paper/HAT_paper_complete.md

Hierarchical Attention Tree: Extending LLM Context Through Structural Memory

Authors: AI Research Lab Date: January 2026 Status: Draft v1.0

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Abstract

We present the Hierarchical Attention Tree (HAT), a novel index structure that extends the effective context of language models by an order of magnitude. A model with 10K native context achieves 100% recall on 60K+ token conversations through hierarchical attention state storage and retrieval, with 3.1ms average latency. Unlike approximate nearest neighbor algorithms that learn topology from data (e.g., HNSW), HAT exploits the known semantic hierarchy inherent in AI conversations: sessions contain documents, documents contain chunks. This structural prior enables O(log n) query complexity with zero training required.

Our experiments demonstrate:

1. 100% recall vs 70% for HNSW on hierarchically-structured data
2. 70x faster index construction than HNSW
3. Neither geometric sophistication (subspace routing) nor learned parameters improve upon simple centroid-based routing

HAT works immediately upon deployment with deterministic behavior, functioning as an artificial hippocampus for AI systems.

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1. Introduction

1.1 The Context Window Problem

Large language models have a fundamental limitation: finite context windows. A model with 10K context can only "see" the most recent 10K tokens, losing access to earlier conversation history. Current solutions include:

• Longer context models: Expensive to train and run (128K+ context)
• Summarization: Lossy compression that discards detail
• RAG retrieval: Re-embeds and recomputes attention on every query

1.2 The HAT Solution

HAT takes a different approach: exploit known structure.

Unlike general-purpose vector databases that treat all data as unstructured point clouds, AI conversation data has inherent hierarchy:

Session (conversation boundary)
  └── Document (topic or turn)
       └── Chunk (individual message)

HAT exploits this structure to achieve O(log n) queries with 100% recall, without any training or learning.

1.3 Core Claim

A 10K context model with HAT achieves 100% recall on 60K+ tokens with 3.1ms latency.

This is validated by our end-to-end experiments integrating HAT with a local LLM (gemma3:1b).

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2. Background and Motivation

2.1 HAT vs RAG: Complementary, Not Competing

Aspect	RAG + HNSW	HAT
Content type	Static knowledge (handbooks, catalogs)	Dynamic conversations
Structure	Unknown → learned topology	Known hierarchy exploited
Returns	Text chunks (must recompute attention)	Attention states (pre-computed)
Use case	"What does the handbook say about X?"	"Remember when we discussed Y?"

HAT solves a different problem: retrievable compute (attention states) vs retrievable knowledge (text).

2.2 The Hippocampus Analogy

HAT mirrors human memory architecture:

Human Memory	HAT Equivalent
Working memory (7±2 items)	Current context window
Short-term memory	Recent session containers
Long-term episodic	HAT hierarchical storage
Memory consolidation (sleep)	HAT consolidation phases
Hippocampal indexing	Centroid-based routing

This isn't just a metaphor—it's a design principle.

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3. Algorithm

3.1 Data Structure

HAT organizes points into a tree with four levels:

Global (root)
  └── Session (conversation boundaries)
       └── Document (topic groupings)
            └── Chunk (leaf nodes with points)

Each non-leaf container maintains:

• Centroid: Mean of descendant embeddings
• Children: Pointers to child containers
• Timestamp: For temporal locality

3.2 Beam Search Query

Algorithm 1: HAT Query
─────────────────────────────────────────────────
Input: query point q, number of results k
Output: k nearest neighbors

1: beam ← {root}
2: for level ∈ [Session, Document, Chunk] do
3:     candidates ← ∅
4:     for container ∈ beam do
5:         for child ∈ container.children do
6:             score ← cosine(q, child.centroid)
7:             candidates ← candidates ∪ {(child, score)}
8:     beam ← top-b(candidates)  // b = beam_width
9: return top-k(beam)

Complexity: O(b · d · c) = O(log n) when balanced

3.3 Sparse Centroid Propagation

To avoid O(depth) updates on every insertion:

Algorithm 2: Sparse Propagation
─────────────────────────────────────────────────
Input: new point p, container c, threshold τ

1: δ ← update_centroid(c, p)
2: ancestor ← c.parent
3: while ancestor ≠ null and δ > τ do
4:     δ ← update_centroid(ancestor, p)
5:     ancestor ← ancestor.parent

Amortized cost: O(1) when τ > 0

Result: 1.3-1.7x insertion speedup with negligible recall impact.

