Module signatures

Path signatures for trajectory characterization.

Implements truncated path signatures from rough path theory — a universal and order-aware feature of sequential data. Any continuous function of a path can be approximated by a linear function of its signature.

Key Properties

• Universality: sufficient statistics for trajectory classification
• Reparametrization invariance: captures shape, not sampling rate
• Chen’s Identity: S(α * β) = S(α) ⊗ S(β) — incremental updates in O(K²)
• Hierarchical: depth 1 = displacement, depth 2 = signed area (correlation/volatility)

Usage with CVX

Path signatures operate on region trajectories (K~80 dims at L3), NOT on raw embeddings (D=768). The HNSW graph hierarchy provides the dimensionality reduction that makes signatures tractable:

• Region trajectory at L3: K=80 → depth 2 signature = 80 + 6400 = 6,480 features
• Raw embeddings: D=768 → depth 2 = 768 + 589,824 → intractable

References

• Lyons, T.J. (1998). Differential equations driven by rough signals.
• Chevyrev & Kormilitzin (2016). A primer on the signature method in ML.
• Kidger & Lyons (2021). Signatory: differentiable computations of the signature.

Structs

PathSignatureResult

Computed path signature result.

SignatureConfig

Configuration for signature computation.

Enums

SignatureError

Error types for signature computation.

Functions

compute_log_signature

Compute the log-signature (compact alternative via antisymmetric part).

compute_signature

Compute the truncated path signature of a trajectory.

signature_distance

Compute L2 distance between two signatures.

update_signature_incremental

Incrementally update a signature when a new point is appended.