We introduce a novel approach to feed-forward neural network interpretation based on partitioning the space of sequences of neuron activations. In line with this approach, we propose a model-specific interpretation method, called YASENN. Our method inherits many advantages of model-agnostic distillation, such as an ability to focus on the particular input region and to express an explanation in terms of features different from those observed by a neural network. Moreover, examination of distillation error makes the method applicable to the problems with low tolerance to interpretation mistakes. Technically, YASENN distills the network with an ensemble of layer-wise gradient boosting decision trees and encodes the sequences of neuron activations with leaf indices. The finite number of unique codes induces a partitioning of the input space. Each partition may be described in a variety of ways, including examination of an interpretable model (e.g. a logistic regression or a decision tree) trained to discriminate between objects of those partitions. Our experiments provide an intuition behind the method and demonstrate revealed artifacts in neural network decision making.
Unlike NeuroRule @cite_4 , we work with activations in a more general way: we take into account the whole layer rather than process neurons one by one. In addition, YASENN was designed for deep NNs, and it gains benefits of their depth.
@cite_4
2134973740 992687842 2903535193 1528288284
Deep Neural Network (DNN), which can model a long-span, intricate transform compactly with a deep-layered structure, has recently been investigated for parametric TTS synthesis with a fairly large corpus (33,000 utterances) [6]. In this paper, we examine DNN TTS synthesis with a moderate size corpus of 5 hours, which is more commonly used for parametric TTS training. DNN is used to map input text features into output acoustic features (LSP, F0 and V U). Experimental results show that DNN can outperform the conventional HMM, which is trained in ML first and then refined by MGE. Both objective and subjective measures indicate that DNN can synthesize speech better than HMM-based baseline. The improvement is mainly on the prosody, i.e., the RMSE of natural and generated F0 trajectories by DNN is improved by 2 Hz. This benefit is likely from the key characteristics of DNN, which can exploit feature correlations, e.g., between F0 and spectrum, without using a more restricted, e.g. diagonal Gaussian probability family. Our experimental results also show: the layer-wise BP pre-training can drive weights to a better starting point than random initialization and result in a more effective DNN; state boundary info is important for training DNN to yield better synthesized speech; and a hyperbolic tangent activation function in DNN hidden layers yields faster convergence than a sigmoidal one. Deep Neural nets (NNs) with millions of parameters are at the heart of many state-of-the-art computer vision systems today. However, recent works have shown that much smaller models can achieve similar levels of performance. In this work, we address the problem of pruning parameters in a trained NN model. Instead of removing individual weights one at a time as done in previous works, we remove one neuron at a time. We show how similar neurons are redundant, and propose a systematic way to remove them. Our experiments in pruning the densely connected layers show that we can remove upto 85 of the total parameters in an MNIST-trained network, and about 35 for AlexNet without significantly affecting performance. Our method can be applied on top of most networks with a fully connected layer to give a smaller network. In this paper, we leverage the efficiency of Binarized Neural Networks (BNNs) to learn complex state transition models of planning domains with discretized factored state and action spaces. In order to directly exploit this transition structure for planning, we present two novel compilations of the learned factored planning problem with BNNs based on reductions to Weighted Partial Maximum Boolean Satisfiability (FD-SAT-Plan+) as well as Binary Linear Programming (FD-BLP-Plan+). Theoretically, we show that our SAT-based Bi-Directional Neuron Activation Encoding is asymptotically the most compact encoding in the literature and maintains the generalized arc-consistency property through unit propagation -- an important property that facilitates efficiency in SAT solvers. Experimentally, we validate the computational efficiency of our Bi-Directional Neuron Activation Encoding in comparison to an existing neuron activation encoding and demonstrate the effectiveness of learning complex transition models with BNNs. We test the runtime efficiency of both FD-SAT-Plan+ and FD-BLP-Plan+ on the learned factored planning problem showing that FD-SAT-Plan+ scales better with increasing BNN size and complexity. Finally, we present a finite-time incremental constraint generation algorithm based on generalized landmark constraints to improve the planning accuracy of our encodings through simulated or real-world interaction. Designing a neural network (NN) to process complex-valued signals is a challenging task since a complex nonlinear activation function (AF) cannot be both analytic and bounded everywhere in the complex plane C . To avoid this difficulty, ‘splitting’, i.e., using a pair of real sigmoidal functions for the real and imaginary components has been the traditional approach. However, this ‘ad hoc’ compromise to avoid the unbounded nature of nonlinear complex functions results in a nowhere analytic AF that performs the error back-propagation (BP) using the split derivatives of the real and imaginary components instead of relying on well-defined fully complex derivatives. In this paper, a fully complex multi-layer perceptron (MLP) structure that yields a simplified complex-valued back-propagation (BP) algorithm is presented. The simplified BP verifies that the fully complex BP weight update formula is the complex conjugate form of real BP formula and the split complex BP is a special case of the fully complex BP. This generalization is possible by employing elementary transcendental functions (ETFs) that are almost everywhere (a.e.) bounded and analytic in C . The properties of fully complex MLP are investigated and the advantage of ETFs over split complex AF is shown in numerical examples where nonlinear magnitude and phase distortions of non-constant modulus modulated signals are successfully restored.