10 problems

Consider the unconstrained optimal output sequence $Y^\infty$ arising in the recurrent neural network training problem, and suppose that $Y^\infty$ is non-unique. Let $\mathcal{T}$…

The paper considers recurrent neural network training with truncated backpropagation through time (TBPTT), together with optimal output sequences that may satisfy a geometric relat…

Let an LSTM-based state-reconstruction model have a latent state dimension given by the number of nodes in its hidden layer, and let the underlying data possess a structural or low…

Let $x_t$ be the high-dimensional state and let $y_t=C_t x_t$ be the sensor measurement, where $C_t$ is a time-dependent measurement matrix. Consider an LSTM in a SHRED model train…

The recurrent-architecture difficulty conjecture. LSTM-based, or even RNN-based, architectures might be difficult for the proposed dropout score mechanism.

Annular gradient-eigenspectrum conjecture. The particular annular distribution of eigenvalues of the roaRNN gradient helps the learning dynamics to reach a desired eigenspectrum co…

Annular Jacobian distribution conjecture. The characteristic annular distribution of the eigenvalues of the Jacobians may play a key role.

Consider tensorized recurrent neural-network architectures for forecasting chaotic time series, with tensor complexity measured by the entanglement entropy (EE), and compare matrix…

Chaoticity-preservation conjecture. The system's chaoticity should be maintained especially well in larger RNNs even after innate training, as indicated by persistently positive ML…

Long Short-Term Memory (LSTM) architectures are a variety of recurrent neural networks (RNNs). A probabilistic deterministic finite automaton (PDFA) is a finite-state automaton wit…