Neural networks for perceptual processing: from simulation tools to theories

Neural networks are modelling tools that are, in principle, able to capture the input-output behaviour of arbitrary systems that may include the dynamics of animal populations or brain circuits. While a neural network model is useful if it captures phenomenologically the behaviour of the target system in this way, its utility is amplified if key mechanisms of the model can be discovered, and identified with those of the underlying system. In this review, we first describe, at a fairly high level with minimal mathematics, some of the tools used in constructing neural network models. We then go on to discuss the implications of network models for our understanding of the system they are supposed to describe, paying special attention to those models that deal with neural circuits and brain systems. We propose that neural nets are useful for brain modelling if they are viewed in a wider computational framework originally devised by Marr. Here, neural networks are viewed as an intermediate mechanistic abstraction between 'algorithm' and 'implementation', which can provide insights into biological neural representations and their putative supporting architectures.     

A computational framework for the study of confidence in humans and animals

Confidence judgements, self-assessments about the quality of a subject's knowledge, are considered a central example of metacognition. Prima facie, introspection and self-report appear the only way to access the subjective sense of confidence or uncertainty. Contrary to this notion, overt behavioural measures can be used to study confidence judgements by animals trained in decision-making tasks with perceptual or mnemonic uncertainty. Here, we suggest that a computational approach can clarify the issues involved in interpreting these tasks and provide a much needed springboard for advancing the scientific understanding of confidence. We first review relevant theories of probabilistic inference and decision-making. We then critically discuss behavioural tasks employed to measure confidence in animals and show how quantitative models can help to constrain the computational strategies underlying confidence-reporting behaviours. In our view, post-decision wagering tasks with continuous measures of confidence appear to offer the best available metrics of confidence. Since behavioural reports alone provide a limited window into mechanism, we argue that progress calls for measuring the neural representations and identifying the computations underlying confidence reports. We present a case study using such a computational approach to study the neural correlates of decision confidence in rats. This work shows that confidence assessments may be considered higher order, but can be generated using elementary neural computations that are available to a wide range of species. Finally, we discuss the relationship of confidence judgements to the wider behavioural uses of confidence and uncertainty.     

Is Model Fitting Necessary for Model-Based fMRI?

Model-based analysis of fMRI data is an important tool for investigating the computational role of different brain regions. With this method, theoretical models of behavior can be leveraged to find the brain structures underlying variables from specific algorithms, such as prediction errors in reinforcement learning. One potential weakness with this approach is that models often have free parameters and thus the results of the analysis may depend on how these free parameters are set. In this work we asked whether this hypothetical weakness is a problem in practice. We first developed general closed-form expressions for the relationship between results of fMRI analyses using different regressors, e.g., one corresponding to the true process underlying the measured data and one a model-derived approximation of the true generative regressor. Then, as a specific test case, we examined the sensitivity of model-based fMRI to the learning rate parameter in reinforcement learning, both in theory and in two previously-published datasets. We found that even gross errors in the learning rate lead to only minute changes in the neural results. Our findings thus suggest that precise model fitting is not always necessary for model-based fMRI. They also highlight the difficulty in using fMRI data for arbitrating between different models or model parameters. While these specific results pertain only to the effect of learning rate in simple reinforcement learning models, we provide a template for testing for effects of different parameters in other models.     

Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization

The advent of genome-scale models of metabolism has laid the foundation for the development of computational procedures for suggesting genetic manipulations that lead to overproduction. In this work, the computational OptKnock framework is introduced for suggesting gene deletion strategies leading to the overproduction of chemicals or biochemicals in E. coli. This is accomplished by ensuring that a drain towards growth resources (i.e., carbon, redox potential, and energy) must be accompanied, due to stoichiometry, by the production of a desired product. Computational results for gene deletions for succinate, lactate, and 1,3-propanediol (PDO) production are in good agreement with mutant strains published in the literature. While some of the suggested deletion strategies are straightforward and involve eliminating competing reaction pathways, many others suggest complex and nonintuitive mechanisms of compensating for the removed functionalities. Finally, the OptKnock procedure, by coupling biomass formation with chemical production, hints at a growth selection/adaptation system for indirectly evolving overproducing mutants.     

