Accurate path integration in continuous attractor network models of grid cells (Burak & Fiete, 2009)

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Vector-based navigation using grid-like representations in artificial agents (Banino et al., 2018)concept0.735
  Demonstrated grid cell emergence in RNNs trained on spatial navigation; related work category 4.
• The representation-based path and the behavior-based path in Llama-3.1 8B activation space trace out similar curves, demonstrating bidirectional geometry alignment.finding0.720
  Key empirical result showing that optimizing for behavioral outputs and fitting representation geometry produce the same path in activation space.
• Attractor networks in morphogenesisconcept0.715
  The idea that bioelectric circuits form dynamical attractors corresponding to stable anatomical states, analogous to Hopfield networks.
• Information paths from A to B can exceed C(m+n, n) distinct routes, where m=position displacement and n=layer displacement.finding0.715
  Quantifies extreme redundancy in transformer routing; supports claim that introspection and interference patterns are architecturally permitted.
• Navigation of problem spaces requires parts to align with system-level goals.claim0.711
  Motivation for studying self-organization: understanding dynamics that facilitate or limit alignment across multiple scales.
• Learning to encode position for transformer with continuous dynamical model (Liu et al., 2020)concept0.711
  Prior work on learned dynamic position encodings; cited alongside Wang et al. as precedent.
• Representing non-linearly separable functions requires a network with multiple layers.claim0.711
  Architectural requirement from machine learning.
• Independently trained model families converge on a common semantic manifold under self-referential processing, suggesting an attractor dynamic that transcends training variancehypothesis0.710
  Hypothesis tested in Experiment 3; independently trained GPT, Claude, Gemini architectures converge on similar descriptive vocabulary