Prediction and Generalisation over Directed Actions by Grid Cells

Knowing how the effects of directed actions generalise to new situations (e.g. moving North, South, East and West, or turning left, right, etc.) is key to rapid generalisation across new situations. Markovian tasks can be characterised by a state space and a transition matrix and recent work has proposed that neural grid codes provide an efficient representation of the state space, as eigenvectors of a transition matrix reflecting diffusion across states, that allows efficient prediction of future state distributions. Here we extend the eigenbasis prediction model, utilising tools from Fourier analysis, to prediction over arbitrary translation-invariant directed transition structures (i.e. displacement and diffusion), showing that a single set of eigenvectors can support predictions over arbitrary directed actions via action-specific eigenvalues. We show how to define a "sense of direction" to combine actions to reach a target state (ignoring task-specific deviations from translation-invariance), and demonstrate that adding the Fourier representations to a deep Q network aids policy learning in continuous control tasks. We show the equivalence between the generalised prediction framework and traditional models of grid cell firing driven by self-motion to perform path integration, either using oscillatory interference (via Fourier components as velocity-controlled oscillators) or continuous attractor networks (via analysis of the update dynamics). We thus provide a unifying framework for the role of the grid system in predictive planning, sense of direction and path integration: supporting generalisable inference over directed actions across different tasks.Comment: In Proceedings of ICLR 202

Counterfactual Choice and Learning in a Neural Network Centered on Human Lateral Frontopolar Cortex

Decision making and learning in a real-world context require organisms to track not only the choices they make and the outcomes that follow but also other untaken, or counterfactual, choices and their outcomes. Although the neural system responsible for tracking the value of choices actually taken is increasingly well understood, whether a neural system tracks counterfactual information is currently unclear. Using a three-alternative decision-making task, a Bayesian reinforcement-learning algorithm, and fMRI, we investigated the coding of counterfactual choices and prediction errors in the human brain. Rather than representing evidence favoring multiple counterfactual choices, lateral frontal polar cortex (lFPC), dorsomedial frontal cortex (DMFC), and posteromedial cortex (PMC) encode the reward-based evidence favoring the best counterfactual option at future decisions. In addition to encoding counterfactual reward expectations, the network carries a signal for learning about counterfactual options when feedback is available—a counterfactual prediction error. Unlike other brain regions that have been associated with the processing of counterfactual outcomes, counterfactual prediction errors within the identified network cannot be related to regret theory. Furthermore, individual variation in counterfactual choice-related activity and prediction error-related activity, respectively, predicts variation in the propensity to switch to profitable choices in the future and the ability to learn from hypothetical feedback. Taken together, these data provide both neural and behavioral evidence to support the existence of a previously unidentified neural system responsible for tracking both counterfactual choice options and their outcomes

Generalisation of structural knowledge in the hippocampal-entorhinal system

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

Actionable Neural Representations: Grid Cells from Minimal Constraints

To afford flexible behaviour, the brain must build internal representations that mirror the structure of variables in the external world. For example, 2D space obeys rules: the same set of actions combine in the same way everywhere (step north, then south, and you won't have moved, wherever you start). We suggest the brain must represent this consistent meaning of actions across space, as it allows you to find new short-cuts and navigate in unfamiliar settings. We term this representation an `actionable representation'. We formulate actionable representations using group and representation theory, and show that, when combined with biological and functional constraints - non-negative firing, bounded neural activity, and precise coding - multiple modules of hexagonal grid cells are the optimal representation of 2D space. We support this claim with intuition, analytic justification, and simulations. Our analytic results normatively explain a set of surprising grid cell phenomena, and make testable predictions for future experiments. Lastly, we highlight the generality of our approach beyond just understanding 2D space. Our work characterises a new principle for understanding and designing flexible internal representations: they should be actionable, allowing animals and machines to predict the consequences of their actions, rather than just encode

Disentangling with Biological Constraints: A Theory of Functional Cell Types

Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons, namely nonnegativity and energy efficiency in both activity and weights, promote such sought after disentangled representations by enforcing neurons to become selective for single factors of task variation. We demonstrate these constraints lead to disentangling in a variety of tasks and architectures, including variational autoencoders. We also use this theory to explain why the brain partitions its cells into distinct cell types such as grid and object-vector cells, and also explain when the brain instead entangles representations in response to entangled task factors. Overall, this work provides a mathematical understanding of why, when, and how neurons represent factors in both brains and machines, and is a first step towards understanding of how task demands structure neural representations

Using diffusion tractography to predict cortical connection strength and distance: a quantitative comparison with tracers in the monkey

Tractography based on diffusion MRI offers the promise of characterizing many aspects of long-distance connectivity in the brain, but requires quantitative validation to assess its strengths and limitations. Here, we evaluate tractography's ability to estimate the presence and strength of connections between areas of macaque neocortex by comparing its results with published data from retrograde tracer injections. Probabilistic tractography was performed on high-quality postmortem diffusion imaging scans from two Old World monkey brains. Tractography connection weights were estimated using a fractional scaling method based on normalized streamline density. We found a correlation between log-transformed tractography and tracer connection weights of r = 0.59, twice that reported in a recent study on the macaque. Using a novel method to estimate interareal connection lengths from tractography streamlines, we regressed out the distance dependence of connection strength and found that the correlation between tractography and tracers remains positive, albeit substantially reduced. Altogether, these observations provide a valuable, data-driven perspective on both the strengths and limitations of tractography for analyzing interareal corticocortical connectivity in nonhuman primates and a framework for assessing future tractography methodological refinements objectively

Accelerating fibre orientation estimation from diffusion weighted magnetic resonance imaging using GPUs

With the performance of central processing units (CPUs) having effectively reached a limit, parallel processing offers an alternative for applications with high computational demands. Modern graphics processing units (GPUs) are massively parallel processors that can execute simultaneously thousands of light-weight processes. In this study, we propose and implement a parallel GPU-based design of a popular method that is used for the analysis of brain magnetic resonance imaging (MRI). More specifically, we are concerned with a model-based approach for extracting tissue structural information from diffusion-weighted (DW) MRI data. DW-MRI offers, through tractography approaches, the only way to study brain structural connectivity, non-invasively and in-vivo. We parallelise the Bayesian inference framework for the ball & stick model, as it is implemented in the tractography toolbox of the popular FSL software package (University of Oxford). For our implementation, we utilise the Compute Unified Device Architecture (CUDA) programming model. We show that the parameter estimation, performed through Markov Chain Monte Carlo (MCMC), is accelerated by at least two orders of magnitude, when comparing a single GPU with the respective sequential single-core CPU version. We also illustrate similar speed-up factors (up to 120x) when comparing a multi-GPU with a multi-CPU implementation

Visualization of the Genesis and Fate of Isotype-switched B Cells during a Primary Immune Response

The life history of isotype-switched B cells is unclear, in part, because of an inability to detect rare antigen-specific B cells at early times during the immune response. To address this issue, a small population of B cells carrying targeted antibody transgenes capable of class switching was monitored in immunized mice. After contacting helper T cells, the first switched B cells appeared in follicles rather than in the red pulp, as was expected. Later, some of the switched B cells transiently occupied the red pulp and marginal zone, whereas others persisted in germinal centers (GCs). Antigen-experienced IgM B cells were rarely found in GCs, indicating that these cells switched rapidly after entering GCs or did not persist in this environment