Clone-structured graph representations enable flexible learning and vicarious evaluation of cognitive maps.

Cognitive maps are mental representations of spatial and conceptual relationships in an environment, and are critical for flexible behavior. To form these abstract maps, the hippocampus has to learn to separate or merge aliased observations appropriately in different contexts in a manner that enables generalization and efficient planning. Here we propose a specific higher-order graph structure, clone-structured cognitive graph (CSCG), which forms clones of an observation for different contexts as a representation that addresses these problems. CSCGs can be learned efficiently using a probabilistic sequence model that is inherently robust to uncertainty. We show that CSCGs can explain a variety of cognitive map phenomena such as discovering spatial relations from aliased sensations, transitive inference between disjoint episodes, and formation of transferable schemas. Learning different clones for different contexts explains the emergence of splitter cells observed in maze navigation and event-specific responses in lap-running experiments. Moreover, learning and inference dynamics of CSCGs offer a coherent explanation for disparate place cell remapping phenomena. By lifting aliased observations into a hidden space, CSCGs reveal latent modularity useful for hierarchical abstraction and planning. Altogether, CSCG provides a simple unifying framework for understanding hippocampal function, and could be a pathway for forming relational abstractions in artificial intelligence.

From CAPTCHA to Commonsense: How Brain Can Teach Us About Artificial Intelligence.

Despite the recent progress in AI powered by deep learning in solving narrow tasks, we are not close to human intelligence in its flexibility, versatility, and efficiency. Efficient learning and effective generalization come from inductive biases, and building Artificial General Intelligence (AGI) is an exercise in finding the right set of inductive biases that make fast learning possible while being general enough to be widely applicable in tasks that humans excel at. To make progress in AGI, we argue that we can look at the human brain for such inductive biases and principles of generalization. To that effect, we propose a strategy to gain insights from the brain by simultaneously looking at the world it acts upon and the computational framework to support efficient learning and generalization. We present a neuroscience-inspired generative model of vision as a case study for such approach and discuss some open problems about the path to AGI.

Beyond imitation: Zero-shot task transfer on robots by learning concepts as cognitive programs.

Humans can infer concepts from image pairs and apply those in the physical world in a completely different setting, enabling tasks like IKEA assembly from diagrams. If robots could represent and infer high-level concepts, then it would notably improve their ability to understand our intent and to transfer tasks between different environments. To that end, we introduce a computational framework that replicates aspects of human concept learning. Concepts are represented as programs on a computer architecture consisting of a visual perception system, working memory, and action controller. The instruction set of this cognitive computer has commands for parsing a visual scene, directing gaze and attention, imagining new objects, manipulating the contents of a visual working memory, and controlling arm movement. Inferring a concept corresponds to inducing a program that can transform the input to the output. Some concepts require the use of imagination and recursion. Previously learned concepts simplify the learning of subsequent, more elaborate concepts and create a hierarchy of abstractions. We demonstrate how a robot can use these abstractions to interpret novel concepts presented to it as schematic images and then apply those concepts in very different situations. By bringing cognitive science ideas on mental imagery, perceptual symbols, embodied cognition, and deictic mechanisms into the realm of machine learning, our work brings us closer to the goal of building robots that have interpretable representations and common sense.

A generative vision model that trains with high data efficiency and breaks text-based CAPTCHAs.

Learning from a few examples and generalizing to markedly different situations are capabilities of human visual intelligence that are yet to be matched by leading machine learning models. By drawing inspiration from systems neuroscience, we introduce a probabilistic generative model for vision in which message-passing-based inference handles recognition, segmentation, and reasoning in a unified way. The model demonstrates excellent generalization and occlusion-reasoning capabilities and outperforms deep neural networks on a challenging scene text recognition benchmark while being 300-fold more data efficient. In addition, the model fundamentally breaks the defense of modern text-based CAPTCHAs (Completely Automated Public Turing test to tell Computers and Humans Apart) by generatively segmenting characters without CAPTCHA-specific heuristics. Our model emphasizes aspects such as data efficiency and compositionality that may be important in the path toward general artificial intelligence.

Laplace Approximation for Divisive Gaussian Processes for Nonstationary Regression.

