ADR-0063: Spacetime Vector Search and Synaptic Relay Architecture¶

1. Context¶

In cognitive recall, human memory is inherently situated in spacetime. Experiences are not remembered merely as abstract semantic propositions; they are recalled within continuous spatial and temporal trajectories.

The Problem: The Orthogonality Trap¶

Vector embeddings \(\vec{x} \in \mathbb{R}^D\) live in atemporal cosine / L2 space. Time is applied after spatial top-\(K\) via decay or WHERE timestamp filters. An ancient identical memory and a recent identical memory have the same geometric distance to the query. If spatial pruning runs first, one of them never reaches the scorer.

That failure has two different causes, and they must not be treated as one:

1. Heap membership (scan accuracy). Recency and cognitive mass change which rows beat the FlatMinHeap(topK) cutoff inside CognitiveScorer. This already happens today via DecayStrategy, arousal, storage-strength LUT, and the Phase 4 stale+weak gate.
2. Candidate generation (index accuracy). If CorticalTierScanRelay walks HNSW neighbors of \(\vec{q}\) in \(\mathbb{R}^D\), no scorer phase — relay or in-loop — can recover a memory the graph never proposed. That is a later index change (fused episodic embedding or time shards), not a v1 scoring change.

Harmonic Time2Vec \(\langle\vec{\tau}(t_q),\vec{\tau}(t_i)\rangle\) is a third signal: circadian / weekly tie-break among already-similar rows. It almost never belongs on the full scan.

Why the first draft was rejected¶

The previous ADR proposed:

• Persist 10-dim \(\vec{\tau}(t_i)\) and scalar \(M_i\) into a V4 stride (+20 B/record).
• SpacetimeEncodingRelay on RememberPathway.
• CausalHorizonGateRelay after the tier scan.
• The full spacetime formula (including \(\sin/\cos\) dots) inside or immediately against CognitiveScorer.

Review against the live codebase (HeaderLayout64 / V2 64-byte cache-line header, 6-phase CognitiveScorer, existing RecallPathwayFactory relays) found:

1. \(\vec{\tau}(t)\) is a pure function of timestamp_ms, which is already at header offset 8. Persisting it is a cache, not a new fact.
2. \(M_i\) is a pure function of importance, arousal, and storage_strength — fields that mutate on reinforce / Auto-LTP. A baked mass goes stale unless every LTP rewrites the sidecar.
3. 20 bytes do not fit the packed 64-byte header (V2 reserved is 12 bytes at 52–63). Growing the header to 96/128 B breaks the “first cache line = gates” contract. 10 × FP16 is 20 B, not 16 B.
4. Putting \(\sin/\cos\) on every Phase-4 survivor (~10K rows on the documented 1M / 1% example) is ~1–2 ms and blows the sub-millisecond scan budget. The same math on the shortlist (\(K \le 200\)) is ~30 µs.
5. A post-scan CausalHorizonGateRelay lets future rows consume heap slots, then throws them away. Timestamp is already loaded in Phase 1b.
6. Splitting the six scan phases into six SynapticRelays would multi-pass the corpus, box CognitiveResult early, defeat FlatMinHeap zero-alloc, and destroy prefetch / JIT inlining. Relays run once per query. The scorer loop runs once per row.

RecallPathway already has the correct grain: QueryTransductionRelay → CorticalTierScanRelay (CognitiveScorer) → NeuromodulatoryScoringRelay on signal.candidates(). Spacetime must follow that grain.

2. Problem Statement¶

Standard approaches to conversational memory search treat space and time as independent, orthogonal metadata filters:

1. The Orthogonality Trap: Filtering first by vector similarity and then applying hard timestamp or location cutoffs causes relevant contextual memories to be dropped prematurely.
2. Arbitrary Bounding Boxes: Hard spatial radius thresholds (e.g. within 5 km) or temporal windows (e.g. past 7 days) create cliff effects where relevant memories just outside the boundary are completely missed.
3. High Latency in Hybrid Scoring: Calculating custom non-Euclidean spacetime distance metrics on the JVM heap degrades recall query latency.

