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Deep neural networks have achieved impressive successes in fields ranging from object recognition to complex games such as Go 1 , 2 . Navigation, however, remains a substantial challenge for artificial agents, with deep neural networks trained by reinforcement learning 3 – 5 failing to rival the proficiency of mammalian spatial behaviour, which is underpinned by grid cells in the entorhinal cortex 6 . Grid cells are thought to provide a multi-scale periodic representation that functions as a metric for coding space 7 , 8 and is critical for integrating self-motion (path integration) 6 , 7 , 9 and planning direct trajectories to goals (vector-based navigation) 7 , 10 , 11 . Here we set out to leverage the computational functions of grid cells to develop a deep reinforcement learning agent with mammal-like navigational abilities. We first trained a recurrent network to perform path integration, leading to the emergence of representations resembling grid cells, as well as other entorhinal cell types 12 . We then showed that this representation provided an effective basis for an agent to locate goals in challenging, unfamiliar, and changeable environments—optimizing the primary objective of navigation through deep reinforcement learning. The performance of agents endowed with grid-like representations surpassed that of an expert human and comparison agents, with the metric quantities necessary for vector-based navigation derived from grid-like units within the network. Furthermore, grid-like representations enabled agents to conduct shortcut behaviours reminiscent of those performed by mammals. Our findings show that emergent grid-like representations furnish agents with a Euclidean spatial metric and associated vector operations, providing a foundation for proficient navigation. As such, our results support neuroscientific theories that see grid cells as critical for vector-based navigation 7 , 10 , 11 , demonstrating that the latter can be combined with path-based strategies to support navigation in challenging environments. Grid-like representations emerge spontaneously within a neural network trained to self-localize, enabling the agent to take shortcuts to destinations using vector-based navigation.

In the mammalian brain, allocentric representations support efficient self-location and flexible navigation. A number of distinct populations of these spatial responses have been identified but no unified function has been shown to account for their emergence. Here we developed a network, trained with a simple predictive objective, that was capable of mapping egocentric information into an allocentric spatial reference frame. The prediction of visual inputs was sufficient to drive the appearance of spatial representations resembling those observed in rodents: head direction, boundary vector, and place cells, along with the recently discovered egocentric boundary cells, suggesting predictive coding as a principle for their emergence in animals. Strikingly, the network learned a solution for head direction tracking and stabilisation convergent with known biological connectivity. Moreover, like mammalian representations, responses were robust to environmental manipulations, including exposure to novel settings. In contrast to existing reinforcement learning approaches, agents equipped with this network were able to flexibly reuse learnt behaviours —adapting rapidly to unfamiliar environments. Thus, our results indicate that these representations, derived from a simple egocentric predictive framework, form an efficient basis-set for cognitive mapping.

Autoregressive models factorize a multivariate joint probability distribution into a product of one-dimensional conditional distributions. The variables are assigned an ordering, and the conditional distribution of each variable modelled using all variables preceding it in that ordering as predictors. Calculating normalized probabilities and sampling has polynomial computational complexity under autoregressive models. Moreover, binary autoregressive models based on neural networks obtain statistical performances similar to that of some intractable models, like restricted Boltzmann machines, on several datasets. The use of autoregressive probability density estimators based on neural networks to model real-valued data, while proposed before, has never been properly investigated and reported. In this thesis we extend the formulation of neural autoregressive distribution estimators (NADE) to real-valued data; a model we call the real-valued neural autoregressive density estimator (RNADE). Its statistical performance on several datasets, including visual and auditory data, is reported and compared to that of other models. RNADE obtained higher test likelihoods than other tractable models, while retaining all the attractive computational properties of autoregressive models. However, autoregressive models are limited by the ordering of the variables inherent to their formulation. Marginalization and imputation tasks can only be solved analytically if the missing variables are at the end of the ordering. We present a new training technique that obtains a set of parameters that can be used for any ordering of the variables. By choosing a model with a convenient ordering of the dimensions at test time, it is possible to solve any marginalization and imputation tasks analytically. The same training procedure also makes it practical to train NADEs and RNADEs with several hidden layers. The resulting deep and tractable models display higher test likelihoods than the equivalent one-hidden-layer models for all the datasets tested. Ensembles of NADEs or RNADEs can be created inexpensively by combining models that share their parameters but differ in the ordering of the variables. These ensembles of autoregressive models obtain state-of-the-art statistical performances for several datasets. Finally, we demonstrate the application of RNADE to speech synthesis, and confirm that capturing the phone-conditional dependencies of acoustic features improves the quality of synthetic speech. Our model generates synthetic speech that was judged by naive listeners as being of higher quality than that generated by mixture density networks, which are considered a state-of-the-art synthesis technique.

