polygram 0.0.1

Polygram — Quantum Interference Laboratory for Polysemantic Feature Dictionaries

Polygram

Quantum Interference Laboratory for Polysemantic Feature Dictionaries

Polygram is a researcher-friendly Python frontend that emits verifiable Q-Orca .q.orca.md machines for mechanistic-interpretability experiments on hierarchical polysemantic feature dictionaries.

It builds on Q-Orca's rung-1 MPS encoding with safe Rz phase knobs (q-orca PR #51) to enable phase-interference sweeps, destructive cancellation studies, entanglement probes, and hybrid measurement-feedback steering on SAE-style dictionaries.

Status

Pre-alpha. v0 milestone is closed (bootstrap → core dictionary → experiment/sweep → animals example, polished with tier stats / plots / CLI / 2D landscapes → SAE import → Cancellation primitive). New work is staged through OpenSpec changes — see openspec/changes/.

Install

pip install -e ".[dev,plot]"   # editable install with test + plot deps
pytest                          # run the suite

Optional extras: [plot] (matplotlib), [notebook] (jupyter + matplotlib), [opt] (scipy — enables the Cancellation method="scipy" backend), [sae] (reserved for a future SAE-Lens / safetensors loader; empty in v0 — JSON loader for the bundled toy fixture has no extra deps), [behavioural] (torch + transformers, required for BehaviouralValidator.validate() / .run(); the torch-free predict() stage stays on the no-extras install).

Layout

polygram/         — Python package
openspec/         — spec-driven change proposals + capability specs
tests/            — pytest suite + bundled fixtures
examples/         — Python scripts + notebook walking tour
docs/img/         — README screenshots

Capacity limits

The rung-1 MPS encoding represents each feature as a 3-qubit state parametrized by α/β/γ/φ. This caps a Dictionary at 8 features (in practice ≤6 is most ergonomic). Real SAEs ship 16k–1M features — which is why the from_sae_lens(...) importer (below) is selection-first: you name the subset you want to study, and Polygram tells you how lossy the projection-vector → β collapse was via SelectionReport.beta_variance_explained. The bridge is to small, focused experiments on a handful of features, not bulk SAE simulation.

Quickstart

import numpy as np

from polygram import Dictionary, Experiment, Feature, MPSRung1

dictionary = Dictionary(
    name="AnimalsInterference",
    features=[
        Feature("dog_poodle",   "dogs",  beta=-0.5),
        Feature("dog_beagle",   "dogs",  beta=-0.5),
        Feature("bird_hawk",    "birds", beta= 0.5),
        Feature("bird_sparrow", "birds", beta= 0.5),
    ],
    hierarchy={"dogs": ["dog_poodle", "dog_beagle"],
               "birds": ["bird_hawk", "bird_sparrow"]},
    encoding=MPSRung1(bond_dim=2, phase_knobs=True),
)

experiment = Experiment(
    name=dictionary.name,
    dictionary=dictionary,
    target_pair=("dog_poodle", "bird_hawk"),
    sweep={"bird_hawk.phi": np.linspace(0.0, np.pi, 40)},
    measures=["overlap", "gram_matrix", "schmidt_rank"],
    assertions=["hierarchical_ordering_preserved"],
)

experiment.materialize("examples/output/")   # emits a verifiable .q.orca.md
result = experiment.run()                    # analytic Gram per sweep point
result.to_csv("examples/output/result.csv")

See examples/animals_interference.py and the matching examples/animals_interference.ipynb notebook for the full walking tour.

Plots

result.plot(path) saves a default figure: 1D sweep → line plot of target-pair overlap with sibling and cross-cluster tier baselines; 2D sweep → heatmap. Requires the [plot] extra (pip install polygram[plot]).

1D sweep — bird_hawk.phi from 0 to π. Single-φ steering on this geometry leaves the cross-cluster overlap above the matched-φ baseline of cos(0.5)⁴ ≈ 0.5931 and below the sibling tier; it never destroys.

2D sweep — (dog_poodle.phi, bird_hawk.phi) 24×24 grid. The landscape rises from the matched-φ ridge of cos(0.5)⁴ ≈ 0.5931 (the β-overlap baseline) toward off-axis cells; the asymmetry is what Cancellation searches over directly.

