The ability to compose learned skills to solve new tasks is an important property of lifelong-learning agents.

Combinatorial dimensions play an important role in the theory of machine learning. For example, VC dimension characterizes PAC learning, SQ dimension characterizes weak learning with statistical queries, and Littlestone dimension characterizes online learning. In this paper we aim to develop combinatorial dimensions that characterize bounded memory learning. We propose a candidate solution for the case of realizable strong learning under a known distribution, based on the SQ dimension of neighboring distributions. We prove both upper and lower bounds for our candidate solution, that match in some regime of parameters. This is the first characterization of strong learning under space constraints in any regime. In this parameter regime there is an equivalence between bounded memory and SQ learning. We conjecture that our characterization holds in a much wider regime of parameters.

Federated Learning (FL) is a distributed machine learning framework that trains accurate global models while preserving clients' privacy-sensitive data. However, most FL approaches assume that clients possess labeled data, which is often not the case in practice. Federated Semi-Supervised Learning (FSSL) addresses this label deficiency problem, targeting situations where only the server has a small amount of labeled data while clients do not. However, a significant performance gap exists between Centralized Semi-Supervised Learning (SSL) and FSSL. This gap arises from confirmation bias, which is more pronounced in FSSL due to multiple local training epochs and the separation of labeled and unlabeled data.

Bayesian neural networks and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their heavy memory and inference cost. This motivates us to study principled approaches to high-quality uncertainty estimation that require only a single deep neural network (DNN). By formalizing the uncertainty quantification as a minimax learning problem, we first identify distance awareness, i.e., the model's ability to properly quantify the distance of a testing example from the training data manifold, as a necessary condition for a DNN to achieve high-quality (i.e., minimax optimal) uncertainty estimation. We then propose Spectral-normalized Neural Gaussian Process (SNGP), a simple method that improves the distance-awareness ability of modern DNNs, by adding a weight normalization step during training and replacing the output layer with a Gaussian Process. On a suite of vision and language understanding tasks and on modern architectures (Wide-ResNet and BERT), SNGP is competitive with deep ensembles in prediction, calibration and out-of-domain detection, and outperforms the other single-model approaches.

Continual learning has primarily focused on the issue of catastrophic forgetting and the associated stability-plasticity tradeoffs. However, little attention has been paid to the efficacy of continually learned representations, as representations are learned alongside classifiers throughout the learning process. Our primary contribution is empirically demonstrating that existing online continually trained deep networks produce inferior representations compared to a simple pre-defined random transforms. Our approach projects raw pixels using a fixed random transform, approximating an RBF-Kernel initialized before any data is seen. We then train a simple linear classifier on top without storing any exemplars, processing one sample at a time in an online continual learning setting. This method, called RanDumb, significantly outperforms state-of-the-art continually learned representations across all standard online continual learning benchmarks. Our study reveals the significant limitations of representation learning, particularly in low-exemplar and online continual learning scenarios. Extending our investigation to popular exemplar-free scenarios with pretrained models, we find that training only a linear classifier on top of pretrained representations surpasses most continual fine-tuning and prompt-tuning strategies. Overall, our investigation challenges the prevailing assumptions about effective representation learning in online continual learning.

Multimodal models trained on modality-complete data are plagued with severe performance degradation when encountering modality-missing data. Prevalent cross-modal knowledge distillation-based methods precisely align the representation of modality-missing data and that of its modality-complete counterpart to enhance robustness. However, due to the irreparable information asymmetry, this determinate alignment is too stringent, easily inducing modality-missing features to capture spurious factors erroneously. In this paper, a novel multimodal Probabilistic Conformal Distillation (PCD) method is proposed, which considers the inherent indeterminacy in this alignment. Given a modality-missing input, our goal is to learn the unknown Probability Density Function (PDF) of the mapped variables in the modality-complete space, rather than relying on the brute-force point alignment. Specifically, PCD models the modality-missing feature as a probabilistic distribution, enabling it to satisfy two characteristics of the PDF. One is the extremes of probabilities of modality-complete feature points on the PDF, and the other is the geometric consistency between the modeled distributions and the peak points of different PDFs. Extensive experiments on a range of benchmark datasets demonstrate the superiority of PCD over state-of-the-art methods. Code is available at: https://github.com/mxchen-mc/PCD.

Learning quickly is of great importance for machine intelligence deployed in online platforms. With the capability of transferring knowledge from learned tasks, meta-learning has shown its effectiveness in online scenarios by continuously updating the model with the learned prior. However, current online meta-learning algorithms are limited to learn a globally-shared meta-learner, which may lead to sub-optimal results when the tasks contain heterogeneous information that are distinct by nature and difficult to share. We overcome this limitation by proposing an online structured meta-learning (OSML) framework. Inspired by the knowledge organization of human and hierarchical feature representation, OSML explicitly disentangles the meta-learner as a meta-hierarchical graph with different knowledge blocks. When a new task is encountered, it constructs a meta-knowledge pathway by either utilizing the most relevant knowledge blocks or exploring new blocks. Through the meta-knowledge pathway, the model is able to quickly adapt to the new task. In addition, new knowledge is further incorporated into the selected blocks. Experiments on three datasets demonstrate the effectiveness and interpretability of our proposed framework in the context of both homogeneous and heterogeneous tasks.

We propose a novel method for learning representations of poses for 3D deformable objects, which specializes in 1) disentangling pose information from the object's identity, 2) facilitating the learning of pose variations, and 3) transferring pose information to other object identities. Based on these properties, our method enables the generation of 3D deformable objects with diversity in both identities and poses, using variations of a single object. It does not require explicit shape parameterization such as skeletons or joints, point-level or shape-level correspondence supervision, or variations of the target object for pose transfer. We first design the pose extractor to represent the pose as a keypoint-based hybrid representation and the pose applier to learn an implicit deformation field. To better distill pose information from the object's geometry, we propose the implicit pose applier to output an intrinsic mesh property, the face Jacobian. Once the extracted pose information is transferred to the target object, the pose applier is fine-tuned in a self-supervised manner to better describe the target object's shapes with pose variations. The extracted poses are also used to train a cascaded diffusion model to enable the generation of novel poses. Our experiments with the DeformThings4D and Human datasets demonstrate state-of-the-art performance in pose transfer and the ability to generate diverse deformed shapes with various objects and poses.

We consider the problem of controlling an unknown linear dynamical system under adversarially changing convex costs and full feedback of both the state and cost function. We present the first computationally-efficient algorithm that attains an optimal -regret rate compared to the best stabilizing linear controller in hindsight, while avoiding stringent assumptions on the costs such as strong convexity. Our approach is based on a careful design of non-convex lower confidence bounds for the online costs, and uses a novel technique for computationally-efficient regret minimization of these bounds that leverages their particular non-convex structure.

Diffusion models have recently advanced Combinatorial Optimization (CO) as a powerful backbone for neural solvers.