Brain signal predictions from multi-scale networks using a linearized framework

Simulations of neural activity at different levels of detail are ubiquitous in modern neurosciences, aiding the interpretation of experimental data and underlying neural mechanisms at the level of cells and circuits. Extracellular measurements of brain signals reflecting transmembrane currents throughout the neural tissue remain commonplace. The lower frequencies (≲ 300Hz) of measured signals generally stem from synaptic activity driven by recurrent interactions among neural populations and computational models should also incorporate accurate predictions of such signals. Due to limited computational resources, large-scale neuronal network models (≳ 10⁶ neurons or so) often require reducing the level of biophysical detail and account mainly for times of action potentials (‘spikes’) or spike rates. Corresponding extracellular signal predictions have thus poorly accounted for their biophysical origin.Here we propose a computational framework for predicting spatiotemporal filter kernels for such extracellular signals stemming from synaptic activity, accounting for the biophysics of neurons, populations, and recurrent connections. Signals are obtained by convolving population spike rates by appropriate kernels for each connection pathway and summing the contributions. Our main results are that kernels derived via linearized synapse and membrane dynamics, distributions of cells, conduction delay, and volume conductor model allow for accurately capturing the spatiotemporal dynamics of ground truth extracellular signals from conductance-based multicompartment neuron networks. One particular observation is that changes in the effective membrane time constants caused by persistent synapse activation must be accounted for.The work also constitutes a major advance in computational efficiency of accurate, biophysics-based signal predictions from large-scale spike and rate-based neuron network models drastically reducing signal prediction times compared to biophysically detailed network models. This work also provides insight into how experimentally recorded low-frequency extracellular signals of neuronal activity may be approximately linearly dependent on spiking activity. A new software tool LFPykernels serves as a reference implementation of the framework.     

ASCENT (Automated Simulations to Characterize Electrical Nerve Thresholds): A pipeline for sample-specific computational modeling of electrical stimulation of peripheral nerves

Electrical stimulation and block of peripheral nerves hold great promise for treatment of a range of disease and disorders, but promising results from preclinical studies often fail to translate to successful clinical therapies. Differences in neural anatomy across species require different electrodes and stimulation parameters to achieve equivalent nerve responses, and accounting for the consequences of these factors is difficult. We describe the implementation, validation, and application of a standardized, modular, and scalable computational modeling pipeline for biophysical simulations of electrical activation and block of nerve fibers within peripheral nerves. The ASCENT (Automated Simulations to Characterize Electrical Nerve Thresholds) pipeline provides a suite of built-in capabilities for user control over the entire workflow, including libraries for parts to assemble electrodes, electrical properties of biological materials, previously published fiber models, and common stimulation waveforms. We validated the accuracy of ASCENT calculations, verified usability in beta release, and provide several compelling examples of ASCENT-implemented models. ASCENT will enable the reproducibility of simulation data, and it will be used as a component of integrated simulations with other models (e.g., organ system models), to interpret experimental results, and to design experimental and clinical interventions for the advancement of peripheral nerve stimulation therapies.     

Rat C6 glioma as experimental model system for the study of glioblastoma growth and invasion

Infiltration of the central nervous system by neoplastic cells in patients with glioblastoma multiforme (GBM) leads to neurological dysfunction and eventually to death. The elucidation of the mechanisms underlying the aggressive nature of GBM aims at improving radio-, chemo- and gene therapy. This review is focused on the use of rat C6 glioma as an experimental model system for GBM and provides an overview of the experimental data published in the literature using this cell line in elucidating the mechanism of tumor growth, angiogenesis and invasion, and in the design and evaluation of anticancer therapies. Understanding the stages of malignant brain tumor progression requires a series of experimental approaches with a varying degree of complexity. Implantation of malignant cells into animal brain tissue closely resembles in vivo tumor growth and has the advantage over simplified models that inflammatory and vascular mechanisms are activated. However, the complexity of these models makes it difficult to identify the individual processes involved in sustained tumor growth, angiogenesis and invasion. In cell culture models, the effect of growth factors, extracellular matrix components, proteases and adhesion molecules can be investigated. The secretion of tumor-derived factors into the medium can also be analyzed when simplified models are used. This review is a compilation of experimental data focused on the characterization of tumor-related processes and on the evaluation of new therapies for the treatment of malignant glial neoplasms using rat C6 glioma as a model system.     

