A memory RNN forms a line attractor without any bifurcation

Haputhanthri et al. train piecewise-linear RNNs (e.g. N=40) on short-term memory tasks and identify slow points (near-zero minima of the network's own speed function) emerging as a phase-space geometric-restructuring event before abrupt skill acquisition [haputhanthri-etal-2025-memory-geometry-restructuring] A concrete example shows a line attractor of slow points forming without any bifurcation, generalizing the group's earlier bifurcation-driven ghost-point mechanism rather than restating it [haputhanthri-etal-2025-memory-geometry-restructuring] A Temporal Consistency Regularizer penalizing frame-to-frame change in memory neurons causally accelerates attractor formation and shortens the learning search phase [haputhanthri-etal-2025-memory-geometry-restructuring] The regularizer enables successful training of strongly-connected recurrent regimes that otherwise fail under standard backpropagation-through-time [haputhanthri-etal-2025-memory-geometry-restructuring]