General ML · supervised learning

Infants possess a remarkable ability to rapidly learn and process visual inputs. As an infant's mobility increases, so does the variety and dynamics of their visual inputs. Is this change in the properties of the visual inputs beneficial or even critical for the proper development of the visual system? To address this question, we used video recordings from infants wearing head-mounted cameras to train a variety of self-supervised learning models. Critically, we separated the infant data by age group and evaluated the importance of training with a curriculum aligned with developmental order. We found that initiating learning with the data from the youngest age group provided the strongest learning signal and led to the best learning outcomes in terms of downstream task performance. We then showed that the benefits of the data from the youngest age group are due to the slowness and simplicity of the visual experience. The results provide strong empirical evidence for the importance of the properties of the early infant experience and developmental progression in training. More broadly, our approach and findings take a noteworthy step towards reverse engineering the learning mechanisms in newborn brains using image-computable models from artificial intelligence.

Non-contrastive SSL methods like BYOL and SimSiam rely on asymmetric predictor networks to avoid representational collapse without negative samples. Yet, how predictor networks facilitate stable learning is not fully understood. While previous theoretical analyses assumed Euclidean losses, most practical implementations rely on cosine similarity. To gain further theoretical insight into non-contrastive SSL, we analytically study learning dynamics in conjunction with Euclidean and cosine similarity in the eigenspace of closed-form linear predictor networks. We show that both avoid collapse through implicit variance regularization albeit through different dynamical mechanisms. Moreover, we find that the eigenvalues act as effective learning rate multipliers and propose a family of isotropic loss functions (IsoLoss) that equalize convergence rates across eigenmodes. Empirically, IsoLoss speeds up the initial learning dynamics and increases robustness, thereby allowing us to dispense with the EMA target network typically used with non-contrastive methods. Our analysis sheds light on the variance regularization mechanisms of non-contrastive SSL and lays the theoretical grounds for crafting novel loss functions that shape the learning dynamics of the predictor's spectrum.

We consider the problem of best arm identification in the multi-armed bandit model, under fixed confidence. Given a confidence input $\delta$, the goal is to identify the arm with the highest mean reward with a probability of at least $1 - \delta$, while minimizing the number of arm pulls. While the literature provides solutions to this problem under the assumption of independent arms distributions, we propose a more flexible scenario where arms can be dependent and rewards can be sampled simultaneously. This framework allows the learner to estimate the covariance among the arms distributions, enabling a more efficient identification of the best arm. The relaxed setting we propose is relevant in various applications, such as clinical trials, where similarities between patients or drugs suggest underlying correlations in the outcomes. We introduce new algorithms that adapt to the unknown covariance of the arms and demonstrate through theoretical guarantees that substantial improvement can be achieved over the standard setting. Additionally, we provide new lower bounds for the relaxed setting and present numerical simulations that support their theoretical findings.

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the variance of the posterior predictive distribution (Bayesian model average) and compare its asymptotics to that of the risk of the MAP estimator. In the regime where the model dimensions grow faster than any constant multiple of the number of samples, asymptotic agreement between these two quantities is governed by the phase transition in the signal-to-noise ratio. They also asymptotically agree with each other when the number of samples grow faster than any constant multiple of model dimensions. Numerical simulations illustrate finer distributional properties of the two quantities for finite dimensions. We conjecture they have Gaussian fluctuations and exhibit similar properties as found by previous authors in a Gaussian sequence model, this is of independent theoretical interest.

Graph-based semi-supervised learning (GSSL) serves as a powerful tool to model the underlying manifold structures of samples in high-dimensional spaces. It involves two phases: constructing an affinity graph from available data and inferring labels for unlabeled nodes on this graph. While numerous algorithms have been developed for label inference, the crucial graph construction phase has received comparatively less attention, despite its significant influence on the subsequent phase. In this paper, we present an optimal asymmetric graph structure for the label inference phase with theoretical motivations. Unlike existing graph construction methods, we differentiate the distinct roles that labeled nodes and unlabeled nodes could play. Accordingly, we design an efficient block-wise graph learning algorithm with a global convergence guarantee. Other benefits induced by our method, such as enhanced robustness to noisy node features, are explored as well. Finally, we perform extensive experiments on synthetic and real-world datasets to demonstrate its superiority to the state-of-the-art graph construction methods in GSSL.

