Why do biological and artificial neurons sometimes modularise, each encoding a single meaningful variable, and sometimes entangle their representation of many variables? In this work, we develop a theory of when biologically inspired networks---those that are nonnegative and energy efficient---modularise their representation of source variables (sources). We derive necessary and sufficient conditions on a sample of sources that determine whether the neurons in an optimal biologically-inspired linear autoencoder modularise. Our theory applies to any dataset, extending far beyond the case of statistical independence studied in previous work. Rather we show that sources modularise if their support is ``sufficiently spread''. From this theory, we extract and validate predictions in a variety of empirical studies on how data distribution affects modularisation in nonlinear feedforward and recurrent neural networks trained on supervised and unsupervised tasks. Furthermore, we apply these ideas to neuroscience data, showing that range independence can be used to understand the mixing or modularising of spatial and reward information in entorhinal recordings in seemingly conflicting experiments. Further, we use these results to suggest alternate origins of mixed-selectivity, beyond the predominant theory of flexible nonlinear classification. In sum, our theory prescribes precise conditions on when neural activities modularise, providing tools for inducing and elucidating modular representations in brains and machines.

Brains reorganise knowledge offline to improve future behaviour, with 'replay' involved in consolidating memories, abstracting patterns from experience, and simulating new scenarios. However, there are few models of how the brain might orchestrate these processes, and of when different types of replay might be useful. Here we propose a framework in which a meta-controller learns to coordinate offline learning of a lower-level agent or model in 'sleep' phases to maximise reward in an 'awake' phase. The meta-controller selects among several actions, such as learning from recent memories in a hippocampal store, abstracting patterns from memories into a 'world model', and learning from generated data. In addition, the meta-controller learns to estimate the value of each episode, enabling the prioritisation of past events in memory replay, or of new simulations in generative replay. Using image classification, maze solving, and relational inference tasks, we show that the meta-controller learns an adaptive curriculum for offline learning. This lays the groundwork for normative predictions about replay in a range of experimental neuroscience tasks.

Contemporary reinforcement learning (RL) theory suggests that potential choices can be evaluated by strategies that may or may not be sensitive to the computational structure of tasks. A paradigmatic model-free (MF) strategy simply repeats actions that have been rewarded in the past; by contrast, model-sensitive (MS) strategies exploit richer information associated with knowledge of task dynamics. MF and MS strategies should typically be combined, because they have complementary statistical and computational strengths; however, this tradeoff between MF/MS RL has mostly only been demonstrated in humans, often with only modest numbers of trials. We trained rhesus monkeys to perform a two-stage decision task designed to elicit and discriminate the use of MF and MS methods. A descriptive analysis of choice behaviour revealed directly that the structure of the task (of MS importance) and the reward history (of MF and MS importance) significantly influenced both choice and response vigour. A detailed, trial-by-trial computational analysis confirmed that choices were made according to a combination of strategies, with a dominant influence of a particular form of model sensitivity that persisted over weeks of testing. The residuals from this model necessitated development of a new combined RL model which incorporates a particular credit assignment weighting procedure. Finally, response vigor exhibited a subtly different collection of MF and MS influences. These results provide new illumination onto RL behavioural processes in non-human primates.

Humans and animals show remarkable flexibility in adjusting their behaviour when their goals, or rewards in the environment change. While such flexibility is a hallmark of intelligent behaviour, these multi-task scenarios remain an important challenge for machine learning algorithms and neurobiological models alike. We investigated two approaches that could enable this flexibility: factorized representations, which abstract away general aspects of a task from those prone to change, and nonparametric, memory-based approaches, which can provide a principled way of using similarity to past experiences to guide current behaviour. In particular, we combine the successor representation (SR), that factors the value of actions into expected outcomes and corresponding rewards, with evaluating task similarity through clustering the space of rewards. The proposed algorithm inverts a generative model over tasks, and dynamically samples from a flexible number of distinct SR maps while accumulating evidence about the current task context through amortized inference. It improves SR's transfer capabilities and outperforms competing algorithms and baselines in settings with both known and unsignalled rewards changes. Further, as a neurobiological model of spatial coding in the hippocampus, it explains important signatures of this representation, such as the "flickering" behaviour of hippocampal maps, and trajectory-dependent place cells (so-called splitter cells) and their dynamics. We thus provide a novel algorithmic approach for multi-task learning, as well as a common normative framework that links together these different characteristics of the brain's spatial representation.

