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Belief circuit. Circuit for calculating the belief distribution over coincidence patterns by integrating the sequence of bottom-up inputs with the top-down inputs. The pentagon-shaped neurons are the belief neurons. These neurons pool over all the neurons representing the same coincidence in different Markov chains to calculate the belief value for each coincidence pattern. This circuit implements the Equation 6 in Table 1.
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The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is...
Citations
... Using these seeds, we query a background human interactome of 471,200 interacIons between 18,614 proteins created using curated, experimentally determined protein interacIons from canSAR 13 , KEGG 14 , and HI-union 15 . This returns fragmented networks connecIng the seeds. ...
... ; https://doi.org/10.1101/2024.06.04.597409 doi: bioRxiv preprint Markov chains provide stochastic models in which the probability of each event is dependent only on its immediately prior state. Computationally efficient because of their memorylessness, Markov chain models 12 , have been applied to a variety of biological questions, including molecular phylogenetics in bioinformatics 13 , stochastic chemical kinetics in systems biology 14 , and modeling of cortical micro-circuits in neuroscience 15 . In particular, Markov chain models have important features that lend themselves well to our question of interest. ...
Over half cancer patients lack safe, effective, targeted therapies despite abundant molecular profiling data. Statistically recurrent cancer drivers have provided fertile ground for drug discovery where they exist. But in rare, complex, and heterogeneous cancers, strong driver signals are elusive. Moreover, therapeutically exploitable molecular vulnerabilities extend beyond classical drivers. Here we describe a novel, integrative, generalizable graph-based, cooperativity-led Markov chain model, A3D3a's MVP (Adaptive AI-Augmented Drug Discovery and Development Molecular Vulnerability Picker), to identify and prioritize key druggable molecular vulnerabilities in cancer. The algorithm exploits cooperativity of weak signals within a cancer molecular network to enhance the signal of true molecular vulnerabilities. We apply A3D3a's MVP to 19 solid cancer types and demonstrate that it outperforms standard approaches for target hypothesis generation by >3-fold as benchmarked against cell line genetic perturbation and drug screening data. Importantly, we demonstrate its ability to identify non-driver druggable vulnerabilities and highlight 43 novel or emergent druggable targets for these tumors.
... In most of these applications, HTM achieved state-of-the-art accuracy. George et al. [17] believed that there are still many unknowns about the Neocortex that have not been modeled by the HTM algorithm. However, they still considered HTM an ideal starting point for biological brain modeling. ...
... Ahmad and Hawkins presented a distinctive description of Sparse Distributed Representation (SDR) and the information expression form in the Spatial Pooler (SP) [23], which gave valuable direction for further study. Using Bayesian diffusion equations, George et al. [17] introduced a mathematical model for HTM. They discussed how to extend the HTM algorithm to explain cortex properties that the algorithm had not previously implemented. ...
Hierarchical temporal memory (HTM) is a promising unsupervised machine-learning algorithm that models key principles of neocortical computation. One of the main components of HTM is the spatial pooler (SP), which encodes binary input streams into sparse distributed representations (SDRs). In this paper, we propose an information-theoretic framework for the performance comparison of HTM-spatial pooler (SP) algorithms, specifically, for quantifying the similarities and differences between sparse distributed representations in SP algorithms. We evaluate SP's standalone performance, as well as HTM's overall performance. Our comparison of various SP algorithms using Renyi mutual information, Renyi divergence, and Henze–Penrose divergence measures reveals that the SP algorithm with learning and a logarithmic boosting function yields the most effective and useful data representation. Moreover, the most effective SP algorithm leads to superior HTM results. In addition, we utilize our proposed framework to compare HTM with other state-of-the-art sequential learning algorithms. We illustrate that HTM exhibits superior adaptability to pattern changes over time than long short term memory (LSTM), gated recurrent unit (GRU) and online sequential extreme learning machine (OS-ELM) algorithms. This superiority is evident from the lower Renyi divergence of HTM (0.23) compared to LSTM6000 (0.33), LSTM3000 (0.38), GRU (0.41), and OS-ELM (0.49). HTM also achieved the highest Renyi mutual information value of 0.79, outperforming LSTM6000 (0.73), LSTM3000 (0.71), GRU (0.68), and OS-ELM (0.62). These findings not only confirm the numerous advantages of HTM over other sequential learning algorithm, but also demonstrate the effectiveness of our proposed information-theoretic approach as a powerful framework for comparing and evaluating various learning algorithms.
... The DPC model assumes that spatiotemporal inputs are generated by a hierarchical generative model (Fig 1a) (see also [37]). We describe here a two-level hierarchical model (see Discussion for the possibility of extending the model to more levels). ...
