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The above critiques have been called for a revision of the objectives of the Blue Brain project with more transparency. Hence, new strategies such as the division of Allen Institute, MindScope ( Hawrylycz et al., 2016), and the Human Brain Project ( Amunts et al., 2016) aim for adaptive granularity, more focused research on human data, and pooling of resources through cloud-based collaboration and open science ( Fecher and Friesike, 2014). Alternatively, smaller teams developed less resource-intensive simulation tools such as Brian ( Stimberg et al., 2019) and NEST ( Gewaltig and Diesmann, 2007). Hopfield network ( Hopfield, 1982) is a type of RNN inspired by the dynamics of Ising model ( Brush, 1967; Little, 1974). In the original Hopfield mechanism, the units are threshold ( McCulloch and Pitts, 1943) neurons, connected in a recurrent fashion. The state of the system is described by a vector V which represents the states of all units. In other words, the network is in fact, an undirected graph of artificial neurons. The strength of connection between units i and j is described by w ij which is trained by a given learning rule i.e., commonly Storkey ( Storkey, 1997) or Hebbian rule (stating that “neurons that fire together, wire together”) ( Hebb, 1949). After the training, these weights are set, and an energy landscape is defined as a function of V. The system evolves to minimize the energy and moves toward the basin of the closest attractor. This landscape can exhibit the stability and function of the network ( Yan et al., 2013). A potential solution for narrowing this computation gap can be sought at the hardware level. An instance of such a dedicated pipeline is neuromorphic processing units (NPU) that are power efficient and take time and dynamics into the equation from the beginning. An NPU is an array of neurosynaptic cores that contain computing models (neurons) and memory within the same unit. In short, the advantage of using NPUs is that they resemble the brain more realistically than a CPU or GPU because of asynchronous (event-based) communication, extreme parallelism (100–1,000,000 cores), and low power consumption ( Eli, 2022). Their efficiency and robustness also result from the Physical proximity of the computing unit and memory. Below popular examples of such NPUs are listed. Each of them stemmed from different initiatives.
Ferguson, K. A. et al. Network models provide insights into how oriens-lacunosum-moleculare and bistratified cell interactions influence the power of local hippocampal CA1 theta oscillations. Fr. Syst. Neurosci. 9, 110. https://doi.org/10.3389/fnsys.2015.00110 (2015).
de Física, Facultad de Ciencias Exactas y Naturales, Instituto de Física de Buenos Aires (IFIBA), CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina It is important to note that modeling is, and should be, beyond prediction ( Epstein, 2008). Not only does explicit modeling allow for explanation (which is the main point of science), but it also directs experiments and allows for the generation of new scientific questions. In addition to the implicit assumption of the adequacy of training data, the explicit assumption that these models rely on is that the solution is parsimonious, i.e., there are few descriptive parameters. Despite some possibility of error with this assumption in given problems ( Su et al., 2017), it is particularly useful in having arbitrarily less complicated descriptions that are generalizable, interpretable, and less prone to overfitting. Whole-brain phenomenological models like the Virtual Brain ( Sanz Leon et al., 2013) are conventional generators for reconstructing spontaneous brain activity. There are various considerations to have in mind to choose the right model for the right task. A major trade-off is between the complexity and abstractiveness of the parameters ( Breakspear, 2017). In other words, to capture the behavior of detailed cytoarchitectural and physiological make-up with a reasonably-parametrized model. Another consideration is the incorporation of noise, which is a requirement for multistable behavior ( Piccinini et al., 2021) i.e., transitions between stable patterns of reverberating activity (aka attractors) in a neural population in response to perturbation ( Kelso, 2012). 2.2.1.2. Kuramoto Soltesz, I. & Losonczy, A. CA1 pyramidal cell diversity enabling parallel information processing in the hippocampus. Nat Neurosci. 21(4), 484–493. https://doi.org/10.1038/s41593-018-0118-0 (2018).
In addition to network science, another axis for interpreting neural data is based on well-established tools initially developed for parametrizing the time evolution of physical systems. Famous examples of these systems include spin-glass ( Deco et al., 2012), different types of coupled oscillators ( Cabral et al., 2014; Abrevaya et al., 2021), and multistable and chaotic many-body systems ( Deco et al., 2017; Piccinini et al., 2021). This type of modeling has already offered promising and intuitive results. In the following subsections, we review some of the recent literature on various methodologies. 2.2.1. Brain as a Complex System Our focus is on generative models. Generative modeling can, in the current context, be distinguished from discriminative or classification modeling; in the sense that there is a probabilistic model of how observable data is generated by unobservable latent states. Almost invariably, generative models in imaging neuroscience are state space or dynamic models based upon differential equations or density dynamics (in continuous or discrete state spaces). Generative models can be used in one of two ways: first, they can be used to simulate or generate plausible neuronal dynamics (at multiple scales), with an emphasis on reproducing emergent phenomena of the sort seen in real brains. Second, the generative model can be inverted, given some empirical data, to make inferences about the functional form and architecture of distributed neuronal processing. In this use, the generative model is used as an observation model and is optimized to best explain some data. Crucially, this optimization entails identifying both the parameters of the generative model and its structure, via the process of model inversion and selection, respectively. When applied in this context, generative modeling is usually deployed to test hypotheses about functional brain architecture is (or neuronal circuits) using (Bayesian) model selection. In other words, comparing the evidence (a.k.a. marginal likelihood) for one model against some others. Zeng, Y. et al. Understanding the impact of neural variations and random connections on inference. Front. Comput. Neurosci. 15, 612937. https://doi.org/10.3389/fncom.2021.612937 (2021). Compared to detailed biophysical models, coarse-grained approaches rely on a smaller set of biological constraints and might be considered “too simplistic.” However, they are capable of reconstructing many collective phenomena that are still inaccessible to hyper-realistic simulations of neurons ( Piccinini et al., 2021). A famous example of emergence at this level is synchronizations in cortex ( Arenas et al., 2008). Moreover, experiments show that the population-level dynamics that are ignorant about the fine-grained detail better explain the behavior ( Briggman et al., 2005; Churchland et al., 2012).
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Expanding a previous approach 14, where the orientation of wiring was performed through distance-based probability functions applied during pruning procedures, the PMA algorithm introduces the orientation of the probability clouds which are used directly to estimate the pairs of connections. With the present connectivity workflow, the randomization of neuronal processes is restricted to the parameter sampling procedure during network construction. It should be noted that while the pruning procedure in the PMA method is, at the moment, based on randomized sampling, in a further development of the algorithm, probabilistic parameterization based on distance could be introduced. According to the heterogeneity of shapes and orientations of inhibitory interneurons, we have identified 11 classes of cells which were grouped into 7 different shapes generated through combinations of axonal and dendritic probability:
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