Persistent Traces Quick Reference¶

Document Suite: 1. Main Plan: PERSISTENT_TRACES_SEMANTIC_CRYSTALLIZATION.md - Implementation roadmap 2. Mathematical Foundations: PERSISTENT_TRACES_APPENDIX_MATHEMATICAL_FOUNDATIONS.md - Rigorous proofs and derivations 3. Cognitive Science: PERSISTENT_TRACES_COGNITIVE_SCIENCE.md - Theoretical implications 4. This Document: Quick reference and FAQ

Status: Research-ready
Created: December 8, 2025

🎯 TL;DR - What Are We Building?¶

In one sentence: Teaching AI to develop its own efficient internal "thought language" by remembering useful reasoning patterns and consolidating them into reusable symbolic primitives.

Why it matters: - Current LLMs recompute everything from scratch every time - They think in human language (English tokens), not in optimized internal representations - This is like forcing a mathematician to explain every step verbally instead of using symbolic notation

What we're adding: 1. Persistent Attention Traces: Remember which parts of inputs are important across many sequences 2. Semantic Crystallization: Turn frequently-used expert routing paths into reusable "concepts"

Expected result: Model develops hierarchical internal language optimized for computation, not communication.

📊 Key Metrics At A Glance¶

Metric	Baseline	With Traces	With Crystallization	Full System
Memory Overhead	0 MB	~24 MB	~5 MB	~30 MB
Training Speed	100%	95-98%	99%	94-98%
Inference Speed	100%	105-120%	115-130%	125-150%
FLOP Efficiency	Baseline	+5-10%	+15-30%	+20-40%
Long-Context Performance	Baseline	+5-15%	+3-8%	+10-20%

🧮 Core Equations¶

Attention Trace Update¶

$$ M^{(l,h)}{i,j}(t+1) = \begin{cases} \lambda \cdot M^{(l,h)}}(t) + (1-\lambda) \cdot S^{(l,h){i,j}(t) & \text{if } S > \theta \ \gamma \cdot M^{(l,h)} \end{cases} $$}(t) & \text{otherwise

Variables: - $M$: Persistent trace memory (sparse) - $S$: Salience score (attention × gradient × recurrence) - $\lambda$: Retention rate (default: 0.95) - $\gamma$: Decay rate (default: 0.98) - $\theta$: Capture threshold (default: 0.05)

Biased Attention¶

$$ A' = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}} + \alpha \cdot M\right) $$

Variables: - $\alpha$: Bias strength (default: 0.1) - $M$: Sparse trace matrix

Crystallization Score¶

$$ \text{Score}(\pi) = w_1 \log f(\pi) + w_2 U(\pi) - w_3 H(\pi) + w_4 \text{age}(\pi) $$

Variables: - $f(\pi)$: Frequency (how often path occurs) - $U(\pi)$: Utility (performance improvement) - $H(\pi)$: Entropy (routing stability) - Crystallize if Score > threshold

⚙️ Configuration Cheat Sheet¶

Minimal Config (Conservative)¶

persistent_traces:
  enabled: true
  quota_per_head: 1024
  bias_strength: 0.05
  update_interval: 200

semantic_crystallization:
  enabled: false  # Start with traces only

Recommended Config (Balanced)¶

persistent_traces:
  enabled: true
  quota_per_head: 2048
  salience_threshold: 0.05
  retention_rate: 0.95
  decay_rate: 0.98
  bias_strength: 0.1
  update_interval: 100
  warmup_steps: 1000

semantic_crystallization:
  enabled: true
  min_frequency: 100
  min_utility: 0.05
  max_entropy: 1.0
  max_motifs: 512
  prune_interval: 1000

loss_weights:
  task: 1.0
  load_balance: 0.01
  trace_utilization: 0.005
  crystallization: 0.002

Aggressive Config (Maximum Performance)¶

persistent_traces:
  enabled: true
  quota_per_head: 4096
  bias_strength: 0.2
  update_interval: 50

semantic_crystallization:
  enabled: true
  min_frequency: 50
  max_motifs: 1024
  motif_max_length: 12

