Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations

We introduce a method to train Quantized Neural Networks (QNNs) --- neural networks with extremely low precision (e.g., 1-bit) weights and activations, at run-time. At train-time the quantized weights and activations are used for computing the parameter gradients. During the forward pass, QNNs drastically reduce memory size and accesses, and replace most arithmetic operations with bit-wise operations. As a result, power consumption is expected to be drastically reduced. We trained QNNs over the MNIST, CIFAR-10, SVHN and ImageNet datasets. The resulting QNNs achieve prediction accuracy comparable to their 32-bit counterparts. For example, our quantized version of AlexNet with 1-bit weights and 2-bit activations achieves $51\%$ top-1 accuracy. Moreover, we quantize the parameter gradients to 6-bits as well which enables gradients computation using only bit-wise operation. Quantized recurrent neural networks were tested over the Penn Treebank dataset, and achieved comparable accuracy as their 32-bit counterparts using only 4-bits. Last but not least, we programmed a binary matrix multiplication GPU kernel with which it is possible to run our MNIST QNN 7 times faster than with an unoptimized GPU kernel, without suffering any loss in classification accuracy. The QNN code is available online.

Oracle performance for visual captioning

The task of associating images and videos with a natural language description has attracted a great amount of attention recently. Rapid progress has been made in terms of both developing novel algorithms and releasing new datasets. Indeed, the state-of-the-art results on some of the standard datasets have been pushed into the regime where it has become more and more difficult to make significant improvements. Instead of proposing new models, this work investigates the possibility of empirically establishing performance upper bounds on various visual captioning datasets without extra data labelling effort or human evaluation. In particular, it is assumed that visual captioning is decomposed into two steps: from visual inputs to visual concepts, and from visual concepts to natural language descriptions. One would be able to obtain an upper bound when assuming the first step is perfect and only requiring training a conditional language model for the second step. We demonstrate the construction of such bounds on MS-COCO, YouTube2Text and LSMDC (a combination of M-VAD and MPII-MD). Surprisingly, despite of the imperfect process we used for visual concept extraction in the first step and the simplicity of the language model for the second step, we show that current state-of-the-art models fall short when being compared with the learned upper bounds. Furthermore, with such a bound, we quantify several important factors concerning image and video captioning: the number of visual concepts captured by different models, the trade-off between the amount of visual elements captured and their accuracy, and the intrinsic difficulty and blessing of different datasets.

Pointing the Unknown Words

The problem of rare and unknown words is an important issue that can potentially influence the performance of many NLP systems, including both the traditional count-based and the deep learning models. We propose a novel way to deal with the rare and unseen words for the neural network models using attention. Our model uses two softmax layers in order to predict the next word in conditional language models: one predicts the location of a word in the source sentence, and the other predicts a word in the shortlist vocabulary. At each time-step, the decision of which softmax layer to use choose adaptively made by an MLP which is conditioned on the context.~We motivate our work from a psychological evidence that humans naturally have a tendency to point towards objects in the context or the environment when the name of an object is not known.~We observe improvements on two tasks, neural machine translation on the Europarl English to French parallel corpora and text summarization on the Gigaword dataset using our proposed model.

Mollifying Networks

The optimization of deep neural networks can be more challenging than traditional convex optimization problems due to the highly non-convex nature of the loss function, e.g. it can involve pathological landscapes such as saddle-surfaces that can be difficult to escape for algorithms based on simple gradient descent. In this paper, we attack the problem of optimization of highly non-convex neural networks by starting with a smoothed -- or \textit{mollified} -- objective function that gradually has a more non-convex energy landscape during the training. Our proposition is inspired by the recent studies in continuation methods: similar to curriculum methods, we begin learning an easier (possibly convex) objective function and let it evolve during the training, until it eventually goes back to being the original, difficult to optimize, objective function. The complexity of the mollified networks is controlled by a single hyperparameter which is annealed during the training. We show improvements on various difficult optimization tasks and establish a relationship with recent works on continuation methods for neural networks and mollifiers.

Towards Biologically Plausible Deep Learning

Neuroscientists have long criticised deep learning algorithms as incompatible with current knowledge of neurobiology. We explore more biologically plausible versions of deep representation learning, focusing here mostly on unsupervised learning but developing a learning mechanism that could account for supervised, unsupervised and reinforcement learning. The starting point is that the basic learning rule believed to govern synaptic weight updates (Spike-Timing-Dependent Plasticity) arises out of a simple update rule that makes a lot of sense from a machine learning point of view and can be interpreted as gradient descent on some objective function so long as the neuronal dynamics push firing rates towards better values of the objective function (be it supervised, unsupervised, or reward-driven). The second main idea is that this corresponds to a form of the variational EM algorithm, i.e., with approximate rather than exact posteriors, implemented by neural dynamics. Another contribution of this paper is that the gradients required for updating the hidden states in the above variational interpretation can be estimated using an approximation that only requires propagating activations forward and backward, with pairs of layers learning to form a denoising auto-encoder. Finally, we extend the theory about the probabilistic interpretation of auto-encoders to justify improved sampling schemes based on the generative interpretation of denoising auto-encoders, and we validate all these ideas on generative learning tasks.

