Taiki Yamada

Taiki Yamada

We show that the error-gated Hebbian rule for PCA (EGHR-PCA), a three-factor learning rule equivalent to Oja's subspace rule under Gaussian inputs, can be systematically derived from Oja's subspace rule using frame theory. The global third factor in EGHR-PCA arises exactly as a frame coefficient when the learning rule is expanded with respect to a natural frame on the space of symmetric matrices. This provides a principled, non-heuristic derivation of a biologically plausible learning rule from its mathematically canonical counterpart.

Taiki Yamada, Yuichi Katori, Kantaro Fujiwara

Echo state networks (ESNs) are a class of recurrent neural networks in which only the readout layer is trainable, while the recurrent and input layers are fixed. This architectural constraint enables computationally efficient processing of time-series data. Traditionally, the readout layer in ESNs is trained using supervised learning with target outputs. In this study, we focus on input reconstruction (IR), where the readout layer is trained to reconstruct the input time series fed into the ESN. We show that IR can be achieved through unsupervised learning (UL), without access to supervised targets, provided that the ESN parameters are known a priori and satisfy invertibility conditions. This formulation allows applications relying on IR, such as dynamical system replication and noise filtering, to be reformulated within the UL framework via straightforward integration with existing algorithms. Our results suggest that prior knowledge of ESN parameters can reduce reliance on supervision, thereby establishing a new principle: not only by fixing part of the network parameters but also by exploiting their specific values. Furthermore, our UL-based algorithms for input reconstruction and related tasks are suitable for autonomous processing, offering insights into how analogous computational mechanisms might operate in the brain in principle. These findings contribute to a deeper understanding of the mathematical foundations of ESNs and their relevance to models in computational neuroscience.