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1. Brain computation by assemblies of neurons

   https://doi.org/10.1101/869156  

   Papadimitriou, Christos H.; Vempala, Santosh S.; Mitropolsky, Daniel; Collins, Michael; Maass, Wolfgang (January 2020, Proceedings of the National Academy of Sciences of the United States of America)

   null (Ed.)

   Our expanding understanding of the brain at the level of neurons and synapses, and the level of cognitive phenomena such as language, leaves a formidable gap between these two scales. Here we introduce a computational system which promises to bridge this gap: the Assembly Calculus. It encompasses operations on assemblies of neurons, such as project, associate, and merge, which appear to be implicated in cognitive phenomena, and can be shown, analytically as well as through simulations, to be plausibly realizable at the level of neurons and synapses. We demonstrate the reach of this system by proposing a brain architecture for syntactic processing in the production of language, compatible with recent experimental results. 

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2. Assemblies of neurons learn to classify well-separated distributions

   Dabagia, Max; Papadimitriou, Christos; Vempala, Santosh S. (June 2022, Conference on Learning Theory)

   An assembly is a large population of neurons whose synchronous firing represents a memory, concept, word, and other cognitive category. Assemblies are believed to provide a bridge between high-level cognitive phenomena and low-level neural activity. Recently, a computational system called the \emph{Assembly Calculus} (AC), with a repertoire of biologically plausible operations on assemblies, has been shown capable of simulating arbitrary space-bounded computation, but also of simulating complex cognitive phenomena such as language, reasoning, and planning. However, the mechanism whereby assemblies can mediate {\em learning} has not been known. Here we present such a mechanism, and prove rigorously that, for simple classification problems defined on distributions of labeled assemblies, a new assembly representing each class can be reliably formed in response to a few stimuli from the class; this assembly is henceforth reliably recalled in response to new stimuli from the same class. Furthermore, such class assemblies will be distinguishable as long as the respective classes are reasonably separated — for example, when they are clusters of similar assemblies, or more generally separable with margin by a linear threshold function. To prove these results, we draw on random graph theory with dynamic edge weights to estimate sequences of activated vertices, yielding strong generalizations of previous calculations and theorems in this field over the past five years. These theorems are backed up by experiments demonstrating the successful formation of assemblies which represent concept classes on synthetic data drawn from such distributions, and also on MNIST, which lends itself to classification through one assembly per digit. Seen as a learning algorithm, this mechanism is entirely online, generalizes from very few samples, and requires only mild supervision — all key attributes of learning in a model of the brain. We argue that this learning mechanism, supported by separate sensory pre-processing mechanisms for extracting attributes, such as edges or phonemes, from real world data, can be the basis of biological learning in cortex. 

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3. Bridging the Gap Between Neurons and Cognition Through Assemblies of Neurons

   https://doi.org/10.1162/neco_a_01463  

   Papadimitriou, Christos H.; Friederici, Angela D. (January 2022, Neural Computation)

   Abstract During recent decades, our understanding of the brain has advanced dramatically at both the cellular and molecular levels and at the cognitive neurofunctional level; however, a huge gap remains between the microlevel of physiology and the macrolevel of cognition. We propose that computational models based on assemblies of neurons can serve as a blueprint for bridging these two scales. We discuss recently developed computational models of assemblies that have been demonstrated to mediate higher cognitive functions such as the processing of simple sentences, to be realistically realizable by neural activity, and to possess general computational power. 

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4. A biologically plausible parser

   Daniel Mitropolsky, Michael Collins (December 2021, Transactions of the Association for Computational Linguistics)

   We describe a parser of English effectuated by biologically plausible neurons and synapses, and implemented through the Assembly Calculus, a recently proposed computational framework for cognitive function. We demonstrate that this device is capable of correctly parsing reasonably nontrivial sentences.1 While our experiments entail rather simple sentences in English, our results suggest that the parser can be extended beyond what we have implemented, to several directions encompassing much of language. For example, we present a simple Russian version of the parser, and discuss how to handle recursion, embedding, and polysemy. 

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5. Computation with Sequences of Assemblies in a Model of the Brain

   Dabagia, Max; Papadimitriou, Christos; Vempala, Santosh S (March 2024, Algorithmic Learning Theory 2024)

   Even as machine learning exceeds human-level performance on many applications, the generality, robustness, and rapidity of the brain’s learning capabilities remain unmatched. How cognition arises from neural activity is the central open question in neuroscience, inextricable from the study of intelligence itself. A simple formal model of neural activity was proposed in Papadimitriou (2020) and has been subsequently shown, through both mathematical proofs and simulations, to be capable of implementing certain simple cognitive operations via the creation and manipulation of assemblies of neurons. However, many intelligent behaviors rely on the ability to recognize, store, and manipulate temporal sequences of stimuli (planning, language, navigation, to list a few). Here we show that, in the same model, time can be captured naturally as precedence through synaptic weights and plasticity, and, as a result, a range of computations on sequences of assemblies can be carried out. In particular, repeated presentation of a sequence of stimuli leads to the memorization of the sequence through corresponding neural assemblies: upon future presentation of any stimulus in the sequence, the corresponding assembly and its subsequent ones will be activated, one after the other, until the end of the sequence. If the stimulus sequence is presented to two brain areas simultaneously, a scaffolded representation is created, resulting in more efficient memorization and recall, in agreement with cognitive experiments. Finally, we show that any finite state machine can be learned in a similar way, through the presentation of appropriate patterns of sequences. Through an extension of this mechanism, the model can be shown to be capable of universal computation. We support our analysis with a number of experiments to probe the limits of learning in this model in key ways. Taken together, these results provide a concrete hypothesis for the basis of the brain’s remarkable abilities to compute and learn, with sequences playing a vital role. 

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