We introduce dynamic predictive coding, a hierarchical model of spatiotemporal prediction and sequence learning in the neocortex. The model assumes that higher cortical levels modulate the temporal dynamics of lower levels, correcting their predictions of dynamics using prediction errors. As a result, lower levels form representations that encode sequences at shorter timescales (e.g., a single step) while higher levels form representations that encode sequences at longer timescales (e.g., an entire sequence). We tested this model using a two-level neural network, where the top-down modulation creates low-dimensional combinations of a set of learned temporal dynamics to explain input sequences. When trained on natural videos, the lower-level model neurons developed space-time receptive fields similar to those of simple cells in the primary visual cortex while the higher-level responses spanned longer timescales, mimicking temporal response hierarchies in the cortex. Additionally, the network’s hierarchical sequence representation exhibited both predictive and postdictive effects resembling those observed in visual motion processing in humans (e.g., in the flash-lag illusion). When coupled with an associative memory emulating the role of the hippocampus, the model allowed episodic memories to be stored and retrieved, supporting cue-triggered recall of an input sequence similar to activity recall in the visual cortex. When extended to three hierarchical levels, the model learned progressively more abstract temporal representations along the hierarchy. Taken together, our results suggest that cortical processing and learning of sequences can be interpreted as dynamic predictive coding based on a hierarchical spatiotemporal generative model of the visual world.
... However, most Bayesian models in the real world are more complex. When using BP (George and Hawkins, 2009) or MCMC (Buesing et al., 2011) to implement Bayesian model inference, each or each group of neurons generally has to implement a different and complex computation in these neural networks. In addition, since spiking neural networks require multiple iterations to obtain optimal Bayesian inference results, they are more complicated to implement. ...
Spiking neural networks (SNNs), as brain-inspired neural network models based on spikes, have the advantage of processing information with low complexity and efficient energy consumption. Currently, there is a growing trend to design hardware accelerators for dedicated SNNs to overcome the limitation of running under the traditional von Neumann architecture. Probabilistic sampling is an effective modeling approach for implementing SNNs to simulate the brain to achieve Bayesian inference. However, sampling consumes considerable time. It is highly demanding for specific hardware implementation of SNN sampling models to accelerate inference operations. Hereby, we design a hardware accelerator based on FPGA to speed up the execution of SNN algorithms by parallelization. We use streaming pipelining and array partitioning operations to achieve model operation acceleration with the least possible resource consumption, and combine the Python productivity for Zynq (PYNQ) framework to implement the model migration to the FPGA while increasing the speed of model operations. We verify the functionality and performance of the hardware architecture on the Xilinx Zynq ZCU104. The experimental results show that the hardware accelerator of the SNN sampling model proposed can significantly improve the computing speed while ensuring the accuracy of inference. In addition, Bayesian inference for spiking neural networks through the PYNQ framework can fully optimize the high performance and low power consumption of FPGAs in embedded applications. Taken together, our proposed FPGA implementation of Bayesian inference with SNNs has great potential for a wide range of applications, it can be ideal for implementing complex probabilistic model inference in embedded systems.
... Here, context is constituted by a superordinate state-space that-by definition-unfolds at a slower rate. This is why deep discrete state-space models are generally synonymous with deep temporal models that bring a semi-Markovian aspect to the way that content is generated, e.g., natural language [81][82][83]. In the next section, we tackle the problem of structure learning in the setting of state transitions-that supply priors on the latent states-to supplement the likelihood model considered in this section. ...
This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A key move-in the ensuing schemes-is to place priors on the selection of models, based upon expected free energy. In this setting, expected free energy reduces to a constrained mutual information , where the constraints inherit from priors over outcomes (i.e., preferred outcomes). The resulting scheme is first used to perform image classification on the MNIST dataset to illustrate the basic idea, and then tested on a more challenging problem of discovering models with dynamics, using a simple sprite-based visual disentanglement paradigm and the Tower of Hanoi (cf., blocks world) problem. In these examples, generative models are constructed autodidactically to recover (i.e., disentangle) the factorial structure of latent states-and their characteristic paths or dynamics.
... These models necessarily have a grammar; in the sense of dynamics and non-Markovian temporal structure, as evinced in hierarchical structure learning treatments. See for example: (Davis and Johnsrude, 2003;Friston et al., 2017c;George and Hawkins, 2009;MacKay and Peto, 2008;Stoianov et al., 2022;Yildiz et al., 2013;Young et al., 2018;Zorzi et al., 2013). In short, grammar and meaning should be isomorphic with world models. ...
