Vision & Motivation

Beyond Static Vectors

Standard vector databases treat embeddings as frozen snapshots. But in every domain where embeddings matter — NLP, clinical research, political analysis, AI agents — the interesting signal is in how vectors change over time.

CVX was built around one insight: time is not a filter, it’s a dimension.

Three Motivating Problems

1. Clinical Signal in Temporal Drift

A single social media post tells you almost nothing about a user’s mental state. But the trajectory of their language over weeks — gradual vocabulary shifts, increasing negativity, changing topic patterns — reveals clinically meaningful signals.

CVX enables this by projecting user trajectories onto DSM-5 symptom anchors (depressed mood, anhedonia, worthlessness, etc.) and tracking proximity over time. On the eRisk dataset (1.36M posts, 2,285 users), anchor-projected temporal features achieve F1=0.744 — a 24% improvement over static embeddings.

2. Episodic Memory for AI Agents

Standard RAG gives LLM agents access to facts — but not to how a problem was solved before. This maps to the cognitive science distinction between semantic memory (what you know) and episodic memory (what you’ve done and how it went).

CVX provides the temporal structure that standard vector stores lack:

Episode identity: entity_id = episode_id << 16 | step_index — groups steps into episodes
Temporal ordering: Timestamps define step order within episodes
Causal continuation: “Find where someone was in my situation, show me what they did next”

Validated experimentally: an ALFWorld agent with CVX episodic memory achieves 6× improvement in task completion over zero-shot (3.3% → 20.0%).

3. Rhetorical Evolution in Political Discourse

Parliamentary speech evolves over time — influenced by elections, crises, and social movements. CVX tracks rhetorical trajectories of individual MPs and political groups, using anchor projection onto rhetorical dimensions (emotional appeals, policy topics, personal attacks).

On ParlaMint-ES (32K speeches, 841 MPs), CVX rhetorical profiling predicts speaker gender with F1=0.94 and reveals that party affiliation drives rhetorical similarity more than gender.

The Scientific Foundation

Embedding Anisotropy

Modern contextual embeddings occupy a narrow cone in high-dimensional space (Ethayarajh 2019). All vectors share a dominant “average text” direction, compressing the discriminative signal into a small residual. CVX addresses this natively via mean-centering.

Path Signatures

From rough path theory (Lyons 1998), path signatures provide universal, reparametrization-invariant descriptors of trajectories. CVX implements truncated path signatures as trajectory fingerprints — two trajectories with the same shape (regardless of speed) will have similar signatures.

Change Point Detection

PELT (Killick et al. 2012) provides exact offline change point detection in O(N). BOCPD (Adams & MacKay 2007) provides online streaming detection in O(1) amortized. CVX implements both for identifying regime transitions in embedding trajectories.

Temporal Vector Calculus

CVX computes velocity ( $\partial v / \partial t$ ), acceleration ( $\partial^2 v / \partial t^2$ ), drift magnitude, and Hurst exponents on embedding trajectories — treating vector time series as differentiable curves in high-dimensional space.

Design Principles

Principle	Description
Time as Geometry	Time is a dimension of the search space, not a filter
Vectors as Trajectories	Entities are curves in embedding space, not points
Anchors as Coordinates	Domain-specific reference vectors create interpretable projections
Episodes as Sequences	Temporal structure enables “what happened next?” queries
Analytics over Storage	The value is in the 27+ temporal operations, not just kNN