HeMIS: Hetero-Modal Image Segmentation

We introduce a deep learning image segmentation framework that is extremely robust to missing imaging modalities. Instead of attempting to impute or synthesize missing data, the proposed approach learns, for each modality, an embedding of the input image into a single latent vector space for which arithmetic operations (such as taking the mean) are well defined. Points in that space, which are averaged over modalities available at inference time, can then be further processed to yield the desired segmentation. As such, any combinatorial subset of available modalities can be provided as input, without having to learn a combinatorial number of imputation models. Evaluated on two neurological MRI datasets (brain tumors and MS lesions), the approach yields state-of-the-art segmentation results when provided with all modalities; moreover, its performance degrades remarkably gracefully when modalities are removed, significantly more so than alternative mean-filling or other synthesis approaches.

Context-Dependent Word Representation for Neural Machine Translation

We first observe a potential weakness of continuous vector representations of symbols in neural machine translation. That is, the continuous vector representation, or a word embedding vector, of a symbol encodes multiple dimensions of similarity, equivalent to encoding more than one meaning of the word. This has the consequence that the encoder and decoder recurrent networks in neural machine translation need to spend substantial amount of their capacity in disambiguating source and target words based on the context which is defined by a source sentence. Based on this observation, in this paper we propose to contextualize the word embedding vectors using a nonlinear bag-of-words representation of the source sentence. Additionally, we propose to represent special tokens (such as numbers, proper nouns and acronyms) with typed symbols to facilitate translating those words that are not well-suited to be translated via continuous vectors. The experiments on En-Fr and En-De reveal that the proposed approaches of contextualization and symbolization improves the translation quality of neural machine translation systems significantly.

Feedforward Initialization for Fast Inference of Deep Generative Networks is biologically plausible

We consider deep multi-layered generative models such as Boltzmann machines or Hopfield nets in which computation (which implements inference) is both recurrent and stochastic, but where the recurrence is not to model sequential structure, only to perform computation. We find conditions under which a simple feedforward computation is a very good initialization for inference, after the input units are clamped to observed values. It means that after the feedforward initialization, the recurrent network is very close to a fixed point of the network dynamics, where the energy gradient is 0. The main condition is that consecutive layers form a good auto-encoder, or more generally that different groups of inputs into the unit (in particular, bottom-up inputs on one hand, top-down inputs on the other hand) are consistent with each other, producing the same contribution into the total weighted sum of inputs. In biological terms, this would correspond to having each dendritic branch correctly predicting the aggregate input from all the dendritic branches, i.e., the soma potential. This is consistent with the prediction that the synaptic weights into dendritic branches such as those of the apical and basal dendrites of pyramidal cells are trained to minimize the prediction error made by the dendritic branch when the target is the somatic activity. Whereas previous work has shown how to achieve fast negative phase inference (when the model is unclamped) in a predictive recurrent model, this contribution helps to achieve fast positive phase inference (when the target output is clamped) in such recurrent neural models.

Drawing and Recognizing Chinese Characters with Recurrent Neural Network

Recent deep learning based approaches have achieved great success on handwriting recognition. Chinese characters are among the most widely adopted writing systems in the world. Previous research has mainly focused on recognizing handwritten Chinese characters. However, recognition is only one aspect for understanding a language, another challenging and interesting task is to teach a machine to automatically write (pictographic) Chinese characters. In this paper, we propose a framework by using the recurrent neural network (RNN) as both a discriminative model for recognizing Chinese characters and a generative model for drawing (generating) Chinese characters. To recognize Chinese characters, previous methods usually adopt the convolutional neural network (CNN) models which require transforming the online handwriting trajectory into image-like representations. Instead, our RNN based approach is an end-to-end system which directly deals with the sequential structure and does not require any domain-specific knowledge. With the RNN system (combining an LSTM and GRU), state-of-the-art performance can be achieved on the ICDAR-2013 competition database. Furthermore, under the RNN framework, a conditional generative model with character embedding is proposed for automatically drawing recognizable Chinese characters. The generated characters (in vector format) are human-readable and also can be recognized by the discriminative RNN model with high accuracy. Experimental results verify the effectiveness of using RNNs as both generative and discriminative models for the tasks of drawing and recognizing Chinese characters.

A Character-Level Decoder without Explicit Segmentation for Neural Machine Translation

The existing machine translation systems, whether phrase-based or neural, have relied almost exclusively on word-level modelling with explicit segmentation. In this paper, we ask a fundamental question: can neural machine translation generate a character sequence without any explicit segmentation? To answer this question, we evaluate an attention-based encoder-decoder with a subword-level encoder and a character-level decoder on four language pairs--En-Cs, En-De, En-Ru and En-Fi-- using the parallel corpora from WMT'15. Our experiments show that the models with a character-level decoder outperform the ones with a subword-level decoder on all of the four language pairs. Furthermore, the ensembles of neural models with a character-level decoder outperform the state-of-the-art non-neural machine translation systems on En-Cs, En-De and En-Fi and perform comparably on En-Ru.