This paper concerns the distributed intelligence or federated inference that emerges under belief-sharing among agents who share a common world—and world model. Imagine, for example, several animals keeping a lookout for predators. Their collective surveillance rests upon being able to communicate their beliefs—about what they see—among themselves. But, how is this possible? Here, we show how all the necessary components arise from minimising free energy. We use numerical studies to simulate the generation, acquisition and emergence of language in synthetic agents. Specifically, we consider inference, learning and selection as minimising the variational free energy of posterior (i.e., Bayesian) beliefs about the states, parameters and structure of generative models, respectively. The common theme—that attends these optimisation processes—is the selection of actions that minimise expected free energy, leading to active inference, learning and model selection (a.k.a., structure learning). We first illustrate the role of communication in resolving uncertainty about the latent states of a partially observed world, on which agents have complementary perspectives. We then consider the acquisition of the requisite language—entailed by a likelihood mapping from an agent's beliefs to their overt expression (e.g., speech)—showing that language can be transmitted across generations by active learning. Finally, we show that language is an emergent property of free energy minimisation, when agents operate within the same econiche. We conclude with a discussion of various perspectives on these phenomena; ranging from cultural niche construction, through federated learning, to the emergence of complexity in ensembles of self-organising systems.
... The research on the computable model of nervous system includes Cortical Model (see Appendix A), LDPs and Neural Circuits (see Appendix B). Among them, Hierarchical Temporal Memory(HTM) [34] is very noteworthy (see Appendix C). Fig. 1 is our WMN visualization of 48 brain regions form the high accuracy human brain LDP database in documents [35], [36], which consider WMN connection weights and nodes size. ...
... Hierarchical Temporal Memory (HTM) model [34] is a kind of neocortex structure and function by Jeff Hawkins and Dileep et al. It adopted Bayesian Belief Propagation (PBP) theory to explain the neocortex process of recognition and reconstruction (Fig. 16). ...
To address the problems of scientific theory, common technology and engineering application of multimedia and multimodal information computing, this paper is focused on the theoretical model, algorithm framework, and system architecture of brain and mind inspired intelligence (BMI) based on the structure mechanism simulation of the nervous system, the function architecture emulation of the cognitive system and the complex behavior imitation of the natural system. Based on information theory, system theory, cybernetics and bionics, we define related concept and hypothesis of brain and mind inspired computing (BMC) and design a model and framework for frontier BMI theory. Research shows that BMC can effectively improve the performance of semantic processing of multimedia and cross-modal information, such as target detection, classification and recognition. Based on the brain mechanism and mind architecture, a semantic-oriented multimedia neural, cognitive computing model is designed for multimedia semantic computing. Then a hierarchical cross-modal cognitive neural computing framework is proposed for cross-modal information processing. Furthermore, a cross-modal neural, cognitive computing architecture is presented for remote sensing intelligent information extraction platform and unmanned autonomous system.
... In the current setting, we are considering the move from homeostasis to allostasis. This necessarily entails deep (hierarchical) generative models with a separation of temporal scales (Badcock et al., 2019;Friston et al., 2017;George and Hawkins, 2009;Kiebel et al., 2008). The separation of temporal scales speaks to a temporal depth of self-organization, reflected in the anticipatory or pre-emptive aspect of allostasis. ...
... João: Concerning the question of whether Bayesian statistical inference is to be preferred, indeed, in recent years Bayesian statistics has been a key player regarding inferences on brain processes and cognitive modeling (Friston et al., 2016;George & Hawkins, 2009). One of the main reasons is because this framework facilitates statistical modeling and the convergence of algorithms, even in the case of high dimensional data, such as in functional magnetic resonance imaging (fMRI), electroencephalography (EEG), near-infrared spectroscopy (NIRS) and magnetoencephalography (MEG). ...
... In summary, one can imagine centrifugal hierarchies of the sort depicted in Figure 5 as successively nested holographic screens; each reading and writing to each other at increasing levels of abstraction; i.e., coarse-graining over increasing temporal scales (Friston, Fagerholm, et al., 2021;George & Hawkins, 2009). The complete set of screens can thus be read as having a nested, holographic structure. ...
This paper presents a model of consciousness that follows directly from the free-energy principle (FEP). We first rehearse the classical and quantum formulations of the FEP. In particular, we consider the inner screen hypothesis that follows from the quantum information theoretic version of the FEP. We then review applications of the FEP to the known sparse (nested and hierarchical) neuro-anatomy of the brain. We focus on the holographic structure of the brain, and how this structure supports (overt and covert) action.
