skip to main content


This content will become publicly available on March 1, 2025

Title: Computation with Sequences of Assemblies in a Model of the Brain
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.  more » « less
Award ID(s):
2007443
PAR ID:
10547049
Author(s) / Creator(s):
; ;
Publisher / Repository:
Algorithmic Learning Theory 2024
Date Published:
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. 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. 
    more » « less
  2. null (Ed.)
    Abstract Background Availability of plant genome sequences has led to significant advances. However, with few exceptions, the great majority of existing genome assemblies are derived from short read sequencing technologies with highly uneven read coverages indicative of sequencing and assembly issues that could significantly impact any downstream analysis of plant genomes. In tomato for example, 0.6% (5.1 Mb) and 9.7% (79.6 Mb) of short-read based assembly had significantly higher and lower coverage compared to background, respectively. Results To understand what the causes may be for such uneven coverage, we first established machine learning models capable of predicting genomic regions with variable coverages and found that high coverage regions tend to have higher simple sequence repeat and tandem gene densities compared to background regions. To determine if the high coverage regions were misassembled, we examined a recently available tomato long-read based assembly and found that 27.8% (1.41 Mb) of high coverage regions were potentially misassembled of duplicate sequences, compared to 1.4% in background regions. In addition, using a predictive model that can distinguish correctly and incorrectly assembled high coverage regions, we found that misassembled, high coverage regions tend to be flanked by simple sequence repeats, pseudogenes, and transposon elements. Conclusions Our study provides insights on the causes of variable coverage regions and a quantitative assessment of factors contributing to plant genome misassembly when using short reads and the generality of these causes and factors should be tested further in other species. 
    more » « less
  3. Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence u↦y by simply simulating a linear continuous-time state-space representation ˙x=Ax+Bu,y=Cx+Du. Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation. We then incorporate and generalize recent theory on continuous-time memorization to introduce a trainable subset of structured matrices A that endow LSSLs with long-range memory. Empirically, stacking LSSL layers into a simple deep neural network obtains state-of-the-art results across time series benchmarks for long dependencies in sequential image classification, real-world healthcare regression tasks, and speech. On a difficult speech classification task with length-16000 sequences, LSSL outperforms prior approaches by 24 accuracy points, and even outperforms baselines that use hand-crafted features on 100x shorter sequences. 
    more » « less
  4. This study provides a normative theory for how Bayesian causal inference can be implemented in neural circuits. In both cognitive processes such as causal reasoning and perceptual inference such as cue integration, the nervous systems need to choose different models representing the underlying causal structures when making inferences on external stimuli. In multisensory processing, for example, the nervous system has to choose whether to integrate or segregate inputs from different sensory modalities to infer the sensory stimuli, based on whether the inputs are from the same or different sources. Making this choice is a model selection problem requiring the computation of Bayes factor, the ratio of likelihoods between the integration and the segregation models. In this paper, we consider the causal inference in multisensory processing and propose a novel generative model based on neural population code that takes into account both stimulus feature and stimulus reliability in the inference. In the case of circular variables such as heading direction, our normative theory yields an analytical solution for computing the Bayes factor, with a clear geometric interpretation, which can be implemented by simple additive mechanisms with neural population code. Numerical simulation shows that the tunings of the neurons computing Bayes factor are consistent with the "opposite neurons" discovered in dorsal medial superior temporal (MSTd) and the ventral intraparietal (VIP) areas for visual-vestibular processing. This study illuminates a potential neural mechanism for causal inference in the brain. 
    more » « less
  5. Memorization is an essential functionality that enables today's machine learning algorithms to provide a high quality of learning and reasoning for each prediction. Memorization gives algorithms prior knowledge to keep the context and define confidence for their decision. Unfortunately, the existing deep learning algorithms have a weak and nontransparent notion of memorization. Brain-inspired HyperDimensional Computing (HDC) is introduced as a model of human memory. Therefore, it mimics several important functionalities of the brain memory by operating with a vector that is computationally tractable and mathematically rigorous in describing human cognition. In this manuscript, we introduce a brain-inspired system that represents HDC memorization capability over a graph of relations. We propose GrapHD , hyperdimensional memorization that represents graph-based information in high-dimensional space. GrapHD defines an encoding method representing complex graph structure while supporting both weighted and unweighted graphs. Our encoder spreads the information of all nodes and edges across into a full holistic representation so that no component is more responsible for storing any piece of information than another. Then, GrapHD defines several important cognitive functionalities over the encoded memory graph. These operations include memory reconstruction, information retrieval, graph matching, and shortest path. Our extensive evaluation shows that GrapHD : (1) significantly enhances learning capability by giving the notion of short/long term memorization to learning algorithms, (2) enables cognitive computing and reasoning over memorization graph, and (3) enables holographic brain-like computation with substantial robustness to noise and failure. 
    more » « less