Semtrace: Recovering Text from Embedding Vectors

Greedy residual decomposition of embedding vectors into constituent tokens. Given a vector in embedding space, find the tokens whose embeddings sum to approximate it.

Thomas Sawyer & Claude Opus 4.6 · Paper · Results · Design

Quick Start (Container)

# Build (one-time — downloads GPT-2, builds indexes, ~10 min)
podman build -t semtrace .

# Run an experiment
podman run --rm semtrace 001          # Gettysburg Address
podman run --rm semtrace 002          # Mary Had a Little Lamb
podman run --rm semtrace 003          # Tale of Two Cities

# Run with GPU (for Python experiments)
podman run --rm --device nvidia.com/gpu=all semtrace 012

# Interactive shell
podman run --rm -it semtrace bash

Quick Start (Native)

Requires: Crystal >= 1.19, Python 3 with torch + transformers.

# Install Crystal dependencies
shards install

# Download GPT-2 embeddings (one-time)
crystal build src/cli.cr -o bin/semtrace --release
bin/semtrace prepare gpt2

# Run an experiment
./run_all.sh 001

Experiments

#	Name	Type	What It Tests
001	Gettysburg Address	Crystal	Static decomposition across GPT-2 family
002	Mary Had a Little Lamb	Crystal	Short text, 100% recovery on Large/XL
003	Tale of Two Cities	Crystal	Long text capacity limits
004	Optimization	Crystal	Lookahead, normalization, semantic matching
005	Capacity Test	Crystal	Random token baseline vs real text
006	Llama HNSW	Crystal	Llama 3.2 3B with approximate search
007	Metric Comparison	Crystal	Cosine vs L2 vs inner product
008	Llama Brute-Force	Crystal	Exact search reveals HNSW was the bottleneck
009	Union of Metrics	Crystal	Combining three metrics for better recovery
010	Contextual Embeddings	Python	Layer-by-layer analysis, attention is non-additive
011	Attention Bias	Python	Constant bias discovery, partial contextual recovery
012	Coordinate Descent	Python	Iterative optimization, 43%→94% on GPT-2 Small

Key Findings

1. Static decomposition works. 100% on short text, 90%+ on medium text (GPT-2 XL).
2. Dimensionality phase transition at ~1280d — accuracy jumps discontinuously.
3. Semantic coherence helps 6x — real text recovers far better than random tokens.
4. Coordinate descent doubles accuracy on smaller models (43%→94%).
5. Attention adds a constant bias (99.5% of energy) — subtracting it enables contextual decomposition.
6. Normalization destroys magnitude — token count and residual signal are lost.
7. The model remembers — the barrier is the serving layer, not the model itself.

Additional Models

GPT-2 Variants

bin/semtrace prepare gpt2-medium   # 1024d
bin/semtrace prepare gpt2-large    # 1280d
bin/semtrace prepare gpt2-xl       # 1600d

Llama 3.2 3B (required for experiments 006, 008)

Requires Ollama:

# 1. Install Ollama and pull the model
ollama pull llama3.2:3b

# 2. Find the GGUF blob (Linux default location)
GGUF=$(find /var/lib/ollama/blobs -type f -size +1G | head -1)
# If Ollama stores elsewhere, check: ollama show llama3.2:3b --modelfile

# 3. Extract embeddings and vocabulary
bin/semtrace extract-gguf "$GGUF"

# 4. Tokenize test texts for Llama (GPT-2 uses BPE; Llama needs separate tokenization)
python3 -c "
import json
vocab = json.load(open('data/llama-3-2-3b-instruct/vocab.json'))
token_to_id = {v: int(k) for k, v in vocab.items()}
tokens_by_len = sorted(token_to_id.keys(), key=len, reverse=True)
def tokenize(text):
    ids, pos = [], 0
    while pos < len(text):
        for tok in tokens_by_len:
            if text[pos:pos+len(tok)] == tok:
                ids.append(token_to_id[tok]); pos += len(tok); break
        else: pos += 1
    return ids
for name, path in [('gettysburg', 'experiments/texts/gettysburg.txt'),
                    ('tale_ch1', 'experiments/texts/tale-ch1.txt')]:
    ids = tokenize(open(path).read().strip())
    json.dump(ids, open(f'data/llama-3-2-3b-instruct/{name}_ids.json','w'))
    print(f'{name}: {len(ids)} tokens')
"

# 5. Build HNSW index (one-time, ~15 min)
crystal build src/build_index.cr -o bin/build_index --release
bin/build_index --data data/llama-3-2-3b-instruct

Running with a specific model

./run_all.sh 001                                     # GPT-2 Small (default)
bin/exp001 --data data/gpt2-xl --builtin gettysburg   # GPT-2 XL

License

MIT