Self-supervised learning (SSL) has great potential for molecular representation learning given the complexity of molecular graphs, the large amounts of unlabelled data available, the considerable cost of obtaining labels experimentally, and the hence often only small training datasets. The importance of the topic is reflected in the variety of paradigms and architectures that have been investigated recently, most focus on designing views for contrastive learning. In this paper, we study SSL based on persistent homology (PH), a mathematical tool for modeling topological features of data that persist across multiple scales. It has several unique features which particularly suit SSL, naturally offering: different views of the data, stability in terms of distance preservation, and the opportunity to flexibly incorporate domain knowledge. We (1) investigate an autoencoder, which shows the general representational power of PH, and (2) propose a contrastive loss that complements existing approaches. We rigorously evaluate our approach for molecular property prediction and demonstrate its particular features in improving the embedding space: after SSL, the representations are better and offer considerably more predictive power than the baselines over different probing tasks; our loss increases baseline performance, sometimes largely; and we often obtain substantial improvements over very small datasets, a common scenario in practice.

Prior theoretical and empirical works have established that semi-supervised learning algorithms can leverage the unlabeled data to improve over the labeled sample complexity of supervised learning (SL) algorithms. However, existing theoretical work focuses on regimes where the unlabeled data is sufficient to learn a good decision boundary using unsupervised learning (UL) alone. This begs the question: Can SSL algorithms simultaneously improve upon both UL and SL? To this end, we derive a tight lower bound for 2-Gaussian mixture models that explicitly depends on the labeled and the unlabeled dataset size as well as the signal-to-noise ratio of the mixture distribution. Surprisingly, our result implies that no SSL algorithm improves upon the minimax-optimal statistical error rates of SL or UL algorithms for these distributions. Nevertheless, in our real-world experiments, SSL algorithms can often outperform UL and SL algorithms. In summary, our work suggests that while it is possible to prove the performance gains of SSL algorithms, this would require careful tracking of constants in the theoretical analysis.

Analysis of compressible turbulent flows is essential for applications related to propulsion, energy generation, and the environment. Here, we present BLASTNet 2.0, a 2.2 TB network-of-datasets containing 744 full-domain samples from 34 high-fidelity direct numerical simulations, which addresses the current limited availability of 3D high-fidelity reacting and non-reacting compressible turbulent flow simulation data. With this data, we benchmark a total of 49 variations of five deep learning approaches for 3D super-resolution - which can be applied for improving scientific imaging, simulations, turbulence models, as well as in computer vision applications. We perform neural scaling analysis on these models to examine the performance of different machine learning (ML) approaches, including two scientific ML techniques. We demonstrate that (i) predictive performance can scale with model size and cost, (ii) architecture matters significantly, especially for smaller models, and (iii) the benefits of physics-based losses can persist with increasing model size. The outcomes of this benchmark study are anticipated to offer insights that can aid the design of 3D super-resolution models, especially for turbulence models, while this data is expected to foster ML methods for a broad range of flow physics applications. This data is publicly available with download links and browsing tools consolidated at https://blastnet.github.io.

Model-free reinforcement learning algorithms have exhibited great potential in solving single-task sequential decision-making problems with high-dimensional observations and long horizons, but are known to be hard to generalize across tasks. Model-based RL, on the other hand, learns task-agnostic models of the world that naturally enables transfer across different reward functions, but struggles to scale to complex environments due to the compounding error. To get the best of both worlds, we propose a self-supervised reinforcement learning method that enables the transfer of behaviors across tasks with different rewards, while circumventing the challenges of model-based RL. In particular, we show self-supervised pre-training of model-free reinforcement learning with a number of random features as rewards allows implicit modeling of long-horizon environment dynamics. Then, planning techniques like model-predictive control using these implicit models enable fast adaptation to problems with new reward functions. Our method is self-supervised in that it can be trained on offline datasets without reward labels, but can then be quickly deployed on new tasks. We validate that our proposed method enables transfer across tasks on a variety of manipulation and locomotion domains in simulation, opening the door to generalist decision-making agents.

Semi-supervised learning (SSL) has been a fundamental challenge in machine learning for decades. The primary family of SSL algorithms, known as pseudo-labeling, involves assigning pseudo-labels to confident unlabeled instances and incorporating them into the training set. Therefore, the selection criteria of confident instances are crucial to the success of SSL. Recently, there has been growing interest in the development of SSL methods that use dynamic or adaptive thresholds. Yet, these methods typically apply the same threshold to all samples, or use class-dependent thresholds for instances belonging to a certain class, while neglecting instance-level information. In this paper, we propose the study of instance-dependent thresholds, which has the highest degree of freedom compared with existing methods. Specifically, we devise a novel instance-dependent threshold function for all unlabeled instances by utilizing their instance-level ambiguity and the instance-dependent error rates of pseudo-labels, so instances that are more likely to have incorrect pseudo-labels will have higher thresholds. Furthermore, we demonstrate that our instance-dependent threshold function provides a bounded probabilistic guarantee for the correctness of the pseudo-labels it assigns.

