A Local Learning Rule for Independent Component Analysis

Desiderata for Normative Models of Synaptic Plasticity

Normative models of synaptic plasticity use computational rationales to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical work in this realm, but experimental confirmation remains limited. In this review, we organize work on normative plasticity models in terms of a set of desiderata that, when satisfied, are designed to ensure that a given model demonstrates a clear link between plasticity and adaptive behavior, is consistent with known biological evidence about neural plasticity and yields specific testable predictions. As a prototype, we include a detailed analysis of the REINFORCE algorithm. We also discuss how new models have begun to improve on the identified criteria and suggest avenues for further development. Overall, we provide a conceptual guide to help develop neural learning theories that are precise, powerful, and experimentally testable.

Feature alignment as a generative process

Reversibility in artificial neural networks allows us to retrieve the input given an output. We present feature alignment, a method for approximating reversibility in arbitrary neural networks. We train a network by minimizing the distance between the output of a data point and the random output with respect to a random input. We applied the technique to the MNIST, CIFAR-10, CelebA, and STL-10 image datasets. We demonstrate that this method can roughly recover images from just their latent representation without the need of a decoder. By utilizing the formulation of variational autoencoders, we demonstrate that it is possible to produce new images that are statistically comparable to the training data. Furthermore, we demonstrate that the quality of the images can be improved by coupling a generator and a discriminator together. In addition, we show how this method, with a few minor modifications, can be used to train networks locally, which has the potential to save computational memory resources.

Adaptive control of synaptic plasticity integrates micro- and macroscopic network function

Synaptic plasticity configures interactions between neurons and is therefore likely to be a primary driver of behavioral learning and development. How this microscopic-macroscopic interaction occurs is poorly understood, as researchers frequently examine models within particular ranges of abstraction and scale. Computational neuroscience and machine learning models offer theoretically powerful analyses of plasticity in neural networks, but results are often siloed and only coarsely linked to biology. In this review, we examine connections between these areas, asking how network computations change as a function of diverse features of plasticity and vice versa. We review how plasticity can be controlled at synapses by calcium dynamics and neuromodulatory signals, the manifestation of these changes in networks, and their impacts in specialized circuits. We conclude that metaplasticity-defined broadly as the adaptive control of plasticity-forges connections across scales by governing what groups of synapses can and can't learn about, when, and to what ends. The metaplasticity we discuss acts by co-opting Hebbian mechanisms, shifting network properties, and routing activity within and across brain systems. Asking how these operations can go awry should also be useful for understanding pathology, which we address in the context of autism, schizophrenia and Parkinson's disease.

Image based early detection of diabetic retinopathy: A systematic review on Artificial Intelligence (AI) based recent trends and approaches

Diabetic Retinopathy (DR) is a disease that damages the retina of the human eye due to diabetic complications, resulting in a loss of vision. Blindness may be avoided If the DR disease is detected at an early stage. Unfortunately, DR is irreversible process, however, early detection and treatment of DR can significantly reduce the risk of vision loss. The manual diagnosis done by ophthalmologists on DR retina fundus images is time consuming, and error prone process. Nowadays, machine learning and deep learning have become one of the most effective approaches, which have even surpassed the human performance as well as performance of traditional image processing-based algorithms and other computer aided diagnosis systems in the analysis and classification of medical images. This paper addressed and evaluated the various recent state-of-the-art methodologies that have been used for detection and classification of Diabetic Retinopathy disease using machine learning and deep learning approaches in the past decade. Furthermore, this study also provides the authors observation and performance evaluation of available research using several parameters, such as accuracy, disease status, and sensitivity. Finally, we conclude with limitations, remedies, and future directions in DR detection. In addition, various challenging issues that need further study are also discussed.

Data mining analyses for precision medicine in acromegaly: a proof of concept

Predicting which acromegaly patients could benefit from somatostatin receptor ligands (SRL) is a must for personalized medicine. Although many biomarkers linked to SRL response have been identified, there is no consensus criterion on how to assign this pharmacologic treatment according to biomarker levels. Our aim is to provide better predictive tools for an accurate acromegaly patient stratification regarding the ability to respond to SRL. We took advantage of a multicenter study of 71 acromegaly patients and we used advanced mathematical modelling to predict SRL response combining molecular and clinical information. Different models of patient stratification were obtained, with a much higher accuracy when the studied cohort is fragmented according to relevant clinical characteristics. Considering all the models, a patient stratification based on the extrasellar growth of the tumor, sex, age and the expression of E-cadherin, GHRL, IN1-GHRL, DRD2, SSTR5 and PEBP1 is proposed, with accuracies that stand between 71 to 95%. In conclusion, the use of data mining could be very useful for implementation of personalized medicine in acromegaly through an interdisciplinary work between computer science, mathematics, biology and medicine. This new methodology opens a door to more precise and personalized medicine for acromegaly patients.

