In this paper, we consider a challenging but realistic continual learning problem, Few-Shot Continual Active Learning (FoCAL), where a CL agent is provided with unlabeled data for a new or a previously learned task in each increment and the agent only has limited labeling budget available. Towards this, we build on the continual learning and active learning literature and develop a framework that can allow a CL agent to continually learn new object classes from a few labeled training examples. Our framework represents each object class using a uniform Gaussian mixture model (GMM) and uses pseudo-rehearsal to mitigate catastrophic forgetting. The framework also uses uncertainty measures on the Gaussian representations of the previously learned classes to find the most informative samples to be labeled in an increment. We evaluate our approach on the CORe-50 dataset and on a real humanoid robot for the object classification task.

In structured prediction, target objects have rich internal structure which does not factorize into independent components and violates common i.i.d. This challenge becomes apparent through the exponentially large output space in applications such as image segmentation or scene graph generation.We present a novel PAC-Bayesian risk bound for structured prediction wherein the rate of generalization scales not only with the number of structured examples but also with their size.The underlying assumption, conforming to ongoing research on generative models, is that data are generated by the Knothe-Rosenblatt rearrangement of a factorizing reference measure. This allows to explicitly distill the structure between random output variables into a Wasserstein dependency matrix. Our work makes a preliminary step towards leveraging powerful generative models to establish generalization bounds for discriminative downstream tasks in the challenging setting of structured prediction.

Researchers investigating example hardness have increasingly focused on the dynamics by which neural networks learn and forget examples throughout training. Popular metrics derived from these dynamics include (i) the epoch at which examples are first correctly classified; (ii) the number of times their predictions flip during training; and (iii) whether their prediction flips if they are held out. However, these metrics do not distinguish among examples that are hard for distinct reasons, such as membership in a rare subpopulation, being mislabeled, or belonging to a complex subpopulation. In this paper, we propose second-split forgetting time (SSFT), a complementary metric that tracks the epoch (if any) after which an original training example is forgotten as the network is fine-tuned on a randomly held out partition of the data. Across multiple benchmark datasets and modalities, we demonstrate that mislabeled examples are forgotten quickly, and seemingly rare examples are forgotten comparatively slowly.

A desirable objective in self-supervised learning (SSL) is to avoid feature collapse. Whitening loss guarantees collapse avoidance by minimizing the distance between embeddings of positive pairs under the conditioning that the embeddings from different views are whitened. In this paper, we propose a framework with an informative indicator to analyze whitening loss, which provides a clue to demystify several interesting phenomena as well as a pivoting point connecting to other SSL methods. We reveal that batch whitening (BW) based methods do not impose whitening constraints on the embedding, but they only require the embedding to be full-rank. This full-rank constraint is also sufficient to avoid dimensional collapse.

We propose a framework of generative adversarial networks with multiple discriminators, which collaborate to represent a real dataset more effectively. Our approach facilitates learning a generator consistent with the underlying data distribution based on real images and thus mitigates the chronic mode collapse problem. From the inspiration of multiple choice learning, we guide each discriminator to have expertise in a subset of the entire data and allow the generator to find reasonable correspondences between the latent and real data spaces automatically without extra supervision for training examples. Despite the use of multiple discriminators, the backbone networks are shared across the discriminators and the increase in training cost is marginal. We demonstrate the effectiveness of our algorithm using multiple evaluation metrics in the standard datasets for diverse tasks.

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated training data tailored to a given setting, one may instead wish to learn useful information from heterogeneous sources, or from real dynamical systems observations that are messy or incomplete. In this work, we learn general-purpose representations of PDEs from heterogeneous data by implementing joint embedding methods for self-supervised learning (SSL), a framework for unsupervised representation learning that has had notable success in computer vision. Our representation outperforms baseline approaches to invariant tasks, such as regressing the coefficients of a PDE, while also improving the time-stepping performance of neural solvers. We hope that our proposed methodology will prove useful in the eventual development of general-purpose foundation models for PDEs.

A backdoor data poisoning attack is an adversarial attack wherein the attacker injects several watermarked, mislabeled training examples into a training set. The watermark does not impact the test-time performance of the model on typical data; however, the model reliably errs on watermarked examples.To gain a better foundational understanding of backdoor data poisoning attacks, we present a formal theoretical framework within which one can discuss backdoor data poisoning attacks for classification problems. We then use this to analyze important statistical and computational issues surrounding these attacks.On the statistical front, we identify a parameter we call the memorization capacity that captures the intrinsic vulnerability of a learning problem to a backdoor attack. This allows us to argue about the robustness of several natural learning problems to backdoor attacks. Our results favoring the attacker involve presenting explicit constructions of backdoor attacks, and our robustness results show that some natural problem settings cannot yield successful backdoor attacks.From a computational standpoint, we show that under certain assumptions, adversarial training can detect the presence of backdoors in a training set.

Continual Learning (CL) sequentially learns new tasks like human beings, with the goal to achieve better Stability (S, remembering past tasks) and Plasticity (P, adapting to new tasks). Due to the fact that past training data is not available, it is valuable to explore the influence difference on S and P among training examples, which may improve the learning pattern towards better SP. Inspired by Influence Function (IF), we first study example influence via adding perturbation to example weight and computing the influence derivation. To avoid the storage and calculation burden of Hessian inverse in neural networks, we propose a simple yet effective MetaSP algorithm to simulate the two key steps in the computation of IF and obtain the S- and P-aware example influence. Moreover, we propose to fuse two kinds of example influence by solving a dual-objective optimization problem, and obtain a fused influence towards SP Pareto optimality.

Self-Supervised Learning (SSL) surmises that inputs and pairwise positive relationships are enough to learn meaningful representations. Although SSL has recently reached a milestone: outperforming supervised methods in many modalities\dots the theoretical foundations are limited, method-specific, and fail to provide principled design guidelines to practitioners. In this paper, we propose a unifying framework under the helm of spectral manifold learning. Through the course of this study, we will demonstrate that VICReg, SimCLR, BarlowTwins et al. correspond to eponymous spectral methods such as Laplacian Eigenmaps, ISOMAP et al.From this unified viewpoint, we obtain (i) the close-form optimal representation, (ii) the close-form optimal network parameters in the linear regime, (iii) the impact of the pairwise relations used during training on each of those quantities and on downstream task performances, and most importantly, (iv) the first theoretical bridge between contrastive and non-contrastive methods to global and local spectral methods respectively hinting at the benefits and limitations of each. For example, if the pairwise relation is aligned with the downstream task, all SSL methods produce optimal representations for that downstream task.

Dropout training, originally designed for deep neural networks, has been successful on high-dimensional single-layer natural language tasks. This paper proposes a theoretical explanation for this phenomenon: we show that, under a generative Poisson topic model with long documents, dropout training improves the exponent in the generalization bound for empirical risk minimization. Dropout achieves this gain much like a marathon runner who practices at altitude: once a classifier learns to perform reasonably well on training examples that have been artificially corrupted by dropout, it will do very well on the uncorrupted test set. We also show that, under similar conditions, dropout preserves the Bayes decision boundary and should therefore induce minimal bias in high dimensions.