Topological spatial coding for rapid generalization in the hippocampal formation
Bibliographic record
Abstract
The brain navigates complex environments by combining entorhinal grid codes with hippocampal place codes. Although grid codes effectively represent a current environment's geometry, their capacity to generalize across topologically analogous environments with different reward and state structures remains poorly understood. We introduce topology-aware grid coding (TAG), a computational theory that leverages topological invariance to generalize to new environments with the same topological structure but with different geometry. Drawing on the Euler characteristic from algebraic topology, TAG integrates complementary neural codes built on foundational grid bases: place codes serving as 0D vertices for self-localization, boundary codes acting as 1D edges to learn policy-independent grid codes through state prediction errors, and corner codes functioning as 2D faces for identifying topologically significant states. TAG grid codes remain stable under topology-preserving deformations yet discriminate among non-isomorphic structures. TAG develops policy-independent grid codes for novel structures more rapidly and robustly than existing approaches, balancing structure and policy encoding for multi-subgoal navigation without extensive planning. Finally, we show that TAG is compatible with transformer architectures, enabling its integration into scalable neural networks. Together, the TAG theory describes the essential nature of geometric objects to explain how the entorhinal-hippocampal system maps the unique topological structure of spaces.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".