Cancellation

Cancellation is the second experiment primitive: given a target_pair, it searches the two φ values that drive the pair's |<A|B>|² toward a tolerance, optionally constrained to preserve the hierarchical-tier ordering. Two backends ship — a deterministic max_steps × max_steps grid scan over [0, 2π]² (default, no extra deps) and scipy.optimize.differential_evolution behind [opt].

from polygram import Cancellation

cancellation = Cancellation(
    dictionary=dictionary,
    target_pair=("dog_poodle", "bird_hawk"),
    tolerance=0.05,
    preserve_tiers=True,
    optimize={"method": "grid", "max_steps": 50},
)

result = cancellation.run()
print(result.before_overlap, result.after_overlap, result.tolerance_met)
result.materialize("examples/output/")     # writes optimized .q.orca.md
result.plot("examples/output/grid.png")    # heatmap with infeasible mask

Returns a CancellationResult exposing optimized_phis, before_gram / after_gram, trajectory (every (φ_a, φ_b, overlap) evaluation in order), feasible_mask, feasible_count, and dictionary_at_optimum — the new Dictionary baked with the optimized φs and re-emittable via materialize as a verifiable Q-Orca artifact.

Structural floor

Pure-φ search on a fixed (α, β, γ) configuration is bounded: the target-pair overlap factors as |<A|B>|²(δ) = M + V·cos(δ) where δ = φ_A − φ_B, so phase alone cannot drive overlap below M − |V|. Cancellation.structural_floor() returns this analytic minimum (two Gram evaluations, backend-free), and CancellationResult caches it as result.structural_floor. The companion result.cancellation_efficiency reports (before − after) / (before − floor), clamped to [0, 1]: 1.0 means phase search exhausted the available gap (residue is encoding-bound — driving overlap lower needs amplitude matching), None means there was no gap to begin with. The materialized <name>_summary.md reports both, plus a one-line interpretation. See docs/research/cancellation-phase-floor.md for the full derivation.

See examples/cancellation_example.py for the combined SAE → InterferenceSweep → Cancellation walk.

CLI

The polygram console script runs an example or experiment module that exposes main(output_dir=...):

polygram run examples/animals_interference.py --output-dir results/
polygram run examples/import_from_sae.py --output-dir results/
polygram --version

polygram analyze triages an SAE feature subset without any quantum simulation — it builds the rung-1 Dictionary and predicts each pair's (M, V, structural_floor, cancellation_gap) from the analytic Gram:

polygram analyze tests/fixtures/toy_sae.json \
    --features 0,1,4,5 \
    --output analysis_report.md

The report includes per-pair structural floors, per-feature sensitivity (mean |V_ij|), and a single-scalar encoding_suitability_score. See polygram.analysis for the programmatic API.

SAE import

polygram.from_sae_lens(records, feature_ids, ...) builds a Polygram Dictionary from a user-selected subset of SAE features and returns a SelectionReport describing how the lossy projection-vector → β collapse went. Cluster assignment precedence: explicit user override → parsed "<cluster>/<name>" labels → k-means on projection vectors.

from polygram import from_sae_lens, load_toy_sae

records = load_toy_sae("tests/fixtures/toy_sae.json")
# pick 4 features by id (≤8; the rung-1 MPS cap)
dictionary, report = from_sae_lens(records, [0, 1, 4, 5])

print(report.cluster_method)             # "from_labels" / "kmeans" / "user"
print(report.beta_variance_explained)    # cluster-level fidelity stat
print(report.reconstruction_error)       # per-feature distance to centroid
print(report.tier_preservation)          # corr(projection-space cosines,
                                         # analytic Polygram Gram) — None
                                         # for n_selected ≤ 1

SelectionReport surfaces three fidelity stats per call: beta_variance_explained (cluster-level), reconstruction_error (per-feature Euclidean distance from each projection vector to its assigned cluster centroid), and tier_preservation (Pearson correlation between off-diagonal |G|² of the projection-space cosine-overlap matrix and the analytic Polygram Gram of the built Dictionary).

Pass assign_gamma=True to derive each feature's γ from per-cluster PCA on the centered projection vectors (rescaled into gamma_range, default (-0.25, 0.25)); report.gamma_method records "zero" (default) or "projection_pca".

The bundled tests/fixtures/toy_sae.json is a 16-feature, 4-cluster, 8-dim deterministic toy.

Loading from safetensors

polygram.load_sae_safetensors(path, *, names=None) reads a single .safetensors file and returns the dict[int, SAEFeatureRecord] shape from_sae_lens consumes. Decoder weight tensor key is auto-detected via the precedence list ("W_dec", "decoder.weight", "dec"); rows are features (the loader transposes only when the matched key is decoder.weight and the matrix is non-square — that's the PyTorch nn.Linear out × in convention). Requires the [sae] extra (pip install polygram[sae]) which pulls in safetensors>=0.4 only — no torch, no sae_lens, no huggingface_hub.

from polygram import from_sae_lens, load_sae_safetensors

records = load_sae_safetensors("path/to/sae.safetensors")
dictionary, report = from_sae_lens(records, [0, 1, 4, 5])

