A substrate-independent framework to characterize reservoir computers

On complexity of colloid cellular automata

The colloid cellular automata do not imitate the physical structure of colloids but are governed by logical functions derived from them. We analyze the space-time complexity of Boolean circuits derived from the electrical responses of colloids-specifically ZnO (zinc oxide, an inorganic compound also known as calamine or zinc white, which naturally occurs as the mineral zincite), proteinoids (microspheres and crystals of thermal abiotic proteins), and their combinations in response to electrical stimulation. To extract Boolean circuits from colloids, we send all possible configurations of two-, four-, and eight-bit binary strings, encoded as electrical potential values, to the colloids, record their responses, and infer the Boolean functions they implement. We map the discovered functions onto the cell-state transition rules of cellular automata-arrays of binary state machines that update their states synchronously according to the same rule-creating the colloid cellular automata. We then analyze the phenomenology of the space-time configurations of the automata and evaluate their complexity using measures such as compressibility, Shannon entropy, Simpson diversity, and expressivity. A hierarchy of phenomenological and measurable space-time complexity is constructed.

Logical circuits in colloids

Colloid-based computing devices offer remarkable fault tolerance and adaptability to varying environmental conditions due to their amorphous structure. An intriguing observation is that a colloidal suspension of ZnO nanoparticles in dimethylsulfoxide (DMSO) exhibits reconfiguration when exposed to electrical stimulation and produces spikes of electrical potential in response. This study presents a novel laboratory prototype of a ZnO colloidal computer, showcasing its capability to implement various Boolean functions featuring two, four and eight inputs. During our experiments, we input binary strings into the colloid mixture, where a logical 'True' state is represented by an impulse of an electrical potential. In contrast, the absence of the electrical impulse denotes a logical 'False' state. The electrical responses of the colloid mixture are recorded, allowing us to extract truth tables from the recordings. Through this methodological approach, we demonstrate the successful implementation of a wide range of logical functions using colloidal mixtures. We provide detailed distributions of the logical functions discovered and offer speculation on the potential impacts of our findings on future and emerging unconventional computing technologies. This research highlights the exciting possibilities of colloid-based computing and paves the way for further advancements.

Magnetization Vector Rotation Reservoir Computing Operated by Redox Mechanism

Physical reservoir computing is a promising way to develop efficient artificial intelligence using physical devices exhibiting nonlinear dynamics. Although magnetic materials have advantages in miniaturization, the need for a magnetic field and large electric current results in high electric power consumption and a complex device structure. To resolve these issues, we propose a redox-based physical reservoir utilizing the planar Hall effect and anisotropic magnetoresistance, which are phenomena described by different nonlinear functions of the magnetization vector that do not need a magnetic field to be applied. The expressive power of this reservoir based on a compact all-solid-state redox transistor is higher than the previous physical reservoir. The normalized mean square error of the reservoir on a second-order nonlinear equation task was 1.69 × 10-3, which is lower than that of a memristor array (3.13 × 10-3) even though the number of reservoir nodes was fewer than half that of the memristor array.

Dopant network processing units as tuneable extreme learning machines

Inspired by the highly efficient information processing of the brain, which is based on the chemistry and physics of biological tissue, any material system and its physical properties could in principle be exploited for computation. However, it is not always obvious how to use a material system’s computational potential to the fullest. Here, we operate a dopant network processing unit (DNPU) as a tuneable extreme learning machine (ELM) and combine the principles of artificial evolution and ELM to optimise its computational performance on a non-linear classification benchmark task. We find that, for this task, there is an optimal, hybrid operation mode (“tuneable ELM mode”) in between the traditional ELM computing regime with a fixed DNPU and linearly weighted outputs (“fixed-ELM mode”) and the regime where the outputs of the non-linear system are directly tuned to generate the desired output (“direct-output mode”). We show that the tuneable ELM mode reduces the number of parameters needed to perform a formant-based vowel recognition benchmark task. Our results emphasise the power of analog in-matter computing and underline the importance of designing specialised material systems to optimally utilise their physical properties for computation.

Mining logical circuits in fungi

Living substrates are capable for nontrivial mappings of electrical signals due to the substrate nonlinear electrical characteristics. This property can be used to realise Boolean functions. Input logical values are represented by amplitude or frequency of electrical stimuli. Output logical values are decoded from electrical responses of living substrates. We demonstrate how logical circuits can be implemented in mycelium bound composites. The mycelium bound composites (fungal materials) are getting growing recognition as building, packaging, decoration and clothing materials. Presently the fungal materials are passive. To make the fungal materials adaptive, i.e. sensing and computing, we should embed logical circuits into them. We demonstrate experimental laboratory prototypes of many-input Boolean functions implemented in fungal materials from oyster fungi P. ostreatus. We characterise complexity of the functions discovered via complexity of the space-time configurations of one-dimensional cellular automata governed by the functions. We show that the mycelium bound composites can implement representative functions from all classes of cellular automata complexity including the computationally universal. The results presented will make an impact in the field of unconventional computing, experimental demonstration of purposeful computing with fungi, and in the field of intelligent materials, as the prototypes of computing mycelium bound composites.

