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1. Robust computation with rhythmic spike patterns

   https://doi.org/10.1073/pnas.1902653116  

   Frady, E. Paxon; Sommer, Friedrich T. (August 2019, Proceedings of the National Academy of Sciences)

   Information coding by precise timing of spikes can be faster and more energy efficient than traditional rate coding. However, spike-timing codes are often brittle, which has limited their use in theoretical neuroscience and computing applications. Here, we propose a type of attractor neural network in complex state space and show how it can be leveraged to construct spiking neural networks with robust computational properties through a phase-to-timing mapping. Building on Hebbian neural associative memories, like Hopfield networks, we first propose threshold phasor associative memory (TPAM) networks. Complex phasor patterns whose components can assume continuous-valued phase angles and binary magnitudes can be stored and retrieved as stable fixed points in the network dynamics. TPAM achieves high memory capacity when storing sparse phasor patterns, and we derive the energy function that governs its fixed-point attractor dynamics. Second, we construct 2 spiking neural networks to approximate the complex algebraic computations in TPAM, a reductionist model with resonate-and-fire neurons and a biologically plausible network of integrate-and-fire neurons with synaptic delays and recurrently connected inhibitory interneurons. The fixed points of TPAM correspond to stable periodic states of precisely timed spiking activity that are robust to perturbation. The link established between rhythmic firing patterns and complex attractor dynamics has implications for the interpretation of spike patterns seen in neuroscience and can serve as a framework for computation in emerging neuromorphic devices. 

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2. The role of long-term power-law memory in controlling large-scale dynamical networks

   https://doi.org/10.1038/s41598-023-46349-9  

   Reed, Emily_A; Ramos, Guilherme; Bogdan, Paul; Pequito, Sérgio (November 2023, Scientific Reports)

   Abstract Controlling large-scale dynamical networks is crucial to understand and, ultimately, craft the evolution of complex behavior. While broadly speaking we understand how to control Markov dynamical networks, where the current state is only a function of its previous state, we lack a general understanding of how to control dynamical networks whose current state depends on states in the distant past (i.e. long-term memory). Therefore, we require a different way to analyze and control the more prevalent long-term memory dynamical networks. Herein, we propose a new approach to control dynamical networks exhibiting long-term power-law memory dependencies. Our newly proposed method enables us to find the minimum number of driven nodes (i.e. the state vertices in the network that are connected to one and only one input) and their placement to control a long-term power-law memory dynamical network given a specific time-horizon, which we define as the ‘time-to-control’. Remarkably, we provide evidence that long-term power-law memory dynamical networks require considerably fewer driven nodes to steer the network’s state to a desired goal for any given time-to-control as compared with Markov dynamical networks. Finally, our method can be used as a tool to determine the existence of long-term memory dynamics in networks. 

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3. Neural learning rules for generating flexible predictions and computing the successor representation

   https://doi.org/10.7554/eLife.80680  

   Fang, Ching; Aronov, Dmitriy; Abbott, LF; Mackevicius, Emily L (March 2023, eLife)

   Memories are an important part of how we think, understand the world around us, and plan out future actions. In the brain, memories are thought to be stored in a region called the hippocampus. When memories are formed, neurons store events that occur around the same time together. This might explain why often, in the brains of animals, the activity associated with retrieving memories is not just a snapshot of what happened at a specific moment-- it can also include information about what the animal might experience next. This can have a clear utility if animals use memories to predict what they might experience next and plan out future actions. Mathematically, this notion of predictiveness can be summarized by an algorithm known as the successor representation. This algorithm describes what the activity of neurons in the hippocampus looks like when retrieving memories and making predictions based on them. However, even though the successor representation can computationally reproduce the activity seen in the hippocampus when it is making predictions, it is unclear what biological mechanisms underpin this computation in the brain. Fang et al. approached this problem by trying to build a model that could generate the same activity patterns computed by the successor representation using only biological mechanisms known to exist in the hippocampus. First, they used computational methods to design a network of neurons that had the biological properties of neural networks in the hippocampus. They then used the network to simulate neural activity. The results show that the activity of the network they designed was able to exactly match the successor representation. Additionally, the data resulting from the simulated activity in the network fitted experimental observations of hippocampal activity in Tufted Titmice. One advantage of the network designed by Fang et al. is that it can generate predictions in flexible ways,. That is, it canmake both short and long-term predictions from what an individual is experiencing at the moment. This flexibility means that the network can be used to simulate how the hippocampus learns in a variety of cognitive tasks. Additionally, the network is robust to different conditions. Given that the brain has to be able to store memories in many different situations, this is a promising indication that this network may be a reasonable model of how the brain learns. The results of Fang et al. lay the groundwork for connecting biological mechanisms in the hippocampus at the cellular level to cognitive effects, an essential step to understanding the hippocampus, as well as its role in health and disease. For instance, their network may provide a concrete approach to studying how disruptions to the ways neurons make and break connections can impair memory formation. More generally, better models of the biological mechanisms involved in making computations in the hippocampus can help scientists better understand and test out theories about how memories are formed and stored in the brain. 

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4. Gated recurrent units viewed through the lens of continuous time dynamical systems

   https://doi.org/10.3389/fncom.2021.678158  

   Jordan, Ian; Sokol, Piotr; Park, Il Memming (January 2021, Frontiers in computational neuroscience)

   null (Ed.)

   In recent years, the efficacy of using artificial recurrent neural networks to model cortical dynamics has been a topic of interest. Gated recurrent units (GRUs) are specialized memory elements for building these recurrent neural networks. Despite their incredible success in natural language, speech, video processing, and extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network, and how these dynamics play a part in performance and generalization. As a result, it is both difficult to know a priori how successful a GRU network will perform on a given task, and also their capacity to mimic the underlying behavior of their biological counterparts. Using a continuous time analysis, we gain intuition on the inner workings of GRU networks. We restrict our presentation to low dimensions, allowing for a comprehensive visualization. We found a surprisingly rich repertoire of dynamical features that includes stable limit cycles (nonlinear oscillations), multi-stable dynamics with various topologies, and homoclinic bifurcations. At the same time GRU networks are limited in their inability to produce continuous attractors, which are hypothesized to exist in biological neural networks. We contextualize the usefulness of different kinds of observed dynamics and support our claims experimentally. 

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5. Multigrid Neural Memory

   Huynh, Tri; Maire, Michael; Walter, Matthew R. (July 2020, Proceedings of the International Conference on Machine Learning (ICML))

   We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed attentional mechanisms, our memory is internal, distributed, co-located alongside computation, and implicitly addressed, while being drastically simpler than prior efforts. Architecting networks with multigrid structure and connectivity, while distributing memory cells alongside computation throughout this topology, we observe the emergence of coherent memory subsystems. Our hierarchical spatial organization, parameterized convolutionally, permits efficient instantiation of large-capacity memories, while multigrid topology provides short internal routing pathways, allowing convolutional networks to efficiently approximate the behavior of fully connected networks. Such networks have an implicit capacity for internal attention; augmented with memory, they learn to read and write specific memory locations in a dynamic data-dependent manner. We demonstrate these capabilities on exploration and mapping tasks, where our network is able to self-organize and retain long-term memory for trajectories of thousands of time steps. On tasks decoupled from any notion of spatial geometry: sorting, associative recall, and question answering, our design functions as a truly generic memory and yields excellent results. 

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