Associations

What are associations?

Associations are bidirectional weighted links between memories. When you retrieve a memory, its associated memories are also activated and returned alongside it — even if they didn’t directly match the search query.

This mirrors spreading activation in human cognition: thinking about “coffee” might activate memories about your favorite cafe, the friend you always meet there, and the book you were reading last time.

How associations form

1. Synaptic tagging (at ingestion)

When multiple memories are extracted from the same conversation, the system creates associations between pairs that have semantic overlap. This is analogous to synaptic tagging in neuroscience — memories encoded close together in time are linked.

The algorithm:

1. For each pair of memories from the same extraction batch
2. Compute cosine similarity between their embeddings
3. If similarity >= 0.4 (the ingestion association threshold), create a bidirectional link
4. Link weight = min(0.5, 0.2 + (sim - 0.4) * 0.5)

# From core.py — simplified
for i in range(len(stored)):
    for j in range(i + 1, len(stored)):
        sim = cosine_similarity(stored[i].embedding, stored[j].embedding)
        if sim >= 0.4:
            weight = min(0.5, 0.2 + (sim - 0.4) * 0.5)
            # Create bidirectional association
            stored[i].associations[stored[j].id] = Association(
                target_id=stored[j].id, weight=weight,
            )
            stored[j].associations[stored[i].id] = Association(
                target_id=stored[i].id, weight=weight,
            )

2. Co-retrieval strengthening

When two memories both appear in the same search result set, their association link is strengthened:

w(a,b) += 0.1, capped at 1.0

This is bidirectional: if A and B are co-retrieved, both the A->B and B->A links strengthen by the same amount.

Over time, frequently co-retrieved memories develop very strong links. This creates semantic clusters that activate together.

Association decay

Links that aren’t reinforced decay exponentially:

w(a,b) *= exp(-dt / 90)

Where dt is days since the last co-retrieval event. The time constant of 90 days means:

Days since co-retrieval	Weight multiplier
0	1.00
30	0.72
60	0.51
90	0.37
180	0.14
365	0.02

Links that haven’t been reinforced for ~90 days drop to about 37% of their original strength. Below the retrieval threshold (default 0.3), they stop activating during search.

How associations affect retrieval

During search, the retrieval pipeline:

1. Finds top-k direct matches via vector similarity
2. For each direct match, looks up its associations with weight >= 0.3
3. Scores each associated memory: sim * R^alpha * association_weight
4. Applies associative boost to retrieved associated memories
5. Merges direct and associative results, sorts by score

Associated memories receive the smaller associative boost (0.03 vs 0.1 for direct matches).

The Association dataclass

@dataclass
class Association:
    target_id: str              # ID of the linked memory
    weight: float = 0.3         # link strength [0, 1]
    last_co_retrieval: datetime  # when the link was last reinforced
    created_at: datetime         # when the link was first created

Configuration

config = CognitiveMemoryConfig(
    association_strengthen_amount=0.1,    # weight increase per co-retrieval
    association_retrieval_threshold=0.3,  # minimum weight to activate
    association_decay_constant_days=90.0, # exponential decay time constant
)

Cross-tier associations

Associations can point to memories in cold storage. When a cold memory is activated through an association link and meets the retrieval threshold, it’s:

1. Scored with its embedding (if available) or given a default relevance of 0.1
2. Given an associative boost
3. Migrated back to hot storage

This means “forgotten” memories can resurface through their connections to active memories — a key mechanism for multi-hop reasoning.