Detecting Gait Events from Accelerations Using Reservoir Computing

Segmenting the gait cycle into multiple phases using gait event detection (GED) is a well-researched subject with many accurate algorithms. However, the algorithms that are able to perform accurate and robust GED for real-life environments and physical diseases tend to be too complex for their implementation on simple hardware systems limited in computing power and memory, such as those used in wearable devices. This study focuses on a numerical implementation of a reservoir computing (RC) algorithm called the echo state network (ESN) that is based on simple computational steps that are easy to implement on portable hardware systems for real-time detection. RC is a neural network method that is widely used for signal processing applications and uses a fast-training method based on a ridge regression adapted to the large quantity and variety of IMU data needed to use RC in various real-life environment GED. In this study, an ESN was used to perform offline GED with gait data from IMU and ground force sensors retrieved from three databases for a total of 28 healthy adults and 15 walking conditions. Our main finding is that despite its low complexity, ESN is robust for GED, with performance comparable to other state-of-the-art algorithms. Our results show the ESN is robust enough to obtain good detection results in all conditions if the algorithm is trained with variable data that match those conditions. The distribution of the mean absolute errors (MAE) between the detection times from the ESN and the force sensors were between 40 and 120 ms for 6 defined gait events (95th percentile). We compared our ESN with four different state-of-the-art algorithms from the literature. The ESN obtained a MAE not more than 10 ms above three other reference algorithms for normal walking indoor and outdoor conditions and yielded the 2nd lowest MAE and the 2nd highest true positive rate and specificity when applied to outdoor walking and running conditions. Our work opens the door to using the ESN as a GED for applications in wearable sensors for long-term patient monitoring.

Quantifying the computational capability of a nanomagnetic reservoir computing platform with emergent magnetisation dynamics

Devices based on arrays of interconnected magnetic nano-rings with emergent magnetization dynamics have recently been proposed for use in reservoir computing applications, but for them to be computationally useful it must be possible to optimise their dynamical responses. Here, we use a phenomenological model to demonstrate that such reservoirs can be optimised for classification tasks by tuning hyperparameters that control the scaling and input-rate of data into the system using rotating magnetic fields. We use task-independent metrics to assess the rings' computational capabilities at each set of these hyperparameters and show how these metrics correlate directly to performance in spoken and written digit recognition tasks. We then show that these metrics, and performance in tasks, can be further improved by expanding the reservoir's output to include multiple, concurrent measures of the ring arrays' magnetic states.

Information Processing Capacity of a Single-Node Reservoir Computer: An Experimental Evaluation

Physical dynamical systems are able to process information in a nontrivial manner. The machine learning paradigm of reservoir computing (RC) provides a suitable framework for information processing in (analog) dynamical systems. The potential of dynamical systems for RC can be quantitatively characterized by the information processing capacity (IPC) measure. Here, we evaluate the IPC measure of a reservoir computer based on a single-analog nonlinear node coupled with delay. We link the extracted IPC measures to the dynamical regime of the reservoir, reporting an experimentally measured nonlinear memory of up to seventh order. In addition, we find a nonhomogeneous distribution of the linear and nonlinear contributions to the IPC as a function of the system operating conditions. Finally, we unveil the role of noise in the IPC of the analog implementation by performing ad hoc numerical simulations. In this manner, we identify the so-called edge of stability as being the most promising operating condition of the experimental implementation for RC purposes in terms of computational power and noise robustness. Similarly, a strong input drive is shown to have beneficial properties, albeit with a reduced memory depth.

Quantum computing using continuous-time evolution

Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of speed. Other types of computation using radically different architectures, including neuromorphic and quantum, promise breakthroughs in both speed and efficiency. Quantum computing exploits the coherence and superposition properties of quantum systems to explore many possible computational paths in parallel. This provides a fundamentally more efficient route to solving some types of computational problems, including several of relevance to biological simulations. In particular, optimization problems, both convex and non-convex, feature in many biological models, including protein folding and molecular dynamics. Early quantum computers will be small, reminiscent of the early days of digital silicon computing. Understanding how to exploit the first generation of quantum hardware is crucial for making progress in both biological simulation and the development of the next generations of quantum computers. This review outlines the current state-of-the-art and future prospects for quantum computing, and provides some indications of how and where to apply it to speed up bottlenecks in biological simulation.