Organization of computation in reservoir computing

Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.

The Impact of Feature Representation on the Accuracy of Photonic Neural Networks

Photonic Neural Networks (PNNs) are gaining significant interest in the research community due to their potential for high parallelization, low latency, and energy efficiency. PNNs compute using light, which leads to several differences in implementation when compared to electronics, such as the need to represent input features in the photonic domain before feeding them into the network. In this encoding process, it is common to combine multiple features into a single input to reduce the number of inputs and associated devices, leading to smaller and more energy-efficient PNNs. Although this alters the network's handling of input data, its impact on PNNs remains understudied. This paper addresses this open question, investigating the effect of commonly used encoding strategies that combine features on the performance and learning capabilities of PNNs. Here, using the concept of feature importance, we develop a mathematical framework for analyzing feature combination. Through this framework, we demonstrate that encoding multiple features together in a single input determines their relative importance, thus limiting the network's ability to learn from the data. Given some prior knowledge of the data, however, this can also be leveraged for higher accuracy. By selecting an optimal encoding method, we achieve up to a 12.3\% improvement in accuracy of PNNs trained on the Iris dataset compared to other encoding techniques, surpassing the performance of networks where features are not combined. These findings highlight the importance of carefully choosing the encoding to the accuracy and decision-making strategies of PNNs, particularly in size or power constrained applications.

Hitless memory-reconfigurable photonic reservoir computing architecture

Reservoir computing is an analog bio-inspired computation model for efficiently processing time-dependent signals, the photonic implementations of which promise a combination of massive parallel information processing, low power consumption, and high speed operation. However, most implementations, especially for the case of time-delay reservoir computing (TDRC), require signal attenuation in the reservoir to achieve the desired system dynamics for a specific task, often resulting in large amounts of power being coupled outside of the system. We propose a novel TDRC architecture based on an asymmetric Mach-Zehnder interferometer (MZI) integrated in a resonant cavity which allows the memory capacity of the system to be tuned without the need for an optical attenuator block. Furthermore, this can be leveraged to find the optimal value for the specific components of the total memory capacity metric. We demonstrate this approach on the temporal bitwise XOR task and conclude that this way of memory capacity reconfiguration allows optimal performance to be achieved for memory-specific tasks.