Decision trees have gained popularity as interpretable surrogate models for learning-based control policies. However, providing safety guarantees for systems controlled by decision trees is an open challenge. We show that the problem is undecidable even for systems with the simplest dynamics, and PSPACE-complete for finite-horizon properties. The latter can be verified for discrete-time systems via bounded model checking. However, for continuous-time systems, such an approach requires discretization, thereby weakening the guarantees for the original system. This paper presents the first algorithm to directly verify decision-tree controlled system in continuous time. The key aspect of our method is exploiting the decision-tree structure to propagate a set-based approximation through the decision nodes. We demonstrate the effectiveness of our approach by verifying safety of several decision trees distilled to imitate neural-network policies for nonlinear systems.

This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to and improves existing finite-dimensional analyses. In contrast to comparable work in the literature, the approach proposed here relies on a direct analysis of the underlying risk functional and completely avoids the explicit RF ridge regression solution formula in terms of random matrices. This removes the need for concentration results in random matrix theory or their generalizations to random operators. The main results established in this paper include strong consistency of vector-valued RF estimators under model misspecification and minimax optimal convergence rates in the well-specified setting. The parameter complexity (number of random features) and sample complexity (number of labeled data) required to achieve such rates are comparable with Monte Carlo intuition and free from logarithmic factors.

A default assumption in reinforcement learning (RL) and optimal control is that observations arrive at discrete time points on a fixed clock cycle. Yet, many applications involve continuous-time systems where the time discretization, in principle, can be managed. The impact of time discretization on RL methods has not been fully characterized in existing theory, but a more detailed analysis of its effect could reveal opportunities for improving data-efficiency. We address this gap by analyzing Monte-Carlo policy evaluation for LQR systems and uncover a fundamental trade-off between approximation and statistical error in value estimation. Importantly, these two errors behave differently to time discretization, leading to an optimal choice of temporal resolution for a given data budget. These findings show that managing the temporal resolution can provably improve policy evaluation efficiency in LQR systems with finite data. Empirically, we demonstrate the trade-off in numerical simulations of LQR instances and standard RL benchmarks for non-linear continuous control.

Supervised training of deep neural networks on pairs of clean image and noisy measurement achieves state-of-the-art performance for many image reconstruction tasks, but such training pairs are difficult to collect. Self-supervised methods enable training based on noisy measurements only, without clean images. In this work, we investigate the cost of self-supervised training in terms of sample complexity for a class of self-supervised methods that enable the computation of unbiased estimates of gradients of the supervised loss, including noise2noise methods. We analytically show that a model trained with such self-supervised training is as good as the same model trained in a supervised fashion, but self-supervised training requires more examples than supervised training. We then study self-supervised denoising and accelerated MRI empirically and characterize the cost of self-supervised training in terms of the number of additional samples required, and find that the performance gap between self-supervised and supervised training vanishes as a function of the training examples, at a problem-dependent rate, as predicted by our theory.

The Maximum Entropy (Max-Ent) framework has been effectively employed in a variety of Reinforcement Learning (RL) tasks. In this paper, we first propose a novel Max-Ent framework for policy evaluation in a distributional RL setting, named *Distributional Maximum Entropy Policy Evaluation* (D-Max-Ent PE). We derive a generalization-error bound that depends on the complexity of the representation employed, showing that this framework can explicitly take into account the features used to represent the state space while evaluating a policy. Then, we exploit these favorable properties to drive the representation learning of the state space in a Structural Risk Minimization fashion. We employ state-aggregation functions as feature functions and we specialize the D-Max-Ent approach into an algorithm, named *D-Max-Ent Progressive Factorization*, which constructs a progressively finer-grained representation of the state space by balancing the trade-off between preserving information (bias) and reducing the effective number of states, i.e., the complexity of the representation space (variance). Finally, we report the results of some illustrative numerical simulations, showing that the proposed algorithm matches the expected theoretical behavior and highlighting the relationship between aggregations and sample regimes.