Unsupervised learning in images and audio to produce neural receptive fields: a primer and accessible notebook

Sensory processing relies on efficient computation driven by a combination of low-level unsupervised, statistical structural learning, and high-level task-dependent learning. In the earliest stages of sensory processing, sparse and independent coding strategies are capable of modeling neural processing using the same coding strategy with only a change in the input (e.g., grayscale images, color images, and audio). We present a consolidated review of Independent Component Analysis (ICA) as an efficient neural coding scheme with the ability to model early visual and auditory neural processing. We created a self-contained, accessible Jupyter notebook using Python to demonstrate the efficient coding principle for different modalities following a consistent five-step strategy. For each modality, derived receptive field models from natural and non-natural inputs are contrasted, demonstrating how neural codes are not produced when the inputs sufficiently deviate from those animals were evolved to process. Additionally, the demonstration shows that ICA produces more neurally-appropriate receptive field models than those based on common compression strategies, such as Principal Component Analysis. The five-step strategy not only produces neural-like models but also promotes reuse of code to emphasize the input-agnostic nature where each modality can be modeled with only a change in inputs. This notebook can be used to readily observe the links between unsupervised machine learning strategies and early sensory neuroscience, improving our understanding of flexible data-driven neural development in nature and future applications.

On the Achievability of Blind Source Separation for High-Dimensional Nonlinear Source Mixtures

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world data that involve nonlinear source mixtures. This work theoretically validates that a cascade of linear PCA and ICA can solve a nonlinear BSS problem accurately-when the sensory inputs are generated from hidden sources via nonlinear mappings with sufficient dimensionality. Our proposed theorem, termed the asymptotic linearization theorem, theoretically guarantees that applying linear PCA to the inputs can reliably extract a subspace spanned by the linear projections from every hidden source as the major components-and thus projecting the inputs onto their major eigenspace can effectively recover a linear transformation of the hidden sources. Then subsequent application of linear ICA can separate all the true independent hidden sources accurately. Zero-element-wise-error nonlinear BSS is asymptotically attained when the source dimensionality is large and the input dimensionality is sufficiently larger than the source dimensionality. Our proposed theorem is validated analytically and numerically. Moreover, the same computation can be performed by using Hebbian-like plasticity rules, implying the biological plausibility of this nonlinear BSS strategy. Our results highlight the utility of linear PCA and ICA for accurately and reliably recovering nonlinearly mixed sources and suggest the importance of employing sensors with sufficient dimensionality to identify true hidden sources of real-world data.

Reverse-Engineering Neural Networks to Characterize Their Cost Functions

This letter considers a class of biologically plausible cost functions for neural networks, where the same cost function is minimized by both neural activity and plasticity. We show that such cost functions can be cast as a variational bound on model evidence under an implicit generative model. Using generative models based on partially observed Markov decision processes (POMDP), we show that neural activity and plasticity perform Bayesian inference and learning, respectively, by maximizing model evidence. Using mathematical and numerical analyses, we establish the formal equivalence between neural network cost functions and variational free energy under some prior beliefs about latent states that generate inputs. These prior beliefs are determined by particular constants (e.g., thresholds) that define the cost function. This means that the Bayes optimal encoding of latent or hidden states is achieved when the network's implicit priors match the process that generates its inputs. This equivalence is potentially important because it suggests that any hyperparameter of a neural network can itself be optimized-by minimization with respect to variational free energy. Furthermore, it enables one to characterize a neural network formally, in terms of its prior beliefs.

Learning to represent signals spike by spike

Networks based on coordinated spike coding can encode information with high efficiency in the spike trains of individual neurons. These networks exhibit single-neuron variability and tuning curves as typically observed in cortex, but paradoxically coincide with a precise, non-redundant spike-based population code. However, it has remained unclear whether the specific synaptic connectivities required in these networks can be learnt with local learning rules. Here, we show how to learn the required architecture. Using coding efficiency as an objective, we derive spike-timing-dependent learning rules for a recurrent neural network, and we provide exact solutions for the networks’ convergence to an optimal state. As a result, we deduce an entire network from its input distribution and a firing cost. After learning, basic biophysical quantities such as voltages, firing thresholds, excitation, inhibition, or spikes acquire precise functional interpretations.

