Modern Hopfield networks (HNs) exhibit properties of a Content Addressable Memory (CAM) that can store and retrieve a large number of memories. They also provide a basis for modelling associative memory in humans. However, the implementation of these networks is often not biologically plausible as they assume the strengths of synaptic connections are symmetric, and utilize functions that rely on many-body synapses. More biologically realistic versions of Modern HNs have been proposed, although these implementations often still utilize the softmax function. Computing the softmax for a single node requires the knowledge of all other neurons, and thus still poses a degree of biological implausibility. We present a Modern HN that uses a version of softmax that can be computed in a more bio-realistic way, and hence moves us closer to a model of memory that is biologically sound. We also show that our proposed network can learn the connection weights using a local learning rule, derived from gradient descent on the energy function. Finally, we verify that our proposed biological network behaves like a Modern HN and explore some of its other interesting properties.

Biological brains learn much more quickly than standard deep neural network reinforcement learning algorithms. One reason for this is that the deep neural networks need to learn a representation that is appropriate for the task at hand, whilst biological systems already possess an appropriate representation. Here, we bypass this problem by imposing on the neural network a representation based on what is observed in biology, such as grid cells. This study explores the impact of using a biologically-inspired grid-cell representation vs. a one-hot representation, on the speed at which a Temporal Difference-based Actor-Critic network learns to solve a simple 2D grid-world reinforcement learning task. The results suggest that the use of grid cells does promote faster learning. Furthermore, the grid cells implemented here have the potential for accurately representing unbounded continuous space. Thus, their promising performance on this discrete task acts as a first step in exploring their utility for reinforcement learning in continuous space.

Path integration, the ability to maintain an estimate of one's location by continuously integrating self-motion cues, is a vital component of the brain's navigation system. We present a spiking neural network model of path integration derived from a starting assumption that the brain represents continuous variables, such as spatial coordinates, using Spatial Semantic Pointers (SSPs). SSPs are a representation for encoding continuous variables as high-dimensional vectors, and can also be used to create structured, hierarchical representations for neural cognitive modelling. Path integration can be performed by a recurrently-connected neural network using SSP representations. Unlike past work, we show that our model can be used to continuously update variables of any dimensionality. We demonstrate that symbol-like object representations can be bound to continuous SSP representations. Specifically, we incorporate a simple model of working memory to remember environment maps with such symbol-like representations situated in 2D space.

Existing models of the basal ganglia assume the existence of separate channels of neuron populations for representing each available action. This type of localist mapping limits models to small, discrete action spaces, since additional actions require additional channels, costing neural resources and imposing new connective tracts. In contrast, evidence suggests that the basal ganglia plays a role in the selection of both discrete action units, and continuously-valued action kinematics. In this work, we model the basal ganglia with distributed action representations, using high-dimensional vectors. This method lends itself to representing both discrete and continuous action spaces. Vectors that represent actions are weighted by a scalar value (their salience to the current task), and bundled together to form a single input vector. This paper provides an overview of the encoding method and network structure, as well as a demonstration of the model solving an action selection task using spiking neurons.