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Register a new userPolicy Manifold Search: Exploring the Manifold Hypothesis for Diversity-based Neuroevolution
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Added by
Nemanja Rakicevic
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Neuroevolution is an alternative to gradient-based optimisation that has the potential to avoid local minima and allows parallelisation. The main limiting factor is that usually it does not scale well with parameter space dimensionality. Inspired by recent work examining neural network intrinsic dimension and loss landscapes, we hypothesise that there exists a low-dimensional manifold, embedded in the policy network parameter space, around which a high-density of diverse and useful policies are located. This paper proposes a novel method for diversity-based policy search via Neuroevolution, that leverages learned representations of the policy network parameters, by performing policy search in this learned representation space. Our method relies on the Quality-Diversity (QD) framework which provides a principled approach to policy search, and maintains a collection of diverse policies, used as a dataset for learning policy representations. Further, we use the Jacobian of the inverse-mapping function to guide the search in the representation space. This ensures that the generated samples remain in the high-density regions, after mapping back to the original space. Finally, we evaluate our contributions on four continuous-control tasks in simulated environments, and compare to diversity-based baselines.
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Diversity-based approaches have recently gained popularity as an alternative paradigm to performance-based policy search. A popular approach from this family, Quality-Diversity (QD), maintains a collection of high-performing policies separated in the diversity-metric space, defined based on policies rollout behaviours. When policies are parameterised as neural networks, i.e. Neuroevolution, QD tends to not scale well with parameter space dimensionality. Our hypothesis is that there exists a low-dimensional manifold embedded in the policy parameter space, containing a high density of diverse and feasible policies. We propose a novel approach to diversity-based policy search via Neuroevolution, that leverages learned latent representations of the policy parameters which capture the local structure of the data. Our approach iteratively collects policies according to the QD framework, in order to (i) build a collection of diverse policies, (ii) use it to learn a latent representation of the policy parameters, (iii) perform policy search in the learned latent space. We use the Jacobian of the inverse transformation (i.e.reconstruction function) to guide the search in the latent space. This ensures that the generated samples remain in the high-density regions of the original space, after reconstruction. We evaluate our contributions on three continuous control tasks in simulated environments, and compare to diversity-based baselines. The findings suggest that our approach yields a more efficient and robust policy search process.
Few-shot learning algorithms aim to learn model parameters capable of adapting to unseen classes with the help of only a few labeled examples. A recent regularization technique - Manifold Mixup focuses on learning a general-purpose representation, robust to small changes in the data distribution. Since the goal of few-shot learning is closely linked to robust representation learning, we study Manifold Mixup in this problem setting. Self-supervised learning is another technique that learns semantically meaningful features, using only the inherent structure of the data. This work investigates the role of learning relevant feature manifold for few-shot tasks using self-supervision and regularization techniques. We observe that regularizing the feature manifold, enriched via self-supervised techniques, with Manifold Mixup significantly improves few-shot learning performance. We show that our proposed method S2M2 beats the current state-of-the-art accuracy on standard few-shot learning datasets like CIFAR-FS, CUB, mini-ImageNet and tiered-ImageNet by 3-8 %. Through extensive experimentation, we show that the features learned using our approach generalize to complex few-shot evaluation tasks, cross-domain scenarios and are robust against slight changes to data distribution.
In this paper, we propose a new neural architecture search (NAS) problem of Symmetric Positive Definite (SPD) manifold networks, aiming to automate the design of SPD neural architectures. To address this problem, we first introduce a geometrically rich and diverse SPD neural architecture search space for an efficient SPD cell design. Further, we model our new NAS problem with a one-shot training process of a single supernet. Based on the supernet modeling, we exploit a differentiable NAS algorithm on our relaxed continuous search space for SPD neural architecture search. Statistical evaluation of our method on drone, action, and emotion recognition tasks mostly provides better results than the state-of-the-art SPD networks and traditional NAS algorithms. Empirical results show that our algorithm excels in discovering better performing SPD network design and provides models that are more than three times lighter than searched by the state-of-the-art NAS algorithms.
In this paper we propose a novel augmentation technique that improves not only the performance of deep neural networks on clean test data, but also significantly increases their robustness to random transformations, both affine and projective. Inspired by ManiFool, the augmentation is performed by a line-search manifold-exploration method that learns affine geometric transformations that lead to the misclassification on an image, while ensuring that it remains on the same manifold as the training data. This augmentation method populates any training dataset with images that lie on the border of the manifolds between two-classes and maximizes the variance the network is exposed to during training. Our method was thoroughly evaluated on the challenging tasks of fine-grained skin lesion classification from limited data, and breast tumor classification of mammograms. Compared with traditional augmentation methods, and with images synthesized by Generative Adversarial Networks our method not only achieves state-of-the-art performance but also significantly improves the networks robustness.
Many measurements or observations in computer vision and machine learning manifest as non-Euclidean data. While recent proposals (like spherical CNN) have extended a number of deep neural network architectures to manifold-valued data, and this has often provided strong improvements in performance, the literature on generative models for manifold data is quite sparse. Partly due to this gap, there are also no modality transfer/translation models for manifold-valued data whereas numerous such methods based on generative models are available for natural images. This paper addresses this gap, motivated by a need in brain imaging -- in doing so, we expand the operating range of certain generative models (as well as generative models for modality transfer) from natural images to images with manifold-valued measurements. Our main result is the design of a two-stream version of GLOW (flow-based invertible generative models) that can synthesize information of a field of one type of manifold-valued measurements given another. On the theoretical side, we introduce three kinds of invertible layers for manifold-valued data, which are not only analogous to their functionality in flow-based generative models (e.g., GLOW) but also preserve the key benefits (determinants of the Jacobian are easy to calculate). For experiments, on a large dataset from the Human Connectome Project (HCP), we show promising results where we can reliably and accurately reconstruct brain images of a field of orientation distribution functions (ODF) from diffusion tensor images (DTI), where the latter has a $5times$ faster acquisition time but at the expense of worse angular resolution.
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