Spiking neural networks can encode information with high efficiency in the spike trains of individual neurons if the synaptic weights between neurons are set to specific, optimal values. In this regime, the networks exhibit irregular spike trains, high trial-to-trial variability, and stimulus tuning, as typically observed in cortex. The strong variability on the level of single neurons paradoxically coincides with a precise, non-redundant, and spike-based population code. However, it has remained unclear whether the specific synaptic connectivities required in these spiking networks can be learnt with local learning rules. In this study, we show how the required architecture can be learnt. We derive local and biophysically plausible learning rules for recurrent neural networks from first principles. We show both mathematically and using numerical simulations that these learning rules drive the networks into the optimal state, and we show that the optimal state is governed by the statistics of the input signals. After learning, the voltages of individual neurons can be interpreted as measuring the instantaneous error of the code, given by the error between the desired output signal and the actual output signal.

On the Sparse Structure of Natural Sounds and Natural Images: Similarities, Differences, and Implications for Neural Coding

Sparse coding models of natural images and sounds have been able to predict several response properties of neurons in the visual and auditory systems. While the success of these models suggests that the structure they capture is universal across domains to some degree, it is not yet clear which aspects of this structure are universal and which vary across sensory modalities. To address this, we fit complete and highly overcomplete sparse coding models to natural images and spectrograms of speech and report on differences in the statistics learned by these models. We find several types of sparse features in natural images, which all appear in similar, approximately Laplace distributions, whereas the many types of sparse features in speech exhibit a broad range of sparse distributions, many of which are highly asymmetric. Moreover, individual sparse coding units tend to exhibit higher lifetime sparseness for overcomplete models trained on images compared to those trained on speech. Conversely, population sparseness tends to be greater for these networks trained on speech compared with sparse coding models of natural images. To illustrate the relevance of these findings to neural coding, we studied how they impact a biologically plausible sparse coding network's representations in each sensory modality. In particular, a sparse coding network with synaptically local plasticity rules learns different sparse features from speech data than are found by more conventional sparse coding algorithms, but the learned features are qualitatively the same for these models when trained on natural images.

Multi-context blind source separation by error-gated Hebbian rule

Animals need to adjust their inferences according to the context they are in. This is required for the multi-context blind source separation (BSS) task, where an agent needs to infer hidden sources from their context-dependent mixtures. The agent is expected to invert this mixing process for all contexts. Here, we show that a neural network that implements the error-gated Hebbian rule (EGHR) with sufficiently redundant sensory inputs can successfully learn this task. After training, the network can perform the multi-context BSS without further updating synapses, by retaining memories of all experienced contexts. This demonstrates an attractive use of the EGHR for dimensionality reduction by extracting low-dimensional sources across contexts. Finally, if there is a common feature shared across contexts, the EGHR can extract it and generalize the task to even inexperienced contexts. The results highlight the utility of the EGHR as a model for perceptual adaptation in animals.

Principles underlying the input-dependent formation and organization of memories

The neuronal system exhibits the remarkable ability to dynamically store and organize incoming information into a web of memory representations (items), which is essential for the generation of complex behaviors. Central to memory function is that such memory items must be (1) discriminated from each other, (2) associated to each other, or (3) brought into a sequential order. However, how these three basic mechanisms are robustly implemented in an input-dependent manner by the underlying complex neuronal and synaptic dynamics is still unknown. Here, we develop a mathematical framework, which provides a direct link between different synaptic mechanisms, determining the neuronal and synaptic dynamics of the network, to create a network that emulates the above mechanisms. Combining correlation-based synaptic plasticity and homeostatic synaptic scaling, we demonstrate that these mechanisms enable the reliable formation of sequences and associations between two memory items still missing the capability for discrimination. We show that this shortcoming can be removed by additionally considering inhibitory synaptic plasticity. Thus, the here-presented framework provides a new, functionally motivated link between different known synaptic mechanisms leading to the self-organization of fundamental memory mechanisms.