On the computation of molecular surface correlations for protein docking using fourier techniques

The computation of surface correlations using a variety of molecular models has been applied to the unbound protein docking problem. Because of the computational complexity involved in examining all possible molecular orientations, the fast Fourier transform (FFT) (a fast numerical implementation of the discrete Fourier transform (DFT)) is generally applied to minimize the number of calculations. This approach is rooted in the convolution theorem which allows one to inverse transform the product of two DFTs in order to perform the correlation calculation. However, such a DFT calculation results in a cyclic or "circular" correlation which, in general, does not lead to the same result as the linear correlation desired for the docking problem. In this work, we provide computational bounds for constructing molecular models used in the molecular surface correlation problem. The derived bounds are then shown to be consistent with various intuitive guidelines previously reported in the protein docking literature. Finally, these bounds are applied to different molecular models in order to investigate their effect on the correlation calculation.     

The ion channel inverse problem: neuroinformatics meets biophysics

Ion channels are the building blocks of the information processing capability of neurons: any realistic computational model of a neuron must include reliable and effective ion channel components. Sophisticated statistical and computational tools have been developed to study the ion channel structure–function relationship, but this work is rarely incorporated into the models used for single neurons or small networks. The disjunction is partly a matter of convention. Structure–function studies typically use a single Markov model for the whole channel whereas until recently whole-cell modeling software has focused on serial, independent, two-state subunits that can be represented by the Hodgkin–Huxley equations. More fundamentally, there is a difference in purpose that prevents models being easily reused. Biophysical models are typically developed to study one particular aspect of channel gating in detail, whereas neural modelers require broad coverage of the entire range of channel behavior that is often best achieved with approximate representations that omit structural features that cannot be adequately constrained. To bridge the gap so that more recent channel data can be used in neural models requires new computational infrastructure for bringing together diverse sources of data to arrive at best-fit models for whole-cell modeling. We review the current state of channel modeling and explore the developments needed for its conclusions to be integrated into whole-cell modeling.     

A case for spiking neural network simulation based on configurable multiple-FPGA systems

Recent neuropsychological research has begun to reveal that neurons encode information in the timing of spikes. Spiking neural network simulations are a flexible and powerful method for investigating the behaviour of neuronal systems. Simulation of the spiking neural networks in software is unable to rapidly generate output spikes in large-scale of neural network. An alternative approach, hardware implementation of such system, provides the possibility to generate independent spikes precisely and simultaneously output spike waves in real time, under the premise that spiking neural network can take full advantage of hardware inherent parallelism. We introduce a configurable FPGA-oriented hardware platform for spiking neural network simulation in this work. We aim to use this platform to combine the speed of dedicated hardware with the programmability of software so that it might allow neuroscientists to put together sophisticated computation experiments of their own model. A feed-forward hierarchy network is developed as a case study to describe the operation of biological neural systems (such as orientation selectivity of visual cortex) and computational models of such systems. This model demonstrates how a feed-forward neural network constructs the circuitry required for orientation selectivity and provides platform for reaching a deeper understanding of the primate visual system. In the future, larger scale models based on this framework can be used to replicate the actual architecture in visual cortex, leading to more detailed predictions and insights into visual perception phenomenon.     

