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MPCS: Neuroplastic Continual Learning via Multi-Component Plasticity and Topology-Aware EWC Combining Trained Models in Reinforcement Learning Training Non-Differentiable Networks via Optimal Transport ShiftLIF: Efficient Multi-Level Spiking Neurons with Power-of-Two Quantization Probe-Geometry Alignment: Erasing the Cross-Sequence Memorization Signature Below Chance Benchmarking local Hebbian learning rules for memory storage and prototype extraction Robust volatility updates for Hierarchical Gaussian Filtering Spiking Sequence Machines and Transformers Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts Scalable Learning in Structured Recurrent Spiking Neural Networks without Backpropagation Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks Attractor FCM Physical Foundation Models: Fixed hardware implementations of large-scale neural networks When Does Structure Matter in Continual Learning? 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Analyzing Echo-state Networks Using Fractal Dimension
Norbert Michael Mayer, Oliver Obst · 2022-05-19 · via cs.NE updates on arXiv.org

This work joins aspects of reservoir optimization, information-theoretic optimal encoding, and at its center fractal analysis. We build on the observation that, due to the recursive nature of recurrent neural networks, input sequences appear as fractal patterns in their hidden state representation. These patterns have a fractal dimension that is lower than the number of units in the reservoir. We show potential usage of this fractal dimension with regard to optimization of recurrent neural network initialization. We connect the idea of `ideal' reservoirs to lossless optimal encoding using arithmetic encoders. Our investigation suggests that the fractal dimension of the mapping from input to hidden state shall be close to the number of units in the network. This connection between fractal dimension and network connectivity is an interesting new direction for recurrent neural network initialization and reservoir computing.

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