Self-supervised visual representation learning aims to learn useful representations without relying on human annotations. Joint embedding approach bases on maximizing the agreement between embedding vectors from different views of the same image. Various methods have been proposed to solve the collapsing problem where all embedding vectors collapse to a trivial constant solution. Among these methods, contrastive learning prevents collapse via negative sample pairs. It has been shown that non-contrastive methods suffer from a lesser collapse problem of a different nature: dimensional collapse, whereby the embedding vectors end up spanning a lower-dimensional subspace instead of the entire available embedding space. Here, we show that dimensional collapse also happens in contrastive learning. In this paper, we shed light on the dynamics at play in contrastive learning that leads to dimensional collapse. Inspired by our theory, we propose a novel contrastive learning method, called DirectCLR, which directly optimizes the representation space without relying on a trainable projector. Experiments show that DirectCLR outperforms SimCLR with a trainable linear projector on ImageNet.
Adversarial attacks expose important vulnerabilities of deep learning models, yet little attention has been paid to settings where data arrives as a stream. In this paper, we formalize the online adversarial attack problem, emphasizing two key elements found in real-world use-cases: attackers must operate under partial knowledge of the target model, and the decisions made by the attacker are irrevocable since they operate on a transient data stream. We first rigorously analyze a deterministic variant of the online threat model by drawing parallels to the well-studied $k$-\textit{secretary problem} and propose \algoname, a simple yet practical algorithm yielding a provably better competitive ratio for $k=2$ over the current best single threshold algorithm. We also introduce the \textit{stochastic $k$-secretary} -- effectively reducing online blackbox attacks to a $k$-secretary problem under noise -- and prove theoretical bounds on the competitive ratios of \textit{any} online algorithms adapted to this setting. Finally, we complement our theoretical results by conducting a systematic suite of experiments on MNIST and CIFAR-10 with both vanilla and robust classifiers, revealing that, by leveraging online secretary algorithms, like \algoname, we can get an online attack success rate close to the one achieved by the optimal offline solution.
Strong empirical evidence that one machine-learning algorithm A outperforms another one B ideally calls for multiple trials optimizing the learning pipeline over sources of variation such as data sampling, data augmentation, parameter initialization, and hyperparameters choices. This is prohibitively expensive, and corners are cut to reach conclusions. We model the whole benchmarking process, revealing that variance due to data sampling, parameter initialization and hyperparameter choice impact markedly the results. We analyze the predominant comparison methods used today in the light of this variance. We show a counter-intuitive result that adding more sources of variation to an imperfect estimator approaches better the ideal estimator at a 51 times reduction in compute cost. Building on these results, we study the error rate of detecting improvements, on five different deep-learning tasks/architectures. This study leads us to propose recommendations for performance comparisons.
We study episodic reinforcement learning in non-stationary linear (a.k.a. low-rank) Markov Decision Processes (MDPs), i.e, both the reward and transition kernel are linear with respect to a given feature map and are allowed to evolve either slowly or abruptly over time. For this problem setting, we propose OPT-WLSVI an optimistic model-free algorithm based on weighted least squares value iteration which uses exponential weights to smoothly forget data that are far in the past. We show that our algorithm, when competing against the best policy at each time, achieves a regret that is upped bounded by $\widetilde{\mathcal{O}}(d^{7/6}H^2 \Delta^{1/3} K^{2/3})$ where $d$ is the dimension of the feature space, $H$ is the planning horizon, $K$ is the number of episodes and $\Delta$ is a suitable measure of non-stationarity of the MDP. This is the first regret bound for non-stationary reinforcement learning with linear function approximation.
We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a possible regularization effect induced by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small number of task-relevant directions. By extrapolating a new analysis of Rademacher complexity bounds in linear models, we propose and study a new heuristic complexity measure for neural networks which captures this phenomenon, in terms of sequences of tangent kernel classes along in the learning trajectories.
