A biological circuit is a neural or biochemical cascade, taking inputs and producing outputs. How have biological circuits learned to solve environmental challenges over the history of life? The answer certainly follows Dobzhansky's famous quote that ``nothing in biology makes sense except in the light of evolution.'' But that quote leaves out the mechanistic basis by which natural selection's trial-and-error learning happens, which is exactly what we have to understand. How does the learning process that designs biological circuits actually work? How much insight can we gain about the form and function of biological circuits by studying the processes that have made those circuits? Because life's circuits must often solve the same problems as those faced by machine learning, such as environmental tracking, homeostatic control, dimensional reduction, or classification, we can begin by considering how machine learning designs computational circuits to solve problems. We can then ask: How much insight do those computational circuits provide about the design of biological circuits? How much does biology differ from computers in the particular circuit designs that it uses to solve problems? This article steps through two classic machine learning models to set the foundation for analyzing broad questions about the design of biological circuits. One insight is the surprising power of randomly connected networks. Another is the central role of internal models of the environment embedded within biological circuits, illustrated by a model of dimensional reduction and trend prediction. Overall, many challenges in biology have machine learning analogs, suggesting hypotheses about how biology's circuits are designed.

Power systems dominated by renewable energy encounter frequently large, random disturbances, and a critical challenge faced in power-system management is how to anticipate accurately whether the perturbed systems will return to the functional state after the transient or collapse. Whereas model-based studies show that the key to addressing the challenge lies in the attracting basins of the functional and dysfunctional states in the phase space, the finding of the attracting basins for realistic power systems remains a challenge, as accurate models describing the system dynamics are generally unavailable. Here we propose a new machine learning technique, namely balanced reservoir computing, to infer the attracting basins of a typical power system based on measured data. Specifically, trained by the time series of a handful of perturbation events, we demonstrate that the trained machine can predict accurately whether the system will return to the functional state in response to a large, random perturbation, thereby reconstructing the attracting basin of the functional state. The working mechanism of the new machine is analyzed, and it is revealed that the success of the new machine is attributed to the good balance between the echo and fading properties of the reservoir network; the effect of noisy signals on the prediction performance is also investigated, and a stochastic-resonance-like phenomenon is observed. Finally, we demonstrate that the new technique can be also utilized to infer the attracting basins of coexisting attractors in typical chaotic systems.

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the mechanism triggering such effective applications of RC is still unclear, awaiting deep and systematic exploration. Here, combining the delayed embedding theory with the generalized embedding theory, we rigorously prove that RC is essentially a high dimensional embedding of the original input nonlinear dynamical system. Thus, using this embedding property, we unify into a universal framework the standard RC and the time-delayed RC where we novelly introduce time delays only into the network's output layer, and we further find a trade-off relation between the time delays and the number of neurons in RC. Based on this finding, we significantly reduce the network size of RC for reconstructing and predicting some representative physical systems, and, more surprisingly, only using a single neuron reservoir with time delays is sometimes sufficient for achieving those tasks.

Artificial neural networks have successfully tackled a large variety of problems by training extremely deep networks via back-propagation. A direct application of back-propagation to spiking neural networks contains biologically implausible components, like the weight transport problem or separate inference and learning phases. Various methods address different components individually, but a complete solution remains intangible. Here, we take an alternate approach that avoids back-propagation and its associated issues entirely. Recent work in deep learning proposed independently training each layer of a network via the information bottleneck (IB). Subsequent studies noted that this layer-wise approach circumvents error propagation across layers, leading to a biologically plausible paradigm. Unfortunately, the IB is computed using a batch of samples. The prior work addresses this with a weight update that only uses two samples (the current and previous sample). Our work takes a different approach by decomposing the weight update into a local and global component. The local component is Hebbian and only depends on the current sample. The global component computes a layer-wise modulatory signal that depends on a batch of samples. We show that this modulatory signal can be learned by an auxiliary circuit with working memory (WM) like a reservoir. Thus, we can use batch sizes greater than two, and the batch size determines the required capacity of the WM. To the best of our knowledge, our rule is the first biologically plausible mechanism to directly couple synaptic updates with a WM of the task. We evaluate our rule on synthetic datasets and image classification datasets like MNIST, and we explore the effect of the WM capacity on learning performance. We hope our work is a first-step towards understanding the mechanistic role of memory in learning.

To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system will be in a transient state preceding its collapse. We develop a model free, machine learning based solution to both problems by exploiting reservoir computing to incorporate a parameter input channel. We demonstrate that, when the machine is trained in the normal functioning regime with a chaotic attractor (i.e., before the critical transition), the transition point can be predicted accurately. Remarkably, for a parameter drift through the critical point, the machine with the input parameter channel is able to predict not only that the system will be in a transient state, but also the average transient time before the final collapse.

In this article, we apply the Free-Energy Principle to the question of motor primitives learning. An echo-state network is used to generate motor trajectories. We combine this network with a perception module and a controller that can influence its dynamics. This new compound network permits the autonomous learning of a repertoire of motor trajectories. To evaluate the repertoires built with our method, we exploit them in a handwriting task where primitives are chained to produce long-range sequences.

A common difficulty in applications of machine learning is the lack of any general principle for guiding the choices of key parameters of the underlying neural network. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, we uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized. In a three-dimensional representation of the error versus time and spectral radius, the interval corresponds to the bottom region of a "valley." Such a valley arises for a variety of spatiotemporal dynamical systems described by nonlinear partial differential equations, regardless of the structure and the edge-weight distribution of the underlying reservoir network. We also find that, while the particular location and size of the valley would depend on the details of the target system to be predicted, the interval tends to be larger for undirected than for directed networks. The valley phenomenon can be beneficial to the design of optimal reservoir computing, representing a small step forward in understanding these machine-learning systems.

We review attempts that have been made towards understanding the computational properties and mechanisms of input-driven dynamical systems like RNNs, and reservoir computing networks in particular. We provide details on methods that have been developed to give quantitative answers to the questions above. Following this, we show how self-organization may be used to improve reservoirs for better performance, in some cases guided by the measures presented before. We also present a possible way to quantify task performance using an information-theoretic approach, and finally discuss promising future directions aimed at a better understanding of how these systems perform their computations and how to best guide self-organized processes for their optimization.