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Publication# Masked Training of Neural Networks with Partial Gradients

Martin Jaggi, Amirkeivan Mohtashami, Sebastian Urban Stich

*JMLR-JOURNAL MACHINE LEARNING RESEARCH, *2022

Article de conférence

Article de conférence

Résumé

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extra-gradient), limiting SGD updates to a subset of parameters for increased efficiency (such as meProp) or a combination of both (such as Dropout). However, the convergence of these methods is often not studied in theory. We propose a unified theoretical framework to study such SGD variants-encompassing the aforementioned algorithms and additionally a broad variety of methods used for communication efficient training or model compression. Our insights can be used as a guide to improve the efficiency of such methods and facilitate generalization to new applications. As an example, we tackle the task of jointly training networks, a version of which (limited to sub-networks) is used to create Slimmable Networks. By training a low-rank Transformer jointly with a standard one we obtain superior performance than when it is trained separately.

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Concepts associés (17)

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L'apprentissage profond ou apprentissage en profondeur (en anglais : deep learning, deep structured learning, hierarchical learning) est un sous-domaine de l’intelligence artificiel

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In this thesis, we propose new algorithms to solve inverse problems in the context of biomedical images. Due to ill-posedness, solving these problems require some prior knowledge of the statistics of the underlying images. The traditional algorithms, in the field, assume prior knowledge related to smoothness or sparsity of these images. Recently, they have been outperformed by the second generation algorithms which harness the power of neural networks to learn required statistics from training data. Even more recently, last generation deep-learning-based methods have emerged which require neither training nor training data. This thesis devises algorithms which progress through these generations. It extends these generations to novel formulations and applications while bringing more robustness. In parallel, it also progresses in terms of complexity, from proposing algorithms for problems with 1D data and an exact known forward model to the ones with 4D data and an unknown parametric forward model. We introduce five main contributions. The last three of them propose deep-learning-based latest-generation algorithms that require no prior training. 1) We develop algorithms to solve the continuous-domain formulation of inverse problems with both classical Tikhonov and total-variation regularizations. We formalize the problems, characterize the solution set, and devise numerical approaches to find the solutions. 2) We propose an algorithm that improves upon end-to-end neural-network-based second generation algorithms. In our method, a neural network is first trained as a projector on a training set, and is then plugged in as a projector inside the projected gradient descent (PGD). Since the problem is nonconvex, we relax the PGD to ensure convergence to a local minimum under some constraints. This method outperforms all the previous generation algorithms for Computed Tomography (CT). 3) We develop a novel time-dependent deep-image-prior algorithm for modalities that involve a temporal sequence of images. We parameterize them as the output of an untrained neural network fed with a sequence of latent variables. To impose temporal directionality, the latent variables are assumed to lie on a 1D manifold. The network is then tuned to minimize the data fidelity. We obtain state-of-the-art results in dynamic magnetic resonance imaging (MRI) and even recover intra-frame images. 4) We propose a novel reconstruction paradigm for cryo-electron-microscopy (CryoEM) called CryoGAN. Motivated by generative adversarial networks (GANs), we reconstruct a biomolecule's 3D structure such that its CryoEM measurements resemble the acquired data in a distributional sense. The algorithm is pose-or-likelihood-estimation-free, needs no ab initio, and is proven to have a theoretical guarantee of recovery of the true structure. 5) We extend CryoGAN to reconstruct continuously varying conformations of a structure from heterogeneous data. We parameterize the conformations as the output of a neural network fed with latent variables on a low-dimensional manifold. The method is shown to recover continuous protein conformations and their energy landscape.

In the last decade, deep neural networks have achieved tremendous success in many fields of machine learning.However, they are shown vulnerable against adversarial attacks: well-designed, yet imperceptible, perturbations can make the state-of-the-art deep neural networks output incorrect results.Understanding adversarial attacks and designing algorithms to make deep neural networks robust against these attacks are key steps to building reliable artificial intelligence in real-life applications.In this thesis, we will first formulate the robust learning problem.Based on the notations of empirical robustness and verified robustness, we design new algorithms to achieve both of these types of robustness.Specifically, we investigate the robust learning problem from the optimization perspectives.Compared with classic empirical risk minimization, we show the slow convergence and large generalization gap in robust learning.Our theoretical and numerical analysis indicates that these challenges arise, respectively, from non-smooth loss landscapes and model's fitting hard adversarial instances.Our insights shed some light on designing algorithms for mitigating these challenges.Robust learning has other challenges, such as large model capacity requirements and high computational complexity.To solve the model capacity issue, we combine robust learning with model compression.We design an algorithm to obtain sparse and binary neural networks and make it robust.To decrease the computational complexity, we accelerate the existing adversarial training algorithm and preserve its performance stability.In addition to making models robust, our research provides other benefits.Our methods demonstrate that robust models, compared with non-robust ones, usually utilize input features in a way more similar to the way human beings use them, hence the robust models are more interpretable.To obtain verified robustness, our methods indicate the geometric similarity of the decision boundaries near data points.Our approaches towards reliable artificial intelligence can not only render deep neural networks more robust in safety-critical applications but also make us better aware of how they work.

The way our brain learns to disentangle complex signals into unambiguous concepts is fascinating but remains largely unknown. There is evidence, however, that hierarchical neural representations play a key role in the cortex. This thesis investigates biologically plausible models of unsupervised learning of hierarchical representations as found in the brain and modern computer vision models. We use computational modeling to address three main questions at the intersection of artificial intelligence (AI) and computational neuroscience.The first question is: What are useful neural representations and when are deep hierarchical representations needed? We approach this point with a systematic study of biologically plausible unsupervised feature learning in a shallow 2-layer networks on digit (MNIST) and object (CIFAR10) classification. Surprisingly, random features support high performance, especially for large hidden layers. When combined with localized receptive fields, random feature networks approach the performance of supervised backpropagation on MNIST, but not on CIFAR10. We suggest that future models of biologically plausible learning should outperform such random feature benchmarks on MNIST, or that such models should be evaluated in different ways.The second question is: How can hierarchical representations be learned with mechanisms supported by neuroscientific evidence? We cover this question by proposing a unifying Hebbian model, inspired by common models of V1 simple and complex cells based on unsupervised sparse coding and temporal invariance learning. In shallow 2-layer networks, our model reproduces learning of simple and complex cell receptive fields, as found in V1. In deeper networks, we stack multiple layers of Hebbian learning but find that it does not yield hierarchical representations of increasing usefulness. From this, we hypothesise that standard Hebbian rules are too constrained to build increasingly useful representations, as observed in higher areas of the visual cortex or deep artificial neural networks.The third question is: Can AI inspire learning models that build deep representations and are still biologically plausible? We address this question by proposing a learning rule that takes inspiration from neuroscience and recent advances in self-supervised deep learning. The proposed rule is Hebbian, i.e. only depends on pre- and post-synaptic neuronal activity, but includes additional local factors, namely predictive dendritic input and widely broadcasted modulation factors. Algorithmically, this rule applies self-supervised contrastive predictive learning to a causal, biological setting using saccades. We find that networks trained with this generalised Hebbian rule build deep hierarchical representations of images, speech and video.We see our modeling as a potential starting point for both, new hypotheses, that can be tested experimentally, and novel AI models that could benefit from added biological realism.