Per B. Sederberg

Brandon G. Jacques, Zoran Tiganj, Aakash Sarkar et al.

Human learners can readily understand speech, or a melody, when it is presented slower or faster than usual. Although deep convolutional neural networks (CNNs) are extremely powerful in extracting information from time series, they require explicit training to generalize to different time scales. This paper presents a deep CNN that incorporates a temporal representation inspired by recent findings from neuroscience. In the mammalian brain, time is represented by populations of neurons with temporal receptive fields. Critically, the peaks of the receptive fields form a geometric series, such that the population codes a set of temporal basis functions over log time. Because memory for the recent past is a function of log time, rescaling the input results in translation of the memory. The Scale-Invariant Temporal History Convolution network (SITHCon) builds a convolutional layer over this logarithmically-distributed temporal memory. A max-pool operation results in a network that is invariant to rescalings of time modulo edge effects. We compare performance of SITHCon to a Temporal Convolution Network (TCN). Although both networks can learn classification and regression problems on both univariate and multivariate time series f(t), only SITHCon generalizes to rescalings f(at). This property, inspired by findings from contemporary neuroscience and consistent with findings from cognitive psychology, may enable networks that learn with fewer training examples, fewer weights and that generalize more robustly to out of sample data.

Brandon Jacques, Zoran Tiganj, Marc W. Howard et al.

Extracting temporal relationships over a range of scales is a hallmark of human perception and cognition -- and thus it is a critical feature of machine learning applied to real-world problems. Neural networks are either plagued by the exploding/vanishing gradient problem in recurrent neural networks (RNNs) or must adjust their parameters to learn the relevant time scales (e.g., in LSTMs). This paper introduces DeepSITH, a network comprising biologically-inspired Scale-Invariant Temporal History (SITH) modules in series with dense connections between layers. SITH modules respond to their inputs with a geometrically-spaced set of time constants, enabling the DeepSITH network to learn problems along a continuum of time-scales. We compare DeepSITH to LSTMs and other recent RNNs on several time series prediction and decoding tasks. DeepSITH achieves state-of-the-art performance on these problems.

Zoran Tiganj, Samuel J. Gershman, Per B. Sederberg et al.

Natural learners must compute an estimate of future outcomes that follow from a stimulus in continuous time. Widely used reinforcement learning algorithms discretize continuous time and estimate either transition functions from one step to the next (model-based algorithms) or a scalar value of exponentially-discounted future reward using the Bellman equation (model-free algorithms). An important drawback of model-based algorithms is that computational cost grows linearly with the amount of time to be simulated. On the other hand, an important drawback of model-free algorithms is the need to select a time-scale required for exponential discounting. We present a computational mechanism, developed based on work in psychology and neuroscience, for computing a scale-invariant timeline of future outcomes. This mechanism efficiently computes an estimate of inputs as a function of future time on a logarithmically-compressed scale, and can be used to generate a scale-invariant power-law-discounted estimate of expected future reward. The representation of future time retains information about what will happen when. The entire timeline can be constructed in a single parallel operation which generates concrete behavioral and neural predictions. This computational mechanism could be incorporated into future reinforcement learning algorithms.

Tyler A. Spears, Brandon G. Jacques, Marc W. Howard et al.

In both the human brain and any general artificial intelligence (AI), a representation of the past is necessary to predict the future. However, perfect storage of all experiences is not feasible. One approach utilized in many applications, including reward prediction in reinforcement learning, is to retain recently active features of experience in a buffer. Despite its prior successes, we show that the fixed length buffer renders Deep Q-learning Networks (DQNs) fragile to changes in the scale over which information can be learned. To enable learning when the relevant temporal scales in the environment are not known *a priori*, recent advances in psychology and neuroscience suggest that the brain maintains a compressed representation of the past. Here we introduce a neurally-plausible, scale-free memory representation we call Scale-Invariant Temporal History (SITH) for use with artificial agents. This representation covers an exponentially large period of time by sacrificing temporal accuracy for events further in the past. We demonstrate the utility of this representation by comparing the performance of agents given SITH, buffer, and exponential decay representations in learning to play video games at different levels of complexity. In these environments, SITH exhibits better learning performance by storing information for longer timescales than a fixed-size buffer, and representing this information more clearly than a set of exponentially decayed features. Finally, we discuss how the application of SITH, along with other human-inspired models of cognition, could improve reinforcement and machine learning algorithms in general.

Justin Ziniel, Philip Schniter, Per Sederberg

For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of compressive sensing. We are particularly motivated by problems where the number of features greatly exceeds the number of training examples, but where only a few features suffice for accurate classification. We show that sum-product GAMP can be used to (approximately) minimize the classification error rate and max-sum GAMP can be used to minimize a wide variety of regularized loss functions. Furthermore, we describe an expectation-maximization (EM)-based scheme to learn the associated model parameters online, as an alternative to cross-validation, and we show that GAMP's state-evolution framework can be used to accurately predict the misclassification rate. Finally, we present a detailed numerical study to confirm the accuracy, speed, and flexibility afforded by our GAMP-based approaches to binary linear classification and feature selection.