The companion polygram sae-import CLI subcommand wraps the loader and emits the same JSON schema as tests/fixtures/toy_sae.json, so the chain sae-import → analyze works without further plumbing:

polygram sae-import sae.safetensors --features 0,12,1042 --output picked.json
polygram analyze picked.json --features 0,12,1042 --assign-gamma --sharing-graph g.json

--assign-gamma is almost always wanted on real-SAE inputs. Without it, every feature in a k-means cluster gets γ = 0 and rung-1 within-cluster overlaps collapse to 1.0 regardless of how diverse the underlying projection vectors are — the SAE's geometry becomes invisible to the triage layer. With the flag set, per-cluster PCA on the centered projections derives each feature's γ. The companion --n-clusters N flag (default 2) tunes the k-means cluster count when label-based clustering isn't available.

For GB-class SAEs (Gemma-2-2B, Llama-3-8B, etc.) where the full decoder tensor would blow past available RAM under np.float64 coercion, pass feature_ids=[...] to load_sae_safetensors to slice only the rows you need — the loader switches to a safetensors.safe_open(...).get_slice(...) path that never materializes the full tensor. Empirically: ~5000× less peak Python memory and ~100× faster than the eager path on a 600 MB SAE when sampling 8 features.

records = load_sae_safetensors(
    "path/to/large-sae.safetensors",
    feature_ids=[0, 12, 1042, 5012],
)

A first-class HuggingFace / SAE-Lens reader (with auto-download + metadata round-trip) is a separate follow-up — both would pull in huggingface_hub and / or sae_lens + torch, which v0 deliberately keeps out of the runtime dep tree until real-data signal arrives.

Hand-rolled loaders

To swap in any SAE format the bundled loaders don't cover yet (custom serialization, multi-file checkpoints, in-memory tensors), hand-roll a dict[int, SAEFeatureRecord] from your loader of choice and pass it to from_sae_lens directly.

See examples/import_from_sae.py for the full flow (toy SAE → Dictionary → InterferenceSweep → verified .q.orca.md + plot).

Choosing an encoding

MPSRung1 is the production default. Each feature is a 3-qubit rung-1 MPS state parameterized by (α, β, γ, φ), with phase_knobs=True exposing a single Rz-axis φ per feature. Its closed-form |⟨A|B⟩|²(δ) = M + V·cos(δ) factorization means the structural floor M − |V| is exact and free to evaluate — Cancellation can certify how close a phase-search result is to the encoding-theoretic minimum without any optimizer calls. Tier-separation and co-firing rankings derived from MPSRung1 transfer to real-model behaviour (Spearman ≥ 0.6 against behavioural Jaccard at blocks.10 on GPT-2 small; see docs/research/behavioural-scaleup-probe.md).

HEA_Rung2 gives a richer θ tensor ((|rotations|, depth, n_qubits) per feature) with independent knobs for circuit depth, entangler topology, and rotation gate set (Ry/Rz by default). The extra expressivity lets the encoding explore geometry beyond a single Pauli-Rz phase axis, and tier_separation_bound (default 0.025) causes the emitter to declare an invariant that Q-Orca can verify. The tradeoff is that no closed-form structural floor exists in the multi-knob case — structural_floor() raises NotImplementedError for HEA_Rung2, so cancellation efficiency is undefined. Cross-encoding stability on GPT-2-small SAEs shows that pair-level tier classifications agree with MPSRung1 at default thresholds, but per-pair overlap magnitudes diverge (up to +0.30 higher cross-cluster current-overlap under HEA); quantitative magnitude claims should be regenerated in the target encoding.

Rule of thumb: use MPSRung1 by default; reach for HEA_Rung2 when you need expressivity beyond a single Pauli-Rz phase axis and can live without a closed-form structural floor.

Rung3 encoding (experimental)

polygram.encoding.Rung3 adds a 5-qubit encoding parallel to MPSRung1: qubits 0–2 carry the same MPS state, qubits 3–4 carry an amplitude branch parameterized by per-feature theta_amp and psi_aux knobs (defaults π/4 and 0.0). At default knobs the Rung3 gram reduces to the MPSRung1-equivalent gram exactly, so a baseline Rung3 dictionary is behaviourally identical to its MPS counterpart. Cancellation(encoding="rung3") runs a joint (φ_a, φ_b, theta_amp, psi_aux) optimizer (5×5 outer grid + 2-φ inner + scipy Nelder-Mead refine) that, in principle, breaks below the MPSRung1 phase-only floor M − |V|.