🔧 Integration Checklist¶

Phase 0: Setup¶

[ ] Create src/aios/core/hrm_models/cognitive/ module
[ ] Add config schemas to config/default.yaml
[ ] Implement TraceManager and RoutingPathTree classes

Phase 1: Traces¶

[ ] Hook Attention.forward() to capture salience
[ ] Implement sparse trace storage (COO format)
[ ] Add gradient-based trace updates
[ ] Test memory footprint < 50 MB

Phase 2: Bias Injection¶

[ ] Convert traces to sparse attention bias
[ ] Add dual-mode attention (Flash / Standard)
[ ] Implement trace decay mechanism
[ ] Verify speedup on copy tasks

Phase 3: Routing Logging¶

[ ] Hook TopKRouter.forward() to log paths
[ ] Build suffix tree for path tracking
[ ] Compute utility and entropy metrics
[ ] Test tree memory < 10 MB

Phase 4: Crystallization¶

[ ] Implement motif detection algorithm
[ ] Add freezing mechanism for high-utility paths
[ ] Create distilled motif experts
[ ] Measure FLOP reduction

Phase 5: Training Integration¶

[ ] Add auxiliary losses (trace, crystallization)
[ ] Integrate EWC for stability
[ ] Tune hyperparameters
[ ] Run ablation studies

Phase 6: Evaluation¶

[ ] Benchmark on bAbI, SQuAD, HellaSwag
[ ] Measure emergent language properties
[ ] Analyze motif hierarchies
[ ] Document findings

❓ FAQ¶

Q: Will this slow down training?¶

A: Minimal impact (~5% overhead) when using Flash Attention + sparse capture scheduling. Traces update periodically, not every step.

Q: How much memory does it use?¶

A: ~30 MB total (24 MB traces + 5 MB routing tree) for a 32-layer model. Negligible compared to model weights (GBs).

Q: Does it work with gradient checkpointing?¶

A: Yes - trace updates happen in separate forward-only passes outside checkpointed regions.

Q: Can I disable it if it doesn't help?¶

A: Absolutely - setting enabled: false reverts to standard transformer with zero overhead.

Q: Will motifs be interpretable?¶

A: Partially. Some motifs will align with human concepts (e.g., "question answering"), others may be alien computational strategies we don't have names for.

Q: Does it work with distributed training?¶

A: Phase 1 focuses on single-GPU. Multi-GPU support requires trace synchronization (future work).

Q: What if crystallization causes catastrophic forgetting?¶

A: Multiple safeguards: EWC penalties, utility monitoring, adaptive unfreezing, periodic revalidation.

Q: How do I visualize motifs?¶

A: We'll provide tools for: activation heatmaps, Sankey diagrams of routing paths, t-SNE embeddings of motifs, dependency graphs.

Q: Can motifs transfer between models?¶

A: Potentially! Extract motif expert weights → initialize new model → fine-tune routing. High-level motifs should transfer better than low-level ones.

🎓 Learning Path¶

Want to understand this deeply? Read in this order:

Beginner (understand the vision)¶

Main plan Executive Summary (PERSISTENT_TRACES_SEMANTIC_CRYSTALLIZATION.md)
Cognitive Science doc Introduction (PERSISTENT_TRACES_COGNITIVE_SCIENCE.md)
This quick reference

Intermediate (understand the implementation)¶

Main plan sections II-IV (Theory, Memory, Architecture)
Integration checklist (this doc)
Configuration examples (this doc)

Advanced (understand the math)¶

Mathematical Foundations full doc (PERSISTENT_TRACES_APPENDIX_MATHEMATICAL_FOUNDATIONS.md)
Theoretical limits section
Complexity analysis

Expert (contribute to research)¶

All documents fully
Open research questions
Experimental design sections
Start implementing!