The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain classes of stochastic smooth games. We propose a novel unbiased estimator for the stochastic Hamiltonian gradient descent (SHGD) and highlight its benefits. Using tools from the optimization literature we show that SHGD converges linearly to the neighbourhood of a stationary point. To guarantee convergence to the exact solution, we analyze SHGD with a decreasing step-size and we also present the first stochastic variance reduced Hamiltonian method. Our results provide the first global non-asymptotic last-iterate convergence guarantees for the class of stochastic unconstrained bilinear games and for the more general class of stochastic games that satisfy a "sufficiently bilinear" condition, notably including some non-convex non-concave problems. We supplement our analysis with experiments on stochastic bilinear and sufficiently bilinear games, where our theory is shown to be tight, and on simple adversarial machine learning formulations.
The \textit{Smoothed Bellman Error Embedding} algorithm~\citep{dai2018sbeed}, known as SBEED, was proposed as a provably convergent reinforcement learning algorithm with general nonlinear function approximation. It has been successfully implemented with neural networks and achieved strong empirical results. In this work, we study the theoretical behavior of SBEED in batch-mode reinforcement learning. We prove a near-optimal performance guarantee that depends on the representation power of the used function classes and a tight notion of the distribution shift. Our results improve upon prior guarantees for SBEED in ~\citet{dai2018sbeed} in terms of the dependence on the planning horizon and on the sample size. Our analysis builds on the recent work of ~\citet{Xie2020} which studies a related algorithm MSBO, that could be interpreted as a \textit{non-smooth} counterpart of SBEED.
The existence of adversarial examples capable of fooling trained neural network classifiers calls for a much better understanding of possible attacks, in order to guide the development of safeguards against them. It includes attack methods in the highly challenging non-interactive blackbox setting, where adversarial attacks are generated without any access, including queries, to the target model. Prior works in this setting have relied mainly on algorithmic innovations derived from empirical observations (e.g., that momentum helps), and the field currently lacks a firm theoretical basis for understanding transferability in adversarial attacks. In this work, we address this gap and lay the theoretical foundations for crafting transferable adversarial examples to entire function classes. We introduce Adversarial Examples Games (AEG), a novel framework that models adversarial examples as two-player min-max games between an attack generator and a representative classifier. We prove that the saddle point of an AEG game corresponds to a generating distribution of adversarial examples against entire function classes. Training the generator only requires the ability to optimize a representative classifier from a given hypothesis class, enabling BlackBox transfer to unseen classifiers from the same class. We demonstrate the efficacy of our approach on the MNIST and CIFAR-10 datasets against both undefended and robustified models, achieving competitive performance with state-of-the-art BlackBox transfer approaches.
By removing parameters from deep neural networks, unstructured pruning methods aim at cutting down memory footprint and computational cost, while maintaining prediction accuracy. In order to tackle this otherwise intractable problem, many of these methods model the loss landscape using first or second order Taylor expansions to identify which parameters can be discarded. We revisit loss modelling for unstructured pruning: we show the importance of ensuring locality of the pruning steps. We systematically compare first and second order Taylor expansions and empirically show that both can reach similar levels of performance. Finally, we show that better preserving the original network function does not necessarily transfer to better performing networks after fine-tuning, suggesting that only considering the impact of pruning on the loss might not be a sufficient objective to design good pruning criteria.
A longstanding goal in NLP is to compute global sentence representations. Such representations would be useful for sample-efficient semi-supervised learning and controllable text generation. To learn to represent global and local information separately, Bowman & al. (2016) proposed to train a sequence-to-sequence model with the variational auto-encoder (VAE) objective. What precisely is encoded in these latent variables expected to capture global features? We measure which words benefit most from the latent information by decomposing the reconstruction loss per position in the sentence. Using this method, we see that VAEs are prone to memorizing the first words and the sentence length, drastically limiting their usefulness. To alleviate this, we propose variants based on bag-of-words assumptions and language model pretraining. These variants learn latents that are more global: they are more predictive of topic or sentiment labels, and their reconstructions are more faithful to the labels of the original documents.