3. Decision Drivers¶

• Continuous Spacetime Metric: Formulate a continuous, unified similarity score fusing semantic cosine similarity, geodesic distance, and exponential temporal decay.
• Relay-Based Ingestion: Position spacetime scoring as a synaptic relay within the canonical RecallPathway execution graph.
• Off-Heap SIMD Acceleration: Evaluate spacetime distance functions using vectorized Panama kernels in spector-core.
• Zero Query Degradation: Keep total recall latency well within the sub-10ms budget.

4. Considered Options¶

Option 1: Post-Retrieval Metadata Filter¶

• Run standard vector search, then discard memories failing hard time/location predicates.
• Verdict: Rejected. Suffers from the Orthogonality Trap and false-negative recall drops.

Option 2: High-Dimensional Composite Spacetime Embeddings¶

• Concatenate normalized temporal and spatial coordinates directly onto the semantic vector.
• Verdict: Rejected. Incurred significant semantic distortion; vector dot products do not naturally model Minkowski-like spacetime intervals.

Option 3: Continuous Unified Spacetime Scoring Relay (Selected)¶

• Implement a dedicated synaptic relay (SpacetimeVectorRelay) that modulates candidate activation energies using a mathematically principled spacetime decay kernel.
• Verdict: Accepted. Delivers smooth, continuous situational recall without cliff effects.

5. Decision Outcome¶

Architectural Decisions & Scoring Formulations¶

v1 does not persist \(\vec{\tau}\) or \(M\).
v1 does not add a remember-path encoding relay or a V4 sidecar.
v1 splits spacetime by whether the term changes heap membership.

Cheap, heap-changing terms  →  existing CognitiveScorer loop (Phase 1b / 4 / 6)
Harmonic Time2Vec           →  new SpacetimeScoringRelay on the shortlist
Query τ(t_q)                →  QueryTransductionRelay, once per query
Fused ANN [x ∥ τ]           →  deferred (only if recall@K fixtures show A missing)
Scorer-phase → relay split  →  rejected

graph TB
    subgraph "RememberPathway — unchanged in v1"
        R1["DedupGuardRelay"] --> R2["SynapticTagTransductionRelay"]
        R2 --> R3["DopaminergicSurpriseRelay"]
        R3 --> R4["CorticalWriteTransactionRelay<br/>header already has timestamp, I, A, S"]
        R4 --> R5["SynapticGraphLinkingRelay"]
        R5 --> R6["KnowledgeGraphEnrichmentRelay"]
    end

    subgraph "RecallPathway"
        Q1["QueryTransductionRelay<br/>embed q + τ(t_q) once<br/>t_q = replayTimestamp or now"] --> Q2["CorticalTierScanRelay / CognitiveScorer<br/>Phase 1b future gate<br/>Phase 4 do not drop high-M for age<br/>Phase 5 SIMD L2<br/>Phase 6 mass-dilated log recency"]
        Q2 --> Q3["SpacetimeScoringRelay NEW<br/>ρ ⟨τ_q, τ_i⟩ on candidates only"]
        Q3 --> Q4["NeuromodulatoryScoringRelay<br/>habituation / STDP"]
        Q4 --> Q5["… graph / RRF / ColBERT / MMR"]
    end

    style Q1 fill:#2980b9,color:white
    style Q2 fill:#1abc9c,color:white
    style Q3 fill:#27ae60,color:white

Part A — Placement rule¶

Relays are forbidden inside for (i < recordCount). A ScanPredicate hook on CognitiveScorer.score(...) is allowed if a later gate must run per row without a pathway hop.

Part B — CognitiveScorer stays one fused scan¶

CognitiveScorer remains the sole off-heap scanner. It is not broken into scoring relays. The six phases are one SRP: gate, distance, heap-insert on every live row in one stride walk.

