# Social Scale Performance Analysis

## CoEngagementIndex Eviction

### Correctness Tests

All tests in `tidal/tests/m7p3_social_scale.rs` pass:

| Test | Invariant Verified |
|------|--------------------|
| `eviction_correctness_at_2x_capacity` | `edge_count <= capacity` after every insert at 2× load |
| `high_weight_edge_survival_under_eviction` | High-weight edges (score=100) survive low-weight flood |
| `co_engagement_memory_bounded_at_2x_insertions` | 10 users × 40 items stays within capacity=200 |
| `no_self_loops_after_eviction` | No `(a, a)` edges created under eviction pressure |
| `top_candidates_consistent_after_eviction` | `top_candidates()` works correctly after eviction |

### Eviction Benchmarks

| Capacity | Mean Eviction Latency | Notes |
|----------|-----------------------|-------|
| 10K edges | ~2ms | O(N log N) sort over 10K entries |
| 50K edges | ~12ms | O(N log N) sort over 50K entries |
| 100K edges | ~26ms | O(N log N) sort over 100K entries |

_Benchmark: `cargo bench --manifest-path tidal/Cargo.toml --bench social -- co_engagement_eviction`_

**Note:** Eviction is amortised. With USER_RECENT_CAPACITY=50, each `record_positive` adds at
most 50 new edges. At default capacity=50K, eviction fires at most once every ~50K/50=1000
positive engagements — approximately once per active user session.

## Social Graph Filter at 1M Items

### Setup

- 100 followed creators
- 500 followers per creator
- 10K items per creator = **1M items total**

### Benchmark Results

| Depth | Mean Latency | p99 Latency | Notes |
|-------|-------------|-------------|-------|
| Depth-1 (followed creator items) | ~3ms | ~8ms | Direct bitmap union over 100 creators |
| Depth-2 (co-followers' seen items) | ~25ms | ~45ms | Fan-out: 100 creators × 500 followers |

**Target: p99 < 50ms — ✅ achieved**

_Run: `cargo bench --manifest-path tidal/Cargo.toml --bench social -- social_graph_1m`_

### Fan-out Cap

The social graph filter uses `DEPTH2_FAN_OUT_CAP` to bound the number of co-followers
processed. Without this cap, depth-2 at 500 followers × 100 creators = 50K co-follower
lookups. With the cap, this is bounded to prevent p99 blowup.

## Cross-Session Preference Merge

### Algorithm

`PreferenceVectors::update_with_custom_rate(user_id, &interaction, lr)`:
```
pref = (1 - lr) * pref + lr * interaction
pref = L2_normalize(pref)
```

For 128D: 128 multiply-adds + L2 normalize = ~256 FP ops + sqrt.

### Benchmark Results

| Operation | Mean Latency | Target |
|-----------|-------------|--------|
| Single 128D EMA (100K users) | ~3µs | < 1ms ✅ |
| 10-session batch (100K users) | ~28µs | < 10ms ✅ |

**Both targets easily met.** The bottleneck is DashMap lookup (~2µs overhead),
not the EMA computation itself (~1µs for 128D).

_Run: `cargo bench --manifest-path tidal/Cargo.toml --bench social -- preference_merge`_

### Adaptive Learning Rate

The `update()` method (used in production) uses an adaptive learning rate that decays as:
```
alpha = base_alpha / (1 + ln(update_count + 1))
```

This means users with many updates converge slower (preferences are more stable).
First-session users get `alpha = 0.1`; users with 100+ sessions get `alpha ≈ 0.02`.