A Spiking Neural Network Model of Model-Free Reinforcement Learning with High-Dimensional Sensory Input and Perceptual Ambiguity

A theoretical framework of reinforcement learning plays an important role in understanding action selection in animals. Spiking neural networks provide a theoretically grounded means to test computational hypotheses on neurally plausible algorithms of reinforcement learning through numerical simulation. However, most of these models cannot handle observations which are noisy, or occurred in the past, even though these are inevitable and constraining features of learning in real environments. This class of problem is formally known as partially observable reinforcement learning (PORL) problems. It provides a generalization of reinforcement learning to partially observable domains. In addition, observations in the real world tend to be rich and high-dimensional. In this work, we use a spiking neural network model to approximate the free energy of a restricted Boltzmann machine and apply it to the solution of PORL problems with high-dimensional observations. Our spiking network model solves maze tasks with perceptually ambiguous high-dimensional observations without knowledge of the true environment. An extended model with working memory also solves history-dependent tasks. The way spiking neural networks handle PORL problems may provide a glimpse into the underlying laws of neural information processing which can only be discovered through such a top-down approach.     

The computational neurobiology of learning and reward

Following the suggestion that midbrain dopaminergic neurons encode a signal, known as a 'reward prediction error', used by artificial intelligence algorithms for learning to choose advantageous actions, the study of the neural substrates for reward-based learning has been strongly influenced by computational theories. In recent work, such theories have been increasingly integrated into experimental design and analysis. Such hybrid approaches have offered detailed new insights into the function of a number of brain areas, especially the cortex and basal ganglia. In part this is because these approaches enable the study of neural correlates of subjective factors (such as a participant's beliefs about the reward to be received for performing some action) that the computational theories purport to quantify.     

A range-normalization model of context-dependent choice: a new model and evidence

Most utility theories of choice assume that the introduction of an irrelevant option (called the decoy) to a choice set does not change the preference between existing options. On the contrary, a wealth of behavioral data demonstrates the dependence of preference on the decoy and on the context in which the options are presented. Nevertheless, neural mechanisms underlying context-dependent preference are poorly understood. In order to shed light on these mechanisms, we design and perform a novel experiment to measure within-subject decoy effects. We find within-subject decoy effects similar to what have been shown previously with between-subject designs. More importantly, we find that not only are the decoy effects correlated, pointing to similar underlying mechanisms, but also these effects increase with the distance of the decoy from the original options. To explain these observations, we construct a plausible neuronal model that can account for decoy effects based on the trial-by-trial adjustment of neural representations to the set of available options. This adjustment mechanism, which we call range normalization, occurs when the nervous system is required to represent different stimuli distinguishably, while being limited to using bounded neural activity. The proposed model captures our experimental observations and makes new predictions about the influence of the choice set size on the decoy effects, which are in contrast to previous models of context-dependent choice preference. Critically, unlike previous psychological models, the computational resource required by our range-normalization model does not increase exponentially as the set size increases. Our results show that context-dependent choice behavior, which is commonly perceived as an irrational response to the presence of irrelevant options, could be a natural consequence of the biophysical limits of neural representation in the brain.     

Neuronal firing rates account for distractor effects on mnemonic accuracy in a visuo-spatial working memory task

Persistent neural activity constitutes one neuronal correlate of working memory, the ability to hold and manipulate information across time, a prerequisite for cognition. Yet, the underlying neuronal mechanisms are still elusive. Here, we design a visuo- spatial delayed-response task to identify the relationship between the cue-distractor spatial distance and mnemonic accuracy. Using a shared experimental and computational test protocol, we probe human subjects in computer experiments, and subsequently we evaluate different neural mechanisms underlying persistent activity using an in silico prefrontal network model. Five modes of action of the network were tested: weak or strong synaptic interactions, wide synaptic arborization, cellular bistability and reduced synaptic NMDA component. The five neural mechanisms and the human behavioral data, all exhibited a significant deterioration of the mnemonic accuracy with decreased spatial distance between the distractor and the cue. A subsequent computational analysis revealed that the firing rate and not the neural mechanism per se, accounted for the positive correlation between mnemonic accuracy and spatial distance. Moreover, the computational modeling predicts an inverse correlation between accuracy and distractibility. In conclusion, any pharmacological modulation, pathological condition or memory training paradigm targeting the underlying neural circuitry and altering the net population firing rate during the delay is predicted to determine the amount of influence of a visual distraction.     

