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Register a new userOptimization Induced Equilibrium Networks
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Added by
Zenan Ling
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Implicit equilibrium models, i.e., deep neural networks (DNNs) defined by implicit equations, have been becoming more and more attractive recently. In this paper, we investigate an emerging question: can an implicit equilibrium models equilibrium point be regarded as the solution of an optimization problem? To this end, we first decompose DNNs into a new class of unit layer that is the proximal operator of an implicit convex function while keeping its output unchanged. Then, the equilibrium model of the unit layer can be derived, named Optimization Induced Equilibrium Networks (OptEq), which can be easily extended to deep layers. The equilibrium point of OptEq can be theoretically connected to the solution of its corresponding convex optimization problem with explicit objectives. Based on this, we can flexibly introduce prior properties to the equilibrium points: 1) modifying the underlying convex problems explicitly so as to change the architectures of OptEq; and 2) merging the information into the fixed point iteration, which guarantees to choose the desired equilibrium point when the fixed point set is non-singleton. We show that deep OptEq outperforms previous implicit models even with fewer parameters. This work establishes the first step towards the optimization-guided design of deep models.
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Artificial neural networks, one of the most successful approaches to supervised learning, were originally inspired by their biological counterparts. However, the most successful learning algorithm for artificial neural networks, backpropagation, is considered biologically implausible. We contribute to the topic of biologically plausible neuronal learning by building upon and extending the equilibrium propagation learning framework. Specifically, we introduce: a new neuronal dynamics and learning rule for arbitrary network architectures; a sparsity-inducing method able to prune irrelevant connections; a dynamical-systems characterization of the models, using Lyapunov theory.
We investigate the parameter-space geometry of recurrent neural networks (RNNs), and develop an adaptation of path-SGD optimization method, attuned to this geometry, that can learn plain RNNs with ReLU activations. On several datasets that require capturing long-term dependency structure, we show that path-SGD can significantly improve trainability of ReLU RNNs compared to RNNs trained with SGD, even with various recently suggested initialization schemes.
Neural Architecture Search (NAS) was first proposed to achieve state-of-the-art performance through the discovery of new architecture patterns, without human intervention. An over-reliance on expert knowledge in the search space design has however led to increased performance (local optima) without significant architectural breakthroughs, thus preventing truly novel solutions from being reached. In this work we 1) are the first to investigate casting NAS as a problem of finding the optimal network generator and 2) we propose a new, hierarchical and graph-based search space capable of representing an extremely large variety of network types, yet only requiring few continuous hyper-parameters. This greatly reduces the dimensionality of the problem, enabling the effective use of Bayesian Optimisation as a search strategy. At the same time, we expand the range of valid architectures, motivating a multi-objective learning approach. We demonstrate the effectiveness of this strategy on six benchmark datasets and show that our search space generates extremely lightweight yet highly competitive models.
An important linear algebra routine, GEneral Matrix Multiplication (GEMM), is a fundamental operator in deep learning. Compilers need to translate these routines into low-level code optimized for specific hardware. Compiler-level optimization of GEMM has significant performance impact on training and executing deep learning models. However, most deep learning frameworks rely on hardware-specific operator libraries in which GEMM optimization has been mostly achieved by manual tuning, which restricts the performance on different target hardware. In this paper, we propose two novel algorithms for GEMM optimization based on the TVM framework, a lightweight Greedy Best First Search (G-BFS) method based on heuristic search, and a Neighborhood Actor Advantage Critic (N-A2C) method based on reinforcement learning. Experimental results show significant performance improvement of the proposed methods, in both the optimality of the solution and the cost of search in terms of time and fraction of the search space explored. Specifically, the proposed methods achieve 24% and 40% savings in GEMM computation time over state-of-the-art XGBoost and RNN methods, respectively, while exploring only 0.1% of the search space. The proposed approaches have potential to be applied to other operator-level optimizations.
This paper proposes the first-ever algorithmic framework for tuning hyper-parameters of stochastic optimization algorithm based on reinforcement learning. Hyper-parameters impose significant influences on the performance of stochastic optimization algorithms, such as evolutionary algorithms (EAs) and meta-heuristics. Yet, it is very time-consuming to determine optimal hyper-parameters due to the stochastic nature of these algorithms. We propose to model the tuning procedure as a Markov decision process, and resort the policy gradient algorithm to tune the hyper-parameters. Experiments on tuning stochastic algorithms with different kinds of hyper-parameters (continuous and discrete) for different optimization problems (continuous and discrete) show that the proposed hyper-parameter tuning algorithms do not require much less running times of the stochastic algorithms than bayesian optimization method. The proposed framework can be used as a standard tool for hyper-parameter tuning in stochastic algorithms.
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