Days-of-Week Cyclic Structure

Key empirical result: days-of-week appear as identical circular manifold in both Llama-3.1-8B internal activations and output token probability distributions.

Source paper

extracted_from

Steering Along Manifolds to Control Neural Networks

(2026) ·

Neighborhood — ranked by edge-count

Claims (1)

claim

Conceptual geometry is consistent across representation space and behavior space.
supports
Interpretive assertion: the same geometric structure (e.g. circular for days) appears identically in both internal activations and output probabilities.

Communities (2)

community

Manifold-aware concept steering in neural representations
members_of
Explores geometry of activation/behavior manifolds to enable selective, non-destructive concept interventions.
Neural geometry as fundamental computational substrate
members_of
Geometric structure in neural representations causally determines computation and behavior across diverse architectures, revealed through analysis of learned manifolds and cyclic concepts.

Concepts (1)

concept

Manifold Steering
supports
Central framework: steering neural networks by intervening along the curved manifold where a concept lives, rather than in straight lines through activation space.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

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

days of the weekconcept0.772
Primary case study demonstrating circular manifold structure in both behavior and representation space of Llama-3.1-8B.
Scheduleconcept0.740
Months of the year as cyclic conceptconcept0.732
Running example used throughout the paper; months cycle with period 12
Cyclic Geometryconcept0.731
One of the geometric structures used to characterize reasoning task representations in language models, used as a test case for manifold steering
Two-stage cyclic computationconcept0.721
Llama's discovered algorithm: first compute integer sum via base-10 addition, then map the sum back to cyclic concept space
language models recapitulate cyclic structure of human concepts from pretraining datahypothesis0.717
Explanation for why manifold geometry emerges: implicit structure in training data (co-occurrence patterns) shapes internal representations.
Cyclic Recurrenceframework0.714
The specific looped mechanism studied: a fixed sequence of layers repeated in a cyclic pattern
Syncopated structureconcept0.708
The irregular, off-beat placement of the four colors that generates a rich, dynamic urban fabric.