Gradients have been used to quantify feature importance in machine learning models. Unfortunately, in nonlinear deep networks, not only individual neurons but also the whole network can saturate, and as a result an important input feature can have a tiny gradient. We study various networks, and observe that this phenomena is indeed widespread, across many inputs. @PARASPLIT We propose to examine interior gradients, which are gradients of counterfactual inputs constructed by scaling down the original input. We apply our method to the GoogleNet architecture for object recognition in images, as well as a ligand-based virtual screening network with categorical features and an LSTM based language model for the Penn Treebank dataset. We visualize how interior gradients better capture feature importance. Furthermore, interior gradients are applicable to a wide variety of deep networks, and have the attribution property that the feature importance scores sum to the the prediction score. @PARASPLIT Best of all, interior gradients can be computed just as easily as gradients. In contrast, previous methods are complex to implement, which hinders practical adoption.
Score back-propagation based methods The second set of approaches involve back-propagating the final prediction score through each layer of the network down to the individual features. These include DeepLift ( @cite_21 ), Layer-wise relevance propagation (LRP) ( @cite_23 ), Deconvolution networks (DeConvNets) ( @cite_14 ), and Guided back-propagation ( @cite_20 ). These methods largely differ in the backpropagation logic for various non-linear activation functions. While DeConvNets, Guided back-propagation and LRP rely on the local gradients at each non-linear activation function, DeepLift relies on the deviation in the neuron's activation from a certain baseline input.
@cite_14 @cite_21 @cite_20 @cite_23
2605409611 2964178496 2527798464 2964115671
The purported "black box" nature of neural networks is a barrier to adoption in applications where interpretability is essential. Here we present DeepLIFT (Deep Learning Important FeaTures), a method for decomposing the output prediction of a neural network on a specific input by backpropagating the contributions of all neurons in the network to every feature of the input. DeepLIFT compares the activation of each neuron to its 'reference activation' and assigns contribution scores according to the difference. By optionally giving separate consideration to positive and negative contributions, DeepLIFT can also reveal dependencies which are missed by other approaches. Scores can be computed efficiently in a single backward pass. We apply DeepLIFT to models trained on MNIST and simulated genomic data, and show significant advantages over gradient-based methods. Video tutorial: http: goo.gl qKb7pL, code: http: goo.gl RM8jvH. Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing (NLP). More precisely, we use it to explain the predictions of a convolutional neural network (CNN) trained on a topic categorization task. Our analysis highlights which words are relevant for a specific prediction of the CNN. We compare our technique to standard sensitivity analysis, both qualitatively and quantitatively, using a “word deleting” perturbation experiment, a PCA analysis, and various visualizations. All experiments validate the suitability of LRP for explaining the CNN predictions, which is also in line with results reported in recent image classification studies. We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point, or stationary distribution) towards a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged towards their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal 'back-propagated' during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2 and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task. Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagating the error backward don't have to be symmetric with the weights used for propagation the activation forward. In fact, random feedback weights work evenly well, because the network learns how to make the feedback useful. In this work, the feedback alignment principle is used for training hidden layers more independently from the rest of the network, and from a zero initial condition. The error is propagated through fixed random feedback connections directly from the output layer to each hidden layer. This simple method is able to achieve zero training error even in convolutional networks and very deep networks, completely without error back-propagation. The method is a step towards biologically plausible machine learning because the error signal is almost local, and no symmetric or reciprocal weights are required. Experiments show that the test performance on MNIST and CIFAR is almost as good as those obtained with back-propagation for fully connected networks. If combined with dropout, the method achieves 1.45 error on the permutation invariant MNIST task.