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities. We take inspiration from neuroscience, specifically the hippocampal-entorhinal system known to be important for generalisation. We propose that to generalise structural knowledge, the representations of the structure of the world, i.e. how entities in the world relate to each other, need to be separated from representations of the entities themselves. We show, under these principles, artificial neural networks embedded with hierarchy and fast Hebbian memory, can learn the statistics of memories and generalise structural knowledge. Spatial neuronal representations mirroring those found in the brain emerge, suggesting spatial cognition is an instance of more general organising principles. We further unify many entorhinal cell types as basis functions for constructing transition graphs, and show these representations effectively utilise memories. We experimentally support model assumptions, showing a preserved relationship between entorhinal grid and hippocampal place cells across environments.

A central question in cognitive neuroscience regards the means by which options are compared and decisions are resolved during value-guided choice. It is clear that several component processes are needed; these include identifying options, a value-based comparison, and implementation of actions to execute the decision. What is less clear is the temporal precedence and functional organisation of these component processes in the brain. Competing models of decision making have proposed that value comparison may occur in the space of alternative actions, or in the space of abstract goods. We hypothesized that the signals observed might in fact depend upon the framing of the decision. We recorded magnetoencephalographic data from humans performing value-guided choices in which two closely related trial types were interleaved. In the first trial type, each option was revealed separately, potentially causing subjects to estimate each action's value as it was revealed and perform comparison in action-space. In the second trial type, both options were presented simultaneously, potentially leading to comparison in abstract goods-space prior to commitment to a specific action. Distinct activity patterns (in distinct brain regions) on the two trial types demonstrated that the observed frame of reference used for decision making indeed differed, despite the information presented being formally identical, between the two trial types. This provides a potential reconciliation of conflicting accounts of value-guided choice.

The trade-off between signal-to-noise ratio (SNR) and spatial specificity governs the choice of spatial resolution in magnetic resonance imaging (MRI); diffusion-weighted (DW) MRI is no exception. Images of lower resolution have higher signal to noise ratio, but also more partial volume artifacts. We present a data-fusion approach for tackling this trade-off by combining DW MRI data acquired both at high and low spatial resolution. We combine all data into a single Bayesian model to estimate the underlying fiber patterns and diffusion parameters. The proposed model, therefore, combines the benefits of each acquisition. We show that fiber crossings at the highest spatial resolution can be inferred more robustly and accurately using such a model compared to a simpler model that operates only on high-resolution data, when both approaches are matched for acquisition time.

Mixture models are commonly used in the statistical segmentation of images. For example, they can be used for the segmentation of structural medical images into different matter types, or of statistical parametric maps into activating and nonactivating brain regions in functional imaging. Spatial mixture models have been developed to augment histogram information with spatial regularization using Markov random fields (MRFs). In previous work, an approximate model was developed to allow adaptive determination of the parameter controlling the strength of spatial regularization. Inference was performed using Markov Chain Monte Carlo (MCMC) sampling. However, this approach is prohibitively slow for large datasets. In this work, a more efficient inference approach is presented. This combines a variational Bayes approximation with a second-order Taylor expansion of the components of the posterior distribution, which would otherwise be intractable to Variational Bayes. This provides inference on fully adaptive spatial mixture models an order of magnitude faster than MCMC. We examine the behavior of this approach when applied to artificial data with different spatial characteristics, and to functional magnetic resonance imaging statistical parametric maps.

Mixture models are often used in the statistical segmentation of medical images. For example, they can be used for the segmentation of structural images into different matter types or of functional statistical parametric maps (SPMs) into activations and nonactivations. Nonspatial mixture models segment using models of just the histogram of intensity values. Spatial mixture models have also been developed which augment this histogram information with spatial regularization using Markov random fields. However, these techniques have control parameters, such as the strength of spatial regularization, which need to be tuned heuristically to particular datasets. We present a novel spatial mixture model within a fully Bayesian framework with the ability to perform fully adaptive spatial regularization using Markov random fields. This means that the amount of spatial regularization does not have to be tuned heuristically but is adaptively determined from the data. We examine the behavior of this model when applied to artificial data with different spatial characteristics, and to functional magnetic resonance imaging SPMs.