3.4 Consolidation Phases

Inspired by sleep-staged memory consolidation:

Phase	Operations	Time
Light (α)	Recompute centroids	9ms/1K points
Medium (β)	+ Merge/split containers	9ms/1K points
Deep (δ)	+ Prune empty, optimize layout	9ms/1K points
Full (θ)	Complete rebuild	10ms/1K points

All phases support non-blocking incremental execution.

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4. Experiments

4.1 HAT vs HNSW: Hierarchical Data

Setup: 1000 points = 20 sessions × 5 documents × 10 chunks, 128 dimensions

Metric	HAT	HNSW	Δ
Recall@1	100.0%	76.0%	+24.0%
Recall@5	100.0%	72.0%	+28.0%
Recall@10	100.0%	70.6%	+29.4%
Build Time	30ms	2.1s	70x faster
Query Latency	1.42ms	0.49ms	HNSW 3x faster

Key finding: The query latency advantage of HNSW is meaningless at 70% recall.

4.2 Scale Analysis

Points	HAT Build	HNSW Build	HAT R@10	HNSW R@10
500	16ms	1.0s	100%	55%
1000	25ms	2.0s	100%	44.5%
2000	50ms	4.3s	100%	67.5%
5000	127ms	11.9s	100%	55%

HAT maintains 100% recall across all tested scales.

4.3 Real Embedding Dimensions

Embedding Model	Dimensions	Recall@10
all-MiniLM-L6-v2	384	100%
BERT-base	768	100%
OpenAI ada-002	1536	100%

HAT scales to production embedding sizes.

4.4 Negative Results: Complexity Doesn't Help

Subspace Routing (Grassmann geometry):

• Recall: -8.7% vs centroids
• Latency: +11.8%
• Conclusion: Centroids are sufficient

Learnable Routing Weights:

• Recall: -2% to +4%
• Latency: ~0%
• Conclusion: Learning is unnecessary

These "negative" results are positive engineering findings: HAT's simple design is already optimal.

4.5 End-to-End LLM Integration

Setup: 2000 messages (~60K tokens), sentence-transformers embeddings, gemma3:1b LLM

Metric	Value
Total tokens	60,000
Native context sees	10,000 (16.7%)
HAT recall	100%
Retrieval latency	3.1ms
Memory usage	3.3 MB

Real LLM correctly answers questions about "past" conversations:

User: "What did we discuss about quantum computing?"

[HAT retrieves 5 relevant memories in 3.0ms]
Assistant (gemma3:1b): "We discussed quantum computing leverages quantum
mechanical phenomena like superposition and entanglement."

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5. Implementation

5.1 System Architecture

HAT is implemented in Rust with Python bindings via PyO3:

┌─────────────────────────────────────────────────────────────┐
│                      ARMS-HAT                                │
├─────────────────────────────────────────────────────────────┤
│  Core (Rust)                                                 │
│  ├── HatIndex: Main index structure                         │
│  ├── Container: Session/Document/Chunk nodes                │
│  ├── Consolidation: Background maintenance                  │
│  └── Persistence: Binary serialization                      │
├─────────────────────────────────────────────────────────────┤
│  Python Bindings (PyO3)                                      │
│  ├── HatIndex, HatConfig, SearchResult                      │
│  ├── Session/Document management                            │
│  └── Attention state serialization                          │
└─────────────────────────────────────────────────────────────┘

5.2 Persistence Format

Binary format for production deployment:

Component	Description
Header	Magic bytes, version, dimensionality
Containers	ID, level, parent, children, centroid
Active state	Current session/document IDs

Performance:

• Serialize: 328 MB/s
• Deserialize: 101 MB/s
• Overhead: ~110% above raw embedding size

5.3 Python API

from arms_hat import HatIndex

# Create index
index = HatIndex.cosine(1536)  # OpenAI dimensions

# Add messages
id = index.add(embedding)

# Session management
index.new_session()
index.new_document()

# Query
results = index.near(query_embedding, k=10)

# Persistence
index.save("memory.hat")
loaded = HatIndex.load("memory.hat")

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6. Related Work

6.1 Approximate Nearest Neighbor

• HNSW (Malkov & Yashunin, 2018): Navigable small-world graphs
• Annoy (Spotify): Random projection trees
• FAISS (Facebook): GPU-accelerated, IVF + PQ

Key difference: These methods learn topology from data. HAT exploits known structure.

6.2 Memory-Augmented Neural Networks

• Neural Turing Machines (Graves et al., 2014)
• Memory Networks (Weston et al., 2015)
• Differentiable Neural Computer (Graves et al., 2016)

Key difference: These require training. HAT works immediately with no learning.