🚨 Common Pitfalls¶

Pitfall 1: Setting bias_strength too high¶

Symptom: Model ignores current input, only uses traces
Fix: Start with α = 0.05, increase gradually

Pitfall 2: Crystallizing too early¶

Symptom: Frozen motifs perform poorly, catastrophic forgetting
Fix: Increase min_frequency and min_age thresholds

Pitfall 3: Trace memory overflow¶

Symptom: OOM errors
Fix: Reduce quota_per_head or increase salience_threshold

Pitfall 4: Router collapse¶

Symptom: All tokens route through same few motifs
Fix: Increase load_balance loss weight, add diversity bonus

Pitfall 5: Ignoring Flash Attention compatibility¶

Symptom: Huge slowdown
Fix: Use dual-mode attention, capture traces only during standard attention mode

📈 Success Indicators¶

Week 1-2 (Infrastructure)¶

✅ Trace storage works, memory < 50 MB
✅ Unit tests pass
✅ No crashes during training

Week 3-4 (Trace Capture)¶

✅ Salience scores computed correctly
✅ Traces accumulate over training
✅ Memory quota enforced

Week 5-6 (Bias Injection)¶

✅ Flash Attention speedup maintained
✅ Copy task performance improves
✅ Trace stability across runs

Week 7-8 (Routing Logging)¶

✅ Suffix tree tracks all paths
✅ Utility scores correlate with loss
✅ Tree memory < 10 MB

Week 9-11 (Crystallization)¶

✅ Motifs detected and frozen
✅ FLOP reduction measured
✅ No catastrophic forgetting

Week 12-13 (Losses)¶

✅ Training stable with aux losses
✅ Combined loss converges faster
✅ Ablations validate components

Week 14-16 (Evaluation)¶

✅ Baseline comparisons complete
✅ Long-range benchmarks pass
✅ Emergent hierarchy detected

Week 17-18 (Hardening)¶

✅ Multi-GPU support working
✅ Edge cases handled
✅ Documentation complete

🎯 Decision Tree: Should I Enable This?¶

Do you have MoE layers?
├─ No → Traces only (no crystallization)
└─ Yes → Full system

Is your model < 500M params?
├─ Yes → Conservative config
└─ No → Recommended config

Training on long documents (> 2048 tokens)?
├─ Yes → Enable traces (high value for long-range dependencies)
└─ No → Traces still help, but less critical

Limited VRAM (< 12 GB)?
├─ Yes → Reduce quotas (quota_per_head: 1024)
└─ No → Use recommended config

Research project or production?
├─ Research → Aggressive config, extensive logging
└─ Production → Conservative config, monitor stability

📞 Getting Help¶

Implementation questions: See main plan section "Architecture Integration"
Math questions: See mathematical foundations appendix
Conceptual questions: See cognitive science document
Bugs/issues: Check common pitfalls above

Open research questions: Documented in all three main files - pick one and start investigating!

Must read before implementing: - Transformer-XL (Dai et al. 2019) - Segment recurrence - Memorizing Transformer (Wu et al. 2022) - kNN memory - Switch Transformers (Fedus et al. 2021) - MoE at scale

Inspirational (different approaches): - RETRO (Borgeaud et al. 2022) - Retrieval-augmented - Compressive Transformer (Rae et al. 2019) - Multi-resolution memory - RMT (Bulatov et al. 2023) - Recurrent memory

Theoretical background: - EWC (Kirkpatrick et al. 2017) - Continual learning - Lottery Ticket Hypothesis (Frankle & Carbin 2019) - Sparse networks - DARTS (Liu et al. 2019) - Architecture search

📝 Citation (if this becomes a paper)¶

@misc{persistent_traces_2025,
  title={Persistent Attention Traces and Semantic Crystallization: 
         Toward Emergent Internal Language in Neural Networks},
  author={AI-OS Core Team},
  year={2025},
  note={Technical specification and research plan}
}

Status: Ready for implementation
Estimated effort: 18 weeks (full roadmap)
Minimal viable: 6 weeks (traces only)
Risk level: Medium-high (pioneering research)
Potential impact: High (novel cognitive architecture)

Next action: Start Phase 0 infrastructure setup ✨