We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks ($G$-CNNs), which we call the $G$-triple-correlation ($G$-TC) layer. The approach leverages the theory of the triple-correlation on groups, which is the unique, lowest-degree polynomial invariant map that is also \textit{complete}. Many commonly used invariant maps\textemdash such as the \texttt{max}\textemdash are incomplete: they remove both group and signal structure. A complete invariant, by contrast, removes only the variation due to the actions of the group, while preserving all information about the structure of the signal. The completeness of the triple correlation endows the $G$-TC layer with strong robustness, which can be observed in its resistance to invariance-based adversarial attacks. In addition, we observe that it yields measurable improvements in classification accuracy over standard Max $G$-Pooling in $G$-CNN architectures. We provide a general and efficient implementation of the method for any discretized group, which requires only a table defining the group's product structure. We demonstrate the benefits of this method for $G$-CNNs defined on both commutative and non-commutative groups\textemdash $SO(2)$, $O(2)$, $SO(3)$, and $O(3)$ (discretized as the cyclic $C8$, dihedral $D16$, chiral octahedral $O$ and full octahedral $O_h$ groups)\textemdash acting on $\mathbb{R}^2$ and $\mathbb{R}^3$ on both $G$-MNIST and $G$-ModelNet10 datasets.

Self-supervised learning (SSL) algorithms can produce useful image representations by learning to associate different parts of natural images with one another. However, when taken to the extreme, SSL models can unintendedly memorize specific parts in individual training samples rather than learning semantically meaningful associations. In this work, we perform a systematic study of the unintended memorization of image-specific information in SSL models -- which we refer to as déjà vu memorization. Concretely, we show that given the trained model and a crop of a training image containing only the background (e.g., water, sky, grass), it is possible to infer the foreground object with high accuracy or even visually reconstruct it. Furthermore, we show that déjà vu memorization is common to different SSL algorithms, is exacerbated by certain design choices, and cannot be detected by conventional techniques for evaluating representation quality. Our study of déjà vu memorization reveals previously unknown privacy risks in SSL models, as well as suggests potential practical mitigation strategies.

Recalibrating probabilistic classifiers is vital for enhancing the reliability and accuracy of predictive models. Despite the development of numerous recalibration algorithms, there is still a lack of a comprehensive theory that integrates calibration and sharpness (which is essential for maintaining predictive power). In this paper, we introduce the concept of minimum-risk recalibration within the framework of mean-squared-error (MSE) decomposition, offering a principled approach for evaluating and recalibrating probabilistic classifiers. Using this framework, we analyze the uniform-mass binning (UMB) recalibration method and establish a finite-sample risk upper bound of order $\tilde{O}(B/n + 1/B^2)$ where $B$ is the number of bins and $n$ is the sample size. By balancing calibration and sharpness, we further determine that the optimal number of bins for UMB scales with $n^{1/3}$, resulting in a risk bound of approximately $O(n^{-2/3})$. Additionally, we tackle the challenge of label shift by proposing a two-stage approach that adjusts the recalibration function using limited labeled data from the target domain. Our results show that transferring a calibrated classifier requires significantly fewer target samples compared to recalibrating from scratch. We validate our theoretical findings through numerical simulations, which confirm the tightness of the proposed bounds, the optimal number of bins, and the effectiveness of label shift adaptation.

Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function independently, joint training of both components remains an open challenge. This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data. Early on, we notice that training transformer-based neural processes from scratch with RL is challenging due to insufficient supervision, especially when rewards are sparse. We formalise this claim with a combinatorial analysis showing that the widely used notion of regret as a reward signal exhibits a logarithmic sparsity pattern in trajectory lengths. To tackle this problem, we augment the RL objective with an auxiliary task that guides part of the architecture to learn a valid probabilistic model as an inductive bias. We demonstrate that our method achieves state-of-the-art regret results against various baselines in experiments on standard hyperparameter optimisation tasks and also outperforms others in the real-world problems of mixed-integer programming tuning, antibody design, and logic synthesis for electronic design automation.

Imitation learning aims to reproduce expert behaviors without relying on an explicit reward signal. However, real-world demonstrations often present challenges, such as multi-modal, data imbalance, and expensive labeling processes. In this work, we propose a novel semi-supervised imitation learning architecture that learns disentangled behavior representations from imbalanced demonstrations using limited labeled data. Specifically, our method consists of three key components. First, we adapt the concept of semi-supervised generative adversarial networks to the imitation learning context. Second, we employ a learnable latent distribution to align the generated and expert data distributions. Finally, we utilize a regularized information maximization approach in conjunction with an approximate label prior to further improve the semi-supervised learning performance. Experimental results demonstrate the efficiency of our method in learning multi-modal behaviors from imbalanced demonstrations compared to baseline methods.