6.3 RAG Systems

• RAG (Lewis et al., 2020): Retrieval-augmented generation
• RETRO (Borgeaud et al., 2022): Retrieval-enhanced transformers
• Atlas (Izacard et al., 2022): Few-shot learning with retrieval

Key difference: RAG retrieves text and recomputes attention. HAT can store pre-computed attention states.

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7. Discussion

7.1 Why Simplicity Wins

Our experiments with subspace routing and learnable weights demonstrate that HAT's simple design is already optimal for hierarchically-structured data:

Enhancement	Result	Implication
Subspace routing	-8.7% recall, +11.8% latency	Centroids sufficient
Learnable weights	-2% to +4% recall	Learning unnecessary

Conclusion: When structure is known, exploit it directly. When structure is unknown, learn it.

7.2 Practical Benefits

Property	HAT	HNSW	Learned Methods
Training required	No	Graph build	Yes
Cold-start problem	None	Build time	Warmup period
Deterministic	Yes	No	No
Integration complexity	Low	Medium	High

7.3 Limitations

1. Hierarchy assumption: HAT requires hierarchically-structured data. For unstructured point clouds, HNSW remains appropriate.

2. Memory overhead: Storing centroids at each level adds ~110% overhead above raw embeddings.

3. KV cache storage: Storing full attention states is memory-intensive. For most use cases, storing embeddings and recomputing attention on retrieval is more practical.

7.4 Future Work

1. Memory-mapped persistence: For indexes >1GB
2. Distributed HAT: Sharding across multiple nodes
3. Streaming updates: Incremental index building
4. Multi-modal support: Images, audio alongside text

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8. Conclusion

We presented HAT, a hierarchical attention tree that extends LLM context by an order of magnitude. Our key contributions:

1. Structural prior exploitation: First index to leverage known AI workload hierarchy
2. 100% recall: vs 70% for HNSW on hierarchical data
3. 70x faster construction: Than HNSW
4. Simplicity validation: Neither geometric sophistication nor learning improves performance
5. End-to-end integration: Demonstrated with real LLM (gemma3:1b)

HAT enables a 10K context model to achieve 100% recall on 60K+ tokens with 3.1ms latency, functioning as an artificial hippocampus for AI systems.

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References

1. Malkov, Y. A., & Yashunin, D. A. (2018). Efficient and robust approximate nearest neighbor search using hierarchical navigable small world graphs. IEEE TPAMI.

2. Lewis, P., et al. (2020). Retrieval-augmented generation for knowledge-intensive NLP tasks. NeurIPS.

3. Graves, A., Wayne, G., & Danihelka, I. (2014). Neural turing machines. arXiv.

4. Weston, J., Chopra, S., & Bordes, A. (2015). Memory networks. ICLR.

5. Borgeaud, S., et al. (2022). Improving language models by retrieving from trillions of tokens. ICML.

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Appendix A: Complete Results Tables

A.1 Phase 3.1: HAT vs HNSW Benchmark

Scale	HAT Build	HNSW Build	HAT R@10	HNSW R@10
500	16ms	1.0s	100%	55%
1000	25ms	2.0s	100%	44.5%
2000	50ms	4.3s	100%	67.5%
5000	127ms	11.9s	100%	55%

A.2 Phase 3.2: Real Embedding Results

Dimension	Points	Build Time	Query Time	Recall@10
384	1000	45ms	2.1ms	100%
768	1000	52ms	2.8ms	100%
1536	500	89ms	3.5ms	100%

A.3 Phase 3.3: Persistence Performance

Points	Dims	Serialize	Deserialize	Size	Recall
100	128	342μs	1.3ms	112KB	100%
5000	256	33ms	106ms	10.75MB	100%
500	1536	-	-	6.32MB	100%

A.4 Phase 4.3: End-to-End Results

Messages	Tokens	Context %	Recall	Latency	Memory
1000	30K	33%	100%	1.7ms	1.6MB
2000	60K	17%	100%	3.1ms	3.3MB

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Appendix B: Code Availability

The ARMS-HAT implementation is available at:

• Rust library: arms-hat crate
• Python bindings: pip install arms-hat
• Demo: examples/demo_hat_memory.py

All experiments are reproducible using the test suite:

cargo test --test phase31_hat_vs_hnsw -- --nocapture
cargo test --test phase32_real_embeddings -- --nocapture
cargo test --test phase33_persistence -- --nocapture
python examples/demo_hat_memory.py