In vitro neural networks minimise variational free energy

In this work, we address the neuronal encoding problem from a Bayesian perspective. Specifically, we ask whether neuronal responses in an in vitro neuronal network are consistent with ideal Bayesian observer responses under the free energy principle. In brief, we stimulated an in vitro cortical cell culture with stimulus trains that had a known statistical structure. We then asked whether recorded neuronal responses were consistent with variational message passing based upon free energy minimisation (i.e., evidence maximisation). Effectively, this required us to solve two problems: first, we had to formulate the Bayes-optimal encoding of the causes or sources of sensory stimulation, and then show that these idealised responses could account for observed electrophysiological responses. We describe a simulation of an optimal neural network (i.e., the ideal Bayesian neural code) and then consider the mapping from idealised in silico responses to recorded in vitro responses. Our objective was to find evidence for functional specialisation and segregation in the in vitro neural network that reproduced in silico learning via free energy minimisation. Finally, we combined the in vitro and in silico results to characterise learning in terms of trajectories in a variational information plane of accuracy and complexity.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Data and Power Efficient Intelligence with Neuromorphic Learning Machines

The success of deep networks and recent industry involvement in brain-inspired computing is igniting a widespread interest in neuromorphic hardware that emulates the biological processes of the brain on an electronic substrate. This review explores interdisciplinary approaches anchored in machine learning theory that enable the applicability of neuromorphic technologies to real-world, human-centric tasks. We find that (1) recent work in binary deep networks and approximate gradient descent learning are strikingly compatible with a neuromorphic substrate; (2) where real-time adaptability and autonomy are necessary, neuromorphic technologies can achieve significant advantages over main-stream ones; and (3) challenges in memory technologies, compounded by a tradition of bottom-up approaches in the field, block the road to major breakthroughs. We suggest that a neuromorphic learning framework, tuned specifically for the spatial and temporal constraints of the neuromorphic substrate, will help guiding hardware algorithm co-design and deploying neuromorphic hardware for proactive learning of real-world data.

A Measure of Information Available for Inference

The mutual information between the state of a neural network and the state of the external world represents the amount of information stored in the neural network that is associated with the external world. In contrast, the surprise of the sensory input indicates the unpredictability of the current input. In other words, this is a measure of inference ability, and an upper bound of the surprise is known as the variational free energy. According to the free-energy principle (FEP), a neural network continuously minimizes the free energy to perceive the external world. For the survival of animals, inference ability is considered to be more important than simply memorized information. In this study, the free energy is shown to represent the gap between the amount of information stored in the neural network and that available for inference. This concept involves both the FEP and the infomax principle, and will be a useful measure for quantifying the amount of information available for inference.

Error-Gated Hebbian Rule: A Local Learning Rule for Principal and Independent Component Analysis

We developed a biologically plausible unsupervised learning algorithm, error-gated Hebbian rule (EGHR)-β, that performs principal component analysis (PCA) and independent component analysis (ICA) in a single-layer feedforward neural network. If parameter β = 1, it can extract the subspace that major principal components span similarly to Oja’s subspace rule for PCA. If β = 0, it can separate independent sources similarly to Bell-Sejnowski’s ICA rule but without requiring the same number of input and output neurons. Unlike these engineering rules, the EGHR-β can be easily implemented in a biological or neuromorphic circuit because it only uses local information available at each synapse. We analytically and numerically demonstrate the reliability of the EGHR-β in extracting and separating major sources given high-dimensional input. By adjusting β, the EGHR-β can extract sources that are missed by the conventional engineering approach that first applies PCA and then ICA. Namely, the proposed rule can successfully extract hidden natural images even in the presence of dominant or non-Gaussian noise components. The results highlight the reliability and utility of the EGHR-β for large-scale parallel computation of PCA and ICA and its future implementation in a neuromorphic hardware.

Learning with three factors: modulating Hebbian plasticity with errors

Synaptic plasticity is a central theme in neuroscience. A framework of three-factor learning rules provides a powerful abstraction, helping to navigate through the abundance of models of synaptic plasticity. It is well-known that the dopamine modulation of learning is related to reward, but theoretical models predict other functional roles of the modulatory third factor; it may encode errors for supervised learning, summary statistics of the population activity for unsupervised learning or attentional feedback. Specialized structures may be needed in order to generate and propagate third factors in the neural network.

Blind Nonnegative Source Separation Using Biological Neural Networks

Blind source separation-the extraction of independent sources from a mixture-is an important problem for both artificial and natural signal processing. Here, we address a special case of this problem when sources (but not the mixing matrix) are known to be nonnegative-for example, due to the physical nature of the sources. We search for the solution to this problem that can be implemented using biologically plausible neural networks. Specifically, we consider the online setting where the data set is streamed to a neural network. The novelty of our approach is that we formulate blind nonnegative source separation as a similarity matching problem and derive neural networks from the similarity matching objective. Importantly, synaptic weights in our networks are updated according to biologically plausible local learning rules.