Temporal Edge Decay

The Problem

Tool relationships change over time. A library that was the go-to choice three years ago may now be abandoned, superseded, or incompatible with modern ecosystems. Static edge weights would preserve stale relationships indefinitely, leading to outdated recommendations. ToolPilot needs a mechanism to let old relationships fade while keeping active ones strong.

The Formula

Edge weights decay exponentially over time using a standard radioactive-decay-style formula:

1// Temporal edge decay formula
2effective_weight = base_weight × e^(-λ × days_since_reinforcement)
3
4// With default parameters:
5//   λ (lambda) = 0.001  (decay constant)
6//   half-life  ≈ 693 days (~2.7 years)
7
8// Examples:
9//   After 30 days:   0.82 × e^(-0.001 × 30)   = 0.82 × 0.970 = 0.796
10//   After 365 days:  0.82 × e^(-0.001 × 365)  = 0.82 × 0.694 = 0.569
11//   After 730 days:  0.82 × e^(-0.001 × 730)  = 0.82 × 0.482 = 0.395
12//   After 1095 days: 0.82 × e^(-0.001 × 1095) = 0.82 × 0.335 = 0.275

Decay Curve

The following visualization shows how an edge with base weight 1.0 decays over time without any reinforcement events:

  Weight
  1.0 ┤ ●
      │  ╲
  0.8 ┤   ╲
      │    ╲
  0.6 ┤     ╲
      │      ╲                  ← half-life (~2.7 years)
  0.5 ┤ · · · ·╲· · · · · · · · · · · · · · · ·
      │         ╲
  0.4 ┤          ╲
      │           ╲
  0.2 ┤             ╲____
      │                   ╲________
  0.0 ┤                            ╲_______________
      └──┬────┬────┬────┬────┬────┬────┬────┬────┬─ Days
         0   365  730  1095 1460 1825 2190 2555 2920
              1yr  2yr  3yr  4yr  5yr  6yr  7yr  8yr

The curve is intentionally gentle. A ~2.7-year half-life means relationships don’t vanish overnight — they slowly lose influence unless reinforced. This balances freshness against stability.

What Triggers Reinforcement

An edge’s decay timer resets (and its weight receives a small boost) when new evidence confirms the relationship is still valid:

• report_outcome with success — An agent confirms a tool worked well in a given context. This resets last_reinforced and adds a +0.05 weight boost (capped at 1.0).
• GitHub indexer co-occurrence — The indexer detects tools appearing together in new repositories (package.json, go.mod, requirements.txt, etc.), refreshing the edge timestamp.
• Manual curation — Admin updates via the web interface can reinforce or adjust edges when automated signals miss context.

1// When report_outcome("success") is called:
2MATCH (a:Tool)-[r:RELATED_TO]->(b:Tool)
3WHERE a.name = $tool_a AND b.name = $tool_b
4SET r.last_reinforced = datetime(),
5    r.weight = min(r.weight + 0.05, 1.0),
6    r.reinforcement_count = r.reinforcement_count + 1

Why This Matters

Temporal decay creates a self-correcting system:

• Abandoned tools fade naturally — No one needs to manually flag them. Without new co-occurrence data or success reports, their edges weaken.
• Rising tools gain prominence — New tools that get used successfully accumulate strong, fresh edges that outcompete decayed ones.
• No manual curation required — The graph evolves organically based on real-world usage patterns, not editorial decisions.