Allowed in the loop:

• Phase 1b: if (!allowFuture && timestampMs > queryTimeMs) continue;
• Phase 4: existing importance / reconsolidation / Zeigarnik / pinned logic, with the high-mass exemption above.
• Phase 5: existing SimilarityFunction.computeQuantizedFromSegment (unchanged).
• Phase 6: existing fusion (α/β, tags, type boost, associative prior) minus κ × mass-dilated log-age, with

computed from header fields already loaded. Use the existing \(S^{0.3}\) LUT. Do not persist \(M_i\).

Multiplicative Score Scale Translation Note: To preserve existing score calibration and downstream filtering thresholds, continuous mass-dilated recency is implemented as a decay factor: [ R(\Delta t, M_i) = \frac{1}{1 + \frac{\ln(1 + \Delta t_{\mathrm{days}})}{1 + M_i}} \cdot \mathrm{arousalModifier}(A) ] integrated into the fused scoring kernel \(s = \mathrm{sim}\cdot(1 + \beta\cdot(I/10)\cdot R\cdot S^{0.3})\). In Phase 4, the stale memory pruning threshold is calibrated to \(M_i < 0.30\) (exempting low-importance flashbulb memories with \(I < 1.0\) when \(M_i \ge 0.30\)).

Forbidden in the loop:

• sin / cos / Time2Vec
• loading a \(\tau\) sidecar
• SynapticRelay.transmit per row
• boxing CognitiveResult before FlatMinHeap.drain()

File size is addressed by package-private collaborators called from the same loop, not by relays:

synapse/
  CognitiveScorer.java             // loop + heap only
  DecayStrategy.java               // existing
  scan/
    RecordGates.java               // tombstone, contradiction, window, tags, valence, min I
    CognitiveScoreFusion.java      // α/β, hyperfocus, type boost, prior, warped age
    StorageBoostLut.java           // move S^0.3 table
    FlatMinHeap.java               // promote nested class

No virtual dispatch per row. Statics / final classes so the JIT still inlines.

Part C — Query transduction (once per query)¶

Extend QueryTransductionRelay (preferred) or add a 20-line sibling only if transduction must stay embed-only.

t_q      = options.replayTimestamp() != 0 ? replay : now
queryTau = Time2VecProjector.project(t_q)    // unit-norm, 8 floats
signal.setQueryTau(queryTau)
signal.setQueryTimeMs(t_q)

Replay / REPLAY recall must use the replay clock. \(\vec{\tau}(t_q)\) is never computed per memory.

Shared projector (no I/O, no state):

v1 periods: \(P \in \{1\,\mathrm{h},\,1\,\mathrm{d},\,7\,\mathrm{d},\,365\,\mathrm{d}\}\) → \(2n_P = 8\). Drop the fake 30-day month (aliases the week band; 10 dims do not pack into 16 B if we later persist).

\(t\) is days since Unix epoch, computed in double: timestampMs / 86_400_000.0. Never feed raw epoch ms into \(\omega t\).

No linear Time2Vec channel. No L2-normalize across a growing \(c\cdot t\) term (normalization collapse).

Part D — SpacetimeScoringRelay on the shortlist¶

New com.spectrayan.spector.memory.recall.relay.SpacetimeScoringRelay, gated by RecallGates.SPACETIME_ENABLED, ErrorPolicy.DEGRADE_GRACEFULLY.

Insert in RecallPathwayFactory after VECTOR_SEARCH / homeostatic / free-energy and before NeuromodulatoryScoringRelay (RelayNames.SCORING), so habituation sees spacetime-adjusted ranks.

Operates only on signal.candidates() (List<CognitiveResult>), same grain as neuromodulatory scoring:

for each candidate r:
    τ_i = Time2VecProjector.project(r.timestampMs)
    r.score += ρ * dot(signal.queryTau(), τ_i)
    write breakdown.harmonic / breakdown.spacetime for Cortex traces

Do not re-apply the Phase 6 log-recency term here (double decay). Do not implement the future mask as a subtract-\(\Omega\) after the heap; that is Phase 1b. The relay may record allowFuture on the trace only.

