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Register a new userAnalytically Tractable Inference in Deep Neural Networks
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Luong-Ha Nguyen
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Since its inception, deep learning has been overwhelmingly reliant on backpropagation and gradient-based optimization algorithms in order to learn weight and bias parameter values. Tractable Approximate Gaussian Inference (TAGI) algorithm was shown to be a viable and scalable alternative to backpropagation for shallow fully-connected neural networks. In this paper, we are demonstrating how TAGI matches or exceeds the performance of backpropagation, for training classic deep neural network architectures. Although TAGIs computational efficiency is still below that of deterministic approaches relying on backpropagation, it outperforms them on classification tasks and matches their performance for information maximizing generative adversarial networks while using smaller architectures trained with fewer epochs.
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With few exceptions, neural networks have been relying on backpropagation and gradient descent as the inference engine in order to learn the model parameters, because the closed-form Bayesian inference for neural networks has been considered to be intractable. In this paper, we show how we can leverage the tractable approximate Gaussian inferences (TAGI) capabilities to infer hidden states, rather than only using it for inferring the networks parameters. One novel aspect it allows is to infer hidden states through the imposition of constraints designed to achieve specific objectives, as illustrated through three examples: (1) the generation of adversarial-attack examples, (2) the usage of a neural network as a black-box optimization method, and (3) the application of inference on continuous-action reinforcement learning. These applications showcase how tasks that were previously reserved to gradient-based optimization approaches can now be approached with analytically tractable inference
Reinforcement learning (RL) has gained increasing interest since the demonstration it was able to reach human performance on video game benchmarks using deep Q-learning (DQN). The current consensus for training neural networks on such complex environments is to rely on gradient-based optimization. Although alternative Bayesian deep learning methods exist, most of them still rely on gradient-based optimization, and they typically do not scale on benchmarks such as the Atari game environment. Moreover none of these approaches allow performing the analytical inference for the weights and biases defining the neural network. In this paper, we present how we can adapt the temporal difference Q-learning framework to make it compatible with the tractable approximate Gaussian inference (TAGI), which allows learning the parameters of a neural network using a closed-form analytical method. Throughout the experiments with on- and off-policy reinforcement learning approaches, we demonstrate that TAGI can reach a performance comparable to backpropagation-trained networks while using fewer hyperparameters, and without relying on gradient-based optimization.
In this paper, we propose an analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables the analytical Gaussian inference of the posterior mean vector and diagonal covariance matrix for weights and biases. The method proposed has a computational complexity of $mathcal{O}(n)$ with respect to the number of parameters $n$, and the tests performed on regression and classification benchmarks confirm that, for a same network architecture, it matches the performance of existing methods relying on gradient backpropagation.
We consider the problem of learning an unknown ReLU network with respect to Gaussian inputs and obtain the first nontrivial results for networks of depth more than two. We give an algorithm whose running time is a fixed polynomial in the ambient dimension and some (exponentially large) function of only the networks parameters. Our bounds depend on the number of hidden units, depth, spectral norm of the weight matrices, and Lipschitz constant of the overall network (we show that some dependence on the Lipschitz constant is necessary). We also give a bound that is doubly exponential in the size of the network but is independent of spectral norm. These results provably cannot be obtained using gradient-based methods and give the first example of a class of efficiently learnable neural networks that gradient descent will fail to learn. In contrast, prior work for learning networks of depth three or higher requires exponential time in the ambient dimension, even when the above parameters are bounded by a constant. Additionally, all prior work for the depth-two case requires well-conditioned weights and/or positive coefficients to obtain efficient run-times. Our algorithm does not require these assumptions. Our main technical tool is a type of filtered PCA that can be used to iteratively recover an approximate basis for the subspace spanned by the hidden units in the first layer. Our analysis leverages new structural results on lattice polynomials from tropical geometry.
Many software engineering tasks, such as testing, and anomaly detection can benefit from the ability to infer a behavioral model of the software.Most existing inference approaches assume access to code to collect execution sequences. In this paper, we investigate a black-box scenario, where the system under analysis cannot be instrumented, in this granular fashion.This scenario is particularly prevalent with control systems log analysis in the form of continuous signals. In this situation, an execution trace amounts to a multivariate time-series of input and output signals, where different states of the system correspond to different `phases` in the time-series. The main challenge is to detect when these phase changes take place. Unfortunately, most existing solutions are either univariate, make assumptions on the data distribution, or have limited learning power.Therefore, we propose a hybrid deep neural network that accepts as input a multivariate time series and applies a set of convolutional and recurrent layers to learn the non-linear correlations between signals and the patterns over time.We show how this approach can be used to accurately detect state changes, and how the inferred models can be successfully applied to transfer-learning scenarios, to accurately process traces from different products with similar execution characteristics. Our experimental results on two UAV autopilot case studies indicate that our approach is highly accurate (over 90% F1 score for state classification) and significantly improves baselines (by up to 102% for change point detection).Using transfer learning we also show that up to 90% of the maximum achievable F1 scores in the open-source case study can be achieved by reusing the trained models from the industrial case and only fine tuning them using as low as 5 labeled samples, which reduces the manual labeling effort by 98%.
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