clinical decision-making. However, these models often encounter a significant performance drop when applied to data that differs from the distribution they were trained on. This challenge is known as the domain shift problem. Existing domain generalization algorithms attempt to address this problem by assuming the availability of domain IDs and training a single model to handle all domains. However, in healthcare settings, patients can be classified into numerous latent domains, where the actual domain categorizations are unknown. Furthermore, each patient domain exhibits distinct clinical characteristics, making it sub-optimal to train a single model for all domains. To overcome these limitations, we propose SLGD, a self-learning framework that iteratively discovers decoupled domains and trains personalized classifiers for each decoupled domain. We evaluate the generalizability of SLGD across spatial and temporal data distribution shifts on two real-world public EHR datasets: eICU and MIMIC-IV. Our results show that SLGD achieves up to 11% improvement in the AUPRC score over the best baseline.

Leveraging the compositional nature of our world to expedite learning and facilitate generalization is a hallmark of human perception. In machine learning, on the other hand, achieving compositional generalization has proven to be an elusive goal, even for models with explicit compositional priors. To get a better handle on compositional generalization, we here approach it from the bottom up: Inspired by identifiable representation learning, we investigate compositionality as a property of the data-generating process rather than the data itself. This reformulation enables us to derive mild conditions on only the support of the training distribution and the model architecture, which are sufficient for compositional generalization. We further demonstrate how our theoretical framework applies to real-world scenarios and validate our findings empirically. Our results set the stage for a principled theoretical study of compositional generalization.

The Kohn-Sham equations underlie many important applications such as the discovery of new catalysts. Recent machine learning work on catalyst modeling has focused on prediction of the energy, but has so far not yet demonstrated significant out-of-distribution generalization. Here we investigate another approach based on the pointwise learning of the Kohn-Sham charge-density. On a new dataset of bulk catalysts with charge densities, we show density models can generalize to new structures with combinations of elements not seen at train time, a form of combinatorial generalization. We show that over 80% of binary and ternary test cases achieve faster convergence than standard baselines in Density Functional Theory, amounting to an average reduction of 13% in the number of iterations required to reach convergence, which may be of independent interest. Our results suggest that density learning is a viable alternative, trading greater inference costs for a step towards combinatorial generalization, a key property for applications.

Brain-machine interfaces (BMIs) can restore motor function to people with paralysis but are currently limited by the accuracy of real-time decoding algorithms. Recurrent neural networks (RNNs) using modern training techniques have shown promise in accurately predicting movements from neural signals but have yet to be rigorously evaluated against other decoding algorithms in a closed-loop setting. Here we compared RNNs to other neural network architectures in real-time, continuous decoding of finger movements using intracortical signals from nonhuman primates. Across one and two finger online tasks, LSTMs (a type of RNN) outperformed convolutional and transformer-based neural networks, averaging 18% higher throughput than the convolution network. On simplified tasks with a reduced movement set, RNN decoders were allowed to memorize movement patterns and matched able-bodied control. Performance gradually dropped as the number of distinct movements increased but did not go below fully continuous decoder performance. Finally, in a two-finger task where one degree-of-freedom had poor input signals, we recovered functional control using RNNs trained to act both like a movement classifier and continuous decoder. Our results suggest that RNNs can enable functional real-time BMI control by learning and generating accurate movement patterns.

We give sharper bounds for uniformly stable randomized algorithms in a PAC-Bayesian framework, which improve the existing results by up to a factor of $\sqrt{n}$ (ignoring a log factor), where $n$ is the sample size. The key idea is to bound the moment generating function of the generalization gap using concentration of weakly dependent random variables due to Bousquet et al (2020). We introduce an assumption of sub-exponential stability parameter, which allows a general treatment that we instantiate in two applications: stochastic gradient descent and randomized coordinate descent. Our results eliminate the requirement of strong convexity from previous results, and hold for non-smooth convex problems.

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning. We then propose a new framework Graph invAriant Learning Assistant (GALA). GALA incorporates an assistant model that needs to be sensitive to graph environment changes or distribution shifts. The correctness of the proxy predictions by the assistant model hence can differentiate the variations in spurious subgraphs. We show that extracting the maximally invariant subgraph to the proxy predictions provably identifies the underlying invariant subgraph for successful OOD generalization under the established minimal assumptions. Extensive experiments on datasets including DrugOOD with various graph distribution shifts confirm the effectiveness of GALA.

The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the `bias-variance trade-off' doctrine in the statistical learning theory. Since the generalization ability of the 'lazy trained' over-parametrized neural network can be well approximated by that of the neural tangent kernel regression, the curve of the excess risk (namely, the learning curve) of kernel ridge regression attracts increasing attention recently. However, most recent arguments on the learning curve are heuristic and are based on the 'Gaussian design' assumption. In this paper, under mild and more realistic assumptions, we rigorously provide a full characterization of the learning curve in the asymptotic sense under a power-law decay condition of the eigenvalues of the kernel and also the target function. The learning curve elaborates the effect and the interplay of the choice of the regularization parameter, the source condition and the noise. In particular, our results suggest that the 'benign overfitting phenomenon' exists in over-parametrized neural networks only when the noise level is small.