The standard Gaussian Process regression (GP) is usually formulated under stationary hypotheses: The noise power is considered constant throughout the input space and the covariance of the prior distribution is typically modeled as depending only on the difference between input samples. These assumptions can be too restrictive and unrealistic for many real-world problems. Although nonstationarity can be achieved using specific covariance functions, they require a prior knowledge of the kind of nonstationarity, not available for most applications. In this paper we propose to use the Laplace approximation to make inference in a divisive GP model to perform nonstationary regression, including heteroscedastic noise cases. The log-concavity of the likelihood ensures a unimodal posterior and makes that the Laplace approximation converges to a unique maximum. The characteristics of the likelihood also allow to obtain accurate posterior approximations when compared to the Expectation Propagation (EP) approximations and the asymptotically exact posterior provided by a Markov Chain Monte Carlo implementation with Elliptical Slice Sampling (ESS), but at a reduced computational load with respect to both, EP and ESS.

A Gaussian process model for data association and a semidefinite programming solution.

In this paper, we propose a Bayesian model for the data association problem, in which trajectory smoothness is enforced through the use of Gaussian process priors. This model allows to score candidate associations using the evidence framework, thus casting the data association problem into an optimization problem. Under some additional mild assumptions, this optimization problem is shown to be equivalent to a constrained Max K-section problem. Furthermore, for K=2, a MaxCut formulation is obtained, to which an approximate solution can be efficiently found using an SDP relaxation. Solving this MaxCut problem is equivalent to finding the optimal association out of the combinatorially many possibilities. The obtained clustering depends only on two hyperparameters, which can also be selected by maximum evidence.

Divisive Gaussian processes for nonstationary regression.

Standard Gaussian process regression (GPR) assumes constant noise power throughout the input space and stationarity when combined with the squared exponential covariance function. This can be unrealistic and too restrictive for many real-world problems. Nonstationarity can be achieved by specific covariance functions, though prior knowledge about this nonstationarity can be difficult to obtain. On the other hand, the homoscedastic assumption is needed to allow GPR inference to be tractable. In this paper, we present a divisive GPR model which performs nonstationary regression under heteroscedastic noise using the pointwise division of two nonparametric latent functions. As the inference on the model is not analytically tractable, we propose a variational posterior approximation using expectation propagation (EP) which allows for accurate inference at reduced cost. We have also made a Markov chain Monte Carlo implementation with elliptical slice sampling to assess the quality of the EP approximation. Experiments support the usefulness of the proposed approach.

Kernel recursive least-squares tracker for time-varying regression.

In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose, we first derive the standard KRLS equations from a Bayesian perspective (including a sensible approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in nonstationary scenarios. The resulting method is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner. In addition to its tracking ability, it has a number of appealing properties. It is online, requires a fixed amount of memory and computation per time step, incorporates regularization in a natural manner and provides confidence intervals along with each prediction. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.

Support vector machines with constraints for sparsity in the primal parameters.

This paper introduces a new support vector machine (SVM) formulation to obtain sparse solutions in the primal SVM parameters, providing a new method for feature selection based on SVMs. This new approach includes additional constraints to the classical ones that drop the weights associated to those features that are likely to be irrelevant. A ν-SVM formulation has been used, where ν indicates the fraction of features to be considered. This paper presents two versions of the proposed sparse classifier, a 2-norm SVM and a 1-norm SVM, the latter having a reduced computational burden with respect to the first one. Additionally, an explanation is provided about how the presented approach can be readily extended to multiclass classification or to problems where groups of features, rather than isolated features, need to be selected. The algorithms have been tested in a variety of synthetic and real data sets and they have been compared against other state of the art SVM-based linear feature selection methods, such as 1-norm SVM and doubly regularized SVM. The results show the good feature selection ability of the approaches.

Marginalized neural network mixtures for large-scale regression.

For regression tasks, traditional neural networks (NNs) have been superseded by gaussian processes, which provide probabilistic predictions (input-dependent error bars), improved accuracy, and virtually no overfitting. Due to their high computational cost, in scenarios with massive data sets, one has to resort to sparse gaussian processes, which strive to achieve similar performance with much smaller computational effort. In this context, we introduce a mixture of NNs with marginalized output weights that can both provide probabilistic predictions and improve on the performance of sparse gaussian processes, at the same computational cost. The effectiveness of this approach is shown experimentally on some representative large data sets.