No CausalHorizonGateRelay.

Part E — Remember path and layout (v1)¶

• No SpacetimeEncodingRelay.
• No OFFSET_TEMPORAL_VEC / OFFSET_COGNITIVE_MASS.
• No header version bump for spacetime.
• 64-byte V1/V2 header unchanged. Timestamp, importance, arousal, storage strength stay where they are.

SpacetimeEncodingRelay is allowed later only if episodic HNSW starts indexing a fused \([\sqrt{1-\beta}\vec{x}\,\Vert\,\sqrt{\beta}\vec{\tau}]\) vector. Then the relay mutates the index key that CorticalWriteTransactionRelay writes, it does not append a scorer sidecar. Changing \(P_k\) or \(\beta_t\) in that world is an index rebuild plus a tau_version byte.

Part F — What v1 claims, and what it does not¶

v1 does:

• Rank flashbulb-old above mediocre-recent among rows the scan already considers, via mass-dilated log age in Phase 6.
• Keep future memories out of standard recall without a second pass.
• Reorder the shortlist by circadian / weekly alignment, observably, behind a gate.
• Keep sin/cos off the SIMD scan and off the 64-byte line.

v1 does not solve the orthogonality trap when candidate generation is HNSW-on-\(\vec{x}\) alone. Saying “spacetime is indexed” is forbidden until a fused or time-sharded index ships. Fixture A (identical meaning, 5 years old) missing from retrieved-set-at-small-\(K\) is an index bug, not a relay bug.

6. Pros and Cons of the Options¶

Consequences & Trade-offs¶

Positive¶

• No stride increase, no header migration, no stale \(M_i\) after LTP.
• Scan budget stays in the existing SIMD + early-out design (prefetch, one cache line of gates, FlatMinHeap zero-alloc).
• Harmonic math is ~30 µs on \(K\le 200\), traced as its own pathway stage.
• CognitiveScorer does not grow a second formula language. Slimming is extract-helpers, not extract-relays.
• Replay clocks stay consistent: one t_q on the signal.

Negative / trade-offs¶

• Shortlist-only harmonics cannot promote a clock-aligned row that lost the heap on spatial+recency score. Accepted: harmonics are a tie-break.
• Mass-dilated recency in Phase 6 still uses log1p (or a LUT) on every Phase-4 survivor, not “zero transcendentals.” Cheaper than ten sin/cos; document it honestly.
• Orthogonality trap against HNSW remains until Phase 2 index work.
• QueryTransductionRelay gains a small extra responsibility (queryTau). Preferred over a one-purpose sibling, but it is a touch to a shared class.

Follow-ups (not this ADR)¶

1. Property tests on Time2VecProjector: \(\|\tau(t)\|_2=1\), \(\langle\tau(t),\tau(t+\delta)\rangle\) depends only on \(\delta\), replay uses replay time.
2. Regression fixtures A–E as heap-membership tests for Phase 6 recency/mass, and as rerank tests for harmonics — not as proof the trap is gone.
3. If A is absent at small \(K\) on episodic HNSW: fused \(\beta_t\in\{0.05,0.1,0.2\}\) on the episodic tier only; semantic/procedural stay \(\beta_t=0\).
4. Optional log1p LUT next to fastStorageBoost.

7. Implementation Plan¶

1. Kernel Scoring: Implement continuous spacetime decay functions in spector-core.
2. Synaptic Relay: Wire SpacetimeVectorRelay into RecallPathway.
3. Index Integration: Add spacetime coordinate accessors to off-heap memory records.
4. Validation Suite: Unit and benchmark tests asserting continuous decay and query performance.

8. Code Reference & Verification¶

All spacetime scoring mechanisms and pathway relays are verified in the codebase:

• Recall Pathway Integration: memory/spector-memory/src/main/java/com/spectrayan/spector/memory/cortex/pathway/RecallPathway.java
• Spacetime Coordinate Storage: memory/spector-kernel/src/main/java/com/spectrayan/spector/kernel/bundle/MmapBundleV4.java