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have demonstrated impressive performance across various domains and applications such as protein and drug design. A prevalent intuition about such models is that the integration of relevant symmetry results in enhanced generalization. Moreover, it is posited that when the data and/or the model exhibits only approximate or partial symmetry, the optimal or best-performing model is one where the model symmetry aligns with the data symmetry. In this paper, we conduct a formal unified investigation of these intuitions. To begin, we present quantitative bounds that demonstrate how models capturing task-specific symmetries lead to improved generalization. Utilizing this quantification, we examine the more general question of dealing with approximate/partial symmetries. We establish, for a given symmetry group, a quantitative comparison between the approximate equivariance of the model and that of the data distribution, precisely connecting model equivariance error and data equivariance error. Our result delineates the conditions under which the model equivariance error is optimal, thereby yielding the best-performing model for the given task and data.

One of the major open problems in machine learning is to characterize generalization in the overparameterized regime, where most traditional generalization bounds become inconsistent even for overparameterized linear regression. In many scenarios, this failure can be attributed to obscuring the crucial interplay between the training algorithm and the underlying data distribution. This paper demonstrate that the generalization behavior of overparameterized model should be analyzed in a both data-relevant and algorithm-relevant manner. To make a formal characterization, We introduce a notion called data-algorithm compatibility, which considers the generalization behavior of the entire data-dependent training trajectory, instead of traditional last-iterate analysis. We validate our claim by studying the setting of solving overparameterized linear regression with gradient descent. Specifically, we perform a data-dependent trajectory analysis and derive a sufficient condition for compatibility in such a setting. Our theoretical results demonstrate that if we take early stopping iterates into consideration, generalization can hold with significantly weaker restrictions on the problem instance than the previous last-iterate analysis.

Dynamically grouping sensory information into structured entities is essential for understanding the world of combinatorial nature. However, the grouping ability and therefore combinatorial generalization are still challenging artificial neural networks. Inspired by the evidence that successful grouping is indicated by neuronal coherence in the human brain, we introduce GUST (Grouping Unsupervisely by Spike Timing network), an iterative network architecture with biological constraints to bias the network towards a dynamical state of neuronal coherence that softly reflects the grouping information in the temporal structure of its spiking activity. We evaluate and analyze the model on synthetic datasets. Interestingly, the segregation ability is directly learned from superimposed stimuli with a succinct unsupervised objective. Two learning stages are present, from coarsely perceiving global features to additionally capturing local features. Further, the learned symbol-like building blocks can be systematically composed to represent novel scenes in a bio-plausible manner.

Deep neural networks have been increasingly used in real-world applications, making it critical to ensure their ability to adapt to new, unseen data. In this paper, we study the generalization capability of neural networks trained with (stochastic) gradient flow. We establish a new connection between the loss dynamics of gradient flow and general kernel machines by proposing a new kernel, called loss path kernel. This kernel measures the similarity between two data points by evaluating the agreement between loss gradients along the path determined by the gradient flow. Based on this connection, we derive a new generalization upper bound that applies to general neural network architectures. This new bound is tight and strongly correlated with the true generalization error. We apply our results to guide the design of neural architecture search (NAS) and demonstrate favorable performance compared with state-of-the-art NAS algorithms through numerical experiments.

We study the problem of $(\epsilon,\delta)$-certified machine unlearning for minimax models. Most of the existing works focus on unlearning from standard statistical learning models that have a single variable and their unlearning steps hinge on the direct Hessian-based conventional Newton update. We develop a new $(\epsilon,\delta)$-certified machine unlearning algorithm for minimax models. It proposes a minimax unlearning step consisting of a total Hessian-based complete Newton update and the Gaussian mechanism borrowed from differential privacy. To obtain the unlearning certification, our method injects calibrated Gaussian noises by carefully analyzing the ''sensitivity'' of the minimax unlearning step (i.e., the closeness between the minimax unlearning variables and the retraining-from-scratch variables). We derive the generalization rates in terms of population strong and weak primal-dual risk for three different cases of loss functions, i.e., (strongly-)convex-(strongly-)concave losses. We also provide the deletion capacity to guarantee that a desired population risk can be maintained as long as the number of deleted samples does not exceed the derived amount. With training samples $n$ and model dimension $d$, it yields the order $\mathcal O(n/d^{1/4})$, which shows a strict gap over the baseline method of differentially private minimax learning that has $\mathcal O(n/d^{1/2})$. In addition, our rates of generalization and deletion capacity match the state-of-the-art rates derived previously for standard statistical learning models.

The capability of generalizing to out-of-distribution data is crucial for the deployment of machine learning models in the real world. Existing domain generalization (DG) mainly embarks on offline and discrete scenarios, where multiple source domains are simultaneously accessible and the distribution shift among domains is abrupt and violent. Nevertheless, such setting may not be universally applicable to all real-world applications, as there are cases where the data distribution gradually changes over time due to various factors, e.g., the process of aging. Additionally, as the domain constantly evolves, new domains will continually emerge. Re-training and updating models with both new and previous domains using existing DG methods can be resource-intensive and inefficient. Therefore, in this paper, we present a problem formulation for Continual Domain Generalization over Temporal Drift (CDGTD). CDGTD addresses the challenge of gradually shifting data distributions over time, where domains arrive sequentially and models can only access the data of the current domain. The goal is to generalize to unseen domains that are not too far into the future. To this end, we propose an Evolving Standardization (EvoS) method, which characterizes the evolving pattern of feature distribution and mitigates the distribution shift by standardizing features with generated statistics of corresponding domain. Specifically, inspired by the powerful ability of transformers to model sequence relations, we design a multi-scale attention module (MSAM) to learn the evolving pattern under sliding time windows of different lengths. MSAM can generate statistics of current domain based on the statistics of previous domains and the learned evolving pattern. Experiments on multiple real-world datasets including images and texts validate the efficacy of our EvoS.