We propose a novel approach to reduce memory consumption of the backpropagation through time (BPTT) algorithm when training recurrent neural networks (RNNs). Our approach uses dynamic programming to balance a trade-off between caching of intermediate results and recomputation. The algorithm is capable of tightly fitting within almost any user-set memory budget while finding an optimal execution policy minimizing the computational cost. Computational devices have limited memory capacity and maximizing a computational performance given a fixed memory budget is a practical use-case. We provide asymptotic computational upper bounds for various regimes. The algorithm is particularly effective for long sequences. For sequences of length 1000, our algorithm saves 95\% of memory usage while using only one third more time per iteration than the standard BPTT.

The blind application of machine learning runs the risk of amplifying biases present in data. Such a danger is facing us with word embedding, a popular framework to represent text data as vectors which has been used in many machine learning and natural language processing tasks. We show that even word embeddings trained on Google News articles exhibit female/male gender stereotypes to a disturbing extent. This raises concerns because their widespread use, as we describe, often tends to amplify these biases. Geometrically, gender bias is first shown to be captured by a direction in the word embedding. Second, gender neutral words are shown to be linearly separable from gender definition words in the word embedding. Using these properties, we provide a methodology for modifying an embedding to remove gender stereotypes, such as the association between the words receptionist and female, while maintaining desired associations such as between the words queen and female. Using crowd-worker evaluation as well as standard benchmarks, we empirically demonstrate that our algorithms significantly reduce gender bias in embeddings while preserving the its useful properties such as the ability to cluster related concepts and to solve analogy tasks. The resulting embeddings can be used in applications without amplifying gender bias.

In this work we develop a theory of hierarchical clustering for graphs. Our modelling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons are a far richer class of graph models than stochastic blockmodels, the primary setting for recent progress in the statistical theory of graph clustering. We define what it means for an algorithm to produce the ``correct clustering, give sufficient conditions in which a method is statistically consistent, and provide an explicit algorithm satisfying these properties.

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by accumulating past gradients which are used to tune the step size adaptively. In certain situations the full-matrix variant of AdaGrad is expected to attain better performance, however in high dimensions it is computationally impractical. We present Ada-LR and RadaGrad two computationally efficient approximations to full-matrix AdaGrad based on randomized dimensionality reduction. They are able to capture dependencies between features and achieve similar performance to full-matrix AdaGrad but at a much smaller computational cost. We show that the regret of Ada-LR is close to the regret of full-matrix AdaGrad which can have an up-to exponentially smaller dependence on the dimension than the diagonal variant. Empirically, we show that Ada-LR and RadaGrad perform similarly to full-matrix AdaGrad. On the task of training convolutional neural networks as well as recurrent neural networks, RadaGrad achieves faster convergence than diagonal AdaGrad.

In this paper we aim at facilitating generalization for deep networks while supporting interpretability of the learned representations. Towards this goal, we propose a clustering based regularization that encourages parsimonious representations. Our k-means style objective is easy to optimize and flexible supporting various forms of clustering, including sample and spatial clustering as well as co-clustering. We demonstrate the effectiveness of our approach on the tasks of unsupervised learning, classification, fine grained categorization and zero-shot learning.

The importance of studying the robustness of learners to malicious data is well established. While much work has been done establishing both robust estimators and effective data injection attacks when the attacker is omniscient, the ability of an attacker to provably harm learning while having access to little information is largely unstudied. We study the potential of a "blind attacker" to provably limit a learner's performance by data injection attack without observing the learner's training set or any parameter of the distribution from which it is drawn. We provide examples of simple yet effective attacks in two settings: firstly, where an "informed learner" knows the strategy chosen by the attacker, and secondly, where a "blind learner" knows only the proportion of malicious data and some family to which the malicious distribution chosen by the attacker belongs. For each attack, we analyze minimax rates of convergence and establish lower bounds on the learner's minimax risk, exhibiting limits on a learner's ability to learn under data injection attack even when the attacker is "blind".

Behavioral experiments on humans and animals suggest that the brain performs probabilistic inference to interpret its environment. Here we present a new general-purpose, biologically-plausible neural implementation of approximate inference. The neural network represents uncertainty using Probabilistic Population Codes (PPCs), which are distributed neural representations that naturally encode probability distributions, and support marginalization and evidence integration in a biologically-plausible manner. By connecting multiple PPCs together as a probabilistic graphical model, we represent multivariate probability distributions. Approximate inference in graphical models can be accomplished by message-passing algorithms that disseminate local information throughout the graph. An attractive and often accurate example of such an algorithm is Loopy Belief Propagation (LBP), which uses local marginalization and evidence integration operations to perform approximate inference efficiently even for complex models.

Gaussian Process bandit optimization has emerged as a powerful tool for optimizing noisy black box functions. One example in machine learning is hyper-parameter optimization where each evaluation of the target function may require training a model which may involve days or even weeks of computation. Most methods for this so-called "Bayesian optimization" only allow sequential exploration of the parameter space. However, it is often desirable to propose batches or sets of parameter values to explore simultaneously, especially when there are large parallel processing facilities at our disposal. Batch methods require modeling the interaction between the different evaluations in the batch, which can be expensive in complex scenarios. In this paper, we propose a new approach for parallelizing Bayesian optimization by modeling the diversity of a batch via Determinantal point processes (DPPs) whose kernels are learned automatically. This allows us to generalize a previous result as well as prove better regret bounds based on DPP sampling. Our experiments on a variety of synthetic and real-world robotics and hyper-parameter optimization tasks indicate that our DPP-based methods, especially those based on DPP sampling, outperform state-of-the-art methods.

A central challenge in sensory neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic transmission and spiking dynamics present a significant obstacle to the creation of accurate computational models of responses to natural stimuli. Here we demonstrate that deep convolutional neural networks (CNNs) capture retinal responses to natural scenes nearly to within the variability of a cell's response, and are markedly more accurate than linear-nonlinear (LN) models and Generalized Linear Models (GLMs). Moreover, we find two additional surprising properties of CNNs: they are less susceptible to overfitting than their LN counterparts when trained on small amounts of data, and generalize better when tested on stimuli drawn from a different distribution (e.g. between natural scenes and white noise). An examination of the learned CNNs reveals several properties.

Learned region sparsity has achieved state-of-the-art performance in classification tasks by exploiting and integrating a sparse set of local information into global decisions. The underlying mechanism resembles how people sample information from an image with their eye movements when making similar decisions. In this paper we incorporate the biologically plausible mechanism of Inhibition of Return into the learned region sparsity model, thereby imposing diversity on the selected regions. We investigate how these mechanisms of sparsity and diversity relate to visual attention by testing our model on three different types of visual search tasks. We report state-of-the-art results in predicting the locations of human gaze fixations, even though our model is trained only on image-level labels without object location annotations. Notably, the classification performance of the extended model remains the same as the original. This work suggests a new computational perspective on visual attention mechanisms and shows how the inclusion of attention-based mechanisms can improve computer vision techniques.