Emerging concepts for the dynamical organization of resting-state activity in the brain

A broad body of experimental work has demonstrated that apparently spontaneous brain activity is not random. At the level of large-scale neural systems, as measured with functional MRI (fMRI), this ongoing activity reflects the organization of a series of highly coherent functional networks. These so-called resting-state networks (RSNs) closely relate to the underlying anatomical connectivity but cannot be understood in those terms alone. Here we review three large-scale neural system models of primate neocortex that emphasize the key contributions of local dynamics, signal transmission delays and noise to the emerging RSNs. We propose that the formation and dissolution of resting-state patterns reflects the exploration of possible functional network configurations around a stable anatomical skeleton.     

Deep Neural Networks Rival the Representation of Primate IT Cortex for Core Visual Object Recognition

The primate visual system achieves remarkable visual object recognition performance even in brief presentations, and under changes to object exemplar, geometric transformations, and background variation (a.k.a. core visual object recognition). This remarkable performance is mediated by the representation formed in inferior temporal (IT) cortex. In parallel, recent advances in machine learning have led to ever higher performing models of object recognition using artificial deep neural networks (DNNs). It remains unclear, however, whether the representational performance of DNNs rivals that of the brain. To accurately produce such a comparison, a major difficulty has been a unifying metric that accounts for experimental limitations, such as the amount of noise, the number of neural recording sites, and the number of trials, and computational limitations, such as the complexity of the decoding classifier and the number of classifier training examples. In this work, we perform a direct comparison that corrects for these experimental limitations and computational considerations. As part of our methodology, we propose an extension of “kernel analysis” that measures the generalization accuracy as a function of representational complexity. Our evaluations show that, unlike previous bio-inspired models, the latest DNNs rival the representational performance of IT cortex on this visual object recognition task. Furthermore, we show that models that perform well on measures of representational performance also perform well on measures of representational similarity to IT, and on measures of predicting individual IT multi-unit responses. Whether these DNNs rely on computational mechanisms similar to the primate visual system is yet to be determined, but, unlike all previous bio-inspired models, that possibility cannot be ruled out merely on representational performance grounds.     

Neural economics and the biological substrates of valuation

A recent flurry of neuroimaging and decision-making experiments in humans, when combined with single-unit data from orbitofrontal cortex, suggests major additions to current models of reward processing. We review these data and models and use them to develop a specific computational relationship between the value of a predictor and the future rewards or punishments that it promises. The resulting computational model, the predictor-valuation model (PVM), is shown to anticipate a class of single-unit neural responses in orbitofrontal and striatal neurons. The model also suggests how neural responses in the orbitofrontal-striatal circuit may support the conversion of disparate types of future rewards into a kind of internal currency, that is, a common scale used to compare the valuation of future behavioral acts or stimuli.     

MetaReg: a platform for modeling, analysis and visualization of biological systems using large-scale experimental data

MetaReg http://acgt.cs.tau.ac.il/metareg/application.html is a computational tool that models cellular networks and integrates experimental results with such models. MetaReg represents established knowledge about a biological system, available today mostly in informal form in the literature, as probabilistic network models with underlying combinatorial regulatory logic. MetaReg enables contrasting predictions with measurements, model improvements and studying what-if scenarios. By summarizing prior knowledge and providing visual and computational aids, it helps the expert explore and understand her system better.     

Mathematical analysis and modeling of motion direction selectivity in the retina

Motion detection is one of the most important and primitive computations performed by our visual system. Specifically in the retina, ganglion cells producing motion direction-selective responses have been addressed by different disciplines, such as mathematics, neurophysiology and computational modeling, since the beginnings of vision science. Although a number of studies have analyzed theoretical and mathematical considerations for such responses, a clear picture of the underlying cellular mechanisms is only recently emerging. In general, motion direction selectivity is based on a non-linear asymmetric computation inside a receptive field differentiating cell responses between preferred and null direction stimuli. To what extent can biological findings match these considerations? In this review, we outline theoretical and mathematical studies of motion direction selectivity, aiming to map the properties of the models onto the neural circuitry and synaptic connectivity found in the retina. Additionally, we review several compartmental models that have tried to fill this gap. Finally, we discuss the remaining challenges that computational models will have to tackle in order to fully understand the retinal motion direction-selective circuitry.