In the mammalian brain, allocentric representations support efficient self-location and flexible navigation. A number of distinct populations of these spatial responses have been identified but no unified function has been shown to account for their emergence. Here we developed a network, trained with a simple predictive objective, that was capable of mapping egocentric information into an allocentric spatial reference frame. The prediction of visual inputs was sufficient to drive the appearance of spatial representations resembling those observed in rodents: head direction, boundary vector, and place cells, along with the recently discovered egocentric boundary cells, suggesting predictive coding as a principle for their emergence in animals. The network learned a solution for head direction tracking convergent with known biological connectivity, while suggesting a possible mechanism of boundary cell remapping. Moreover, like mammalian representations, responses were robust to environmental manipulations, including exposure to novel settings, and could be replayed in the absence of perceptual input, providing the means for offline learning. In contrast to existing reinforcement learning approaches, agents equipped with this network were able to flexibly reuse learnt behaviours - adapting rapidly to unfamiliar environments. Thus, our results indicate that these representations, derived from a simple egocentric predictive framework, form an efficient basis-set for cognitive mapping. Competing Interest Statement The authors have declared no competing interest.

We train a generator by maximum likelihood and we also train the same generator architecture by Wasserstein GAN. We then compare the generated samples, exact log-probability densities and approximate Wasserstein distances. We show that an independent critic trained to approximate Wasserstein distance between the validation set and the generator distribution helps detect overfitting. Finally, we use ideas from the one-shot learning literature to develop a novel fast learning critic.

We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to Holographic Reduced Representations and Long Short-Term Memory networks. Holographic Reduced Representations have limited capacity: as they store more information, each retrieval becomes noisier due to interference. Our system in contrast creates redundant copies of stored information, which enables retrieval with reduced noise. Experiments demonstrate faster learning on multiple memorization tasks.

The Neural Autoregressive Distribution Estimator (NADE) and its real-valued version RNADE are competitive density models of multidimensional data across a variety of domains. These models use a fixed, arbitrary ordering of the data dimensions. One can easily condition on variables at the beginning of the ordering, and marginalize out variables at the end of the ordering, however other inference tasks require approximate inference. In this work we introduce an efficient procedure to simultaneously train a NADE model for each possible ordering of the variables, by sharing parameters across all these models. We can thus use the most convenient model for each inference task at hand, and ensembles of such models with different orderings are immediately available. Moreover, unlike the original NADE, our training procedure scales to deep models. Empirically, ensembles of Deep NADE models obtain state of the art density estimation performance.

We introduce RNADE, a new model for joint density estimation of real-valued vectors. Our model calculates the density of a datapoint as the product of one-dimensional conditionals modeled using mixture density networks with shared parameters. RNADE learns a distributed representation of the data, while having a tractable expression for the calculation of densities. A tractable likelihood allows direct comparison with other methods and training by standard gradient-based optimizers. We compare the performance of RNADE on several datasets of heterogeneous and perceptual data, finding it outperforms mixture models in all but one case.

Deep reinforcement learning methods attain super-human performance in a wide range of environments. Such methods are grossly inefficient, often taking orders of magnitudes more data than humans to achieve reasonable performance. We propose Neural Episodic Control: a deep reinforcement learning agent that is able to rapidly assimilate new experiences and act upon them. Our agent uses a semi-tabular representation of the value function: a buffer of past experience containing slowly changing state representations and rapidly updated estimates of the value function. We show across a wide range of environments that our agent learns significantly faster than other state-of-the-art, general purpose deep reinforcement learning agents.

Automated discovery of early visual concepts from raw image data is a major open challenge in AI research. Addressing this problem, we propose an unsupervised approach for learning disentangled representations of the underlying factors of variation. We draw inspiration from neuroscience, and show how this can be achieved in an unsupervised generative model by applying the same learning pressures as have been suggested to act in the ventral visual stream in the brain. By enforcing redundancy reduction, encouraging statistical independence, and exposure to data with transform continuities analogous to those to which human infants are exposed, we obtain a variational autoencoder (VAE) framework capable of learning disentangled factors. Our approach makes few assumptions and works well across a wide variety of datasets. Furthermore, our solution has useful emergent properties, such as zero-shot inference and an intuitive understanding of \"objectness\".