The learning capabilities of a reservoir computer (RC) can be stifled due to symmetry in its design. Including quadratic terms in the training of a RC produces a "square readout matrix" that breaks the symmetry to quell the influence of "mirror-attractors," which are inverted copies of the RC's solutions in state space. In this paper, we prove analytically that certain symmetries in the training data forbid the square readout matrix to exist. These analytical results are explored numerically from the perspective of "multifunctionality," by training the RC to specifically reconstruct a coexistence of the Lorenz attractor and its mirror-attractor. We demonstrate that the square readout matrix emerges when the position of one attractor is slightly altered, even if there are overlapping regions between the attractors or if there is a second pair of attractors. We also find that at large spectral radius values of the RC's internal connections, the square readout matrix reappears prior to the RC crossing the edge of chaos.
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Article Synopsis
- Reservoir computing (RC) is a neuromorphic approach that excels at processing spatiotemporal signals while cutting down training costs compared to traditional recurrent neural networks.
- Our research presents a dual-memory RC system that uses different types of memristors to enhance memory capabilities, achieving 16 distinct states over short-term memory and incorporating long-term memory in the readout layer.
- Testing this system on tasks like spoken digit recognition and time series prediction, we achieved 98.84% accuracy in recognizing spoken digits and a low error rate in time series forecasting, demonstrating the potential of memristor-based RC systems in handling complex temporal data.
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