Rung3 is experimental; the default encoding remains MPSRung1 pending the §4.5 viability spike's verdict (run examples/rung3_viability_spike.py). The spike measures four calibrated criteria (floor-breaking, gate true-positive rate, ranker preservation, coverage) on the §4.4 8-feature GPT-2-small panel; making Rung3 the production encoding is gated on a strong pass per the proposal's decision rule.

Behavioural validator

polygram.behavioural.BehaviouralValidator runs the four-constraint compression-loop pipeline against a Dictionary of SAE features and emits a structured ValidationReport. Two-stage API: predict() is torch-free and Polygram-only; validate() lazy-imports torch + transformers and runs one ablation forward-pass-batch per selected feature (the per-feature cost cap is a spec contract, not just an optimization). run() is the convenience wrapper.

from polygram import BehaviouralValidator, from_sae_lens, load_sae_safetensors

records = load_sae_safetensors("sae.safetensors", feature_ids=ids)
dictionary, _ = from_sae_lens(records, ids, assign_gamma=True)

validator = BehaviouralValidator(
    dictionary=dictionary,
    sae_checkpoint="sae.safetensors",
    feature_ids=ids,
    prompts=prompts,
    layer=10,
)
report = validator.run()
report.to_json("validation_report.json")
report.to_csv("validation_pairs.csv")
print("confirmed:", report.confirmed)

Defaults encode the §4.4 GPT-2-small calibration: Polygram squared- overlap threshold 0.7, Jaccard threshold 0.30, ablation-KL hook at layer ≥ 5 (layer 0 is rejected by default per docs/research/deeper-layer-ablation-probe.md). The CLI wrapper is polygram validate ... (run polygram validate --help). See examples/behavioural_validate.py for the worked example.

Compression action

polygram.compression.Compressor is the loop's downstream half. It consumes a ValidationReport's confirmed candidate-pair list, collapses it to redundancy clusters via union-find, picks one representative per cluster, and rewrites an SAE checkpoint so the non-representatives are silenced. Two-stage API: plan() is cheap (in-memory union-find, no torch); apply() reads the source .safetensors, applies the zero strategy in-memory, and writes a new .safetensors atomically. run() is the convenience wrapper.

from polygram import Compressor, ValidationReport

report = ValidationReport.from_json("validation_report.json")
compressor = Compressor(
    validation_report=report,
    sae_checkpoint="sae.safetensors",
    strategy="zero",
)
result = compressor.run("sae.compressed.safetensors")
result.report.to_json("compression_report.json")

The zero strategy zeroes the encoder column, encoder bias, and decoder row of every non-representative member. b_dec (global) is untouched. Component-first compression (not pair-by-pair) makes the operation order-independent — see docs/research/compression-action-design.md for the rationale. CLI wrapper: polygram compress .... Worked example: examples/compress_validated.py. The merge strategy is deferred to a follow-up change.

Regrow primitive

polygram.compression.Regrower is the post-compression complement: it takes a checkpoint with zeroed slots and repopulates them with new directions extracted from the SAE's activation residuals. The default residual_kmeans strategy runs k-means on activation - SAE_reconstruct(activation) (the directions the SAE failed to represent), unit-normalizes the cluster centroids, and writes them into the zeroed slots: W_dec[fid, :] = centroid, W_enc[:, fid] = centroid, b_enc[fid] = 0. b_dec stays untouched.

from polygram import Regrower, CompressionReport

# Chained from a prior compression run
report = CompressionReport.from_json("compression_report.json")
regrower = Regrower.from_compression_report(
    report,
    sae_checkpoint="sae.compressed.safetensors",
    strategy="residual_kmeans",
    prompts=prompts,  # captures residuals via one GPT-2 forward
    layer=10,
)
result = regrower.run("sae.regrown.safetensors")

# Or directly from a known zeroed set + cached residuals
import numpy as np
residuals = np.load("residuals.npy")  # (n_tokens, d_model)
regrower = Regrower(
    sae_checkpoint="sae.compressed.safetensors",
    strategy="residual_kmeans",
    zeroed={42, 100, 256},
    cached_residuals=residuals,
)
result = regrower.run("sae.regrown.safetensors")

The output is a "primed but quiet" SAE — every slot has a unit-norm direction, no fine-tune happens here. Downstream consumers (an orca-lang workflow fine-tune node, an external trainer, a research notebook) take it from there. CLI wrapper: polygram regrow .... Optional extra: pip install ".[regrow]" for sklearn. See docs/research/compression-regrow-design.md and examples/regrow_validated.py.

Compression epoch (multi-panel orchestrator)

polygram.compression.EpochCompressor scales the per-panel validate→compress loop to the full SAE via greedy seeded coverage over the cosine-similar pair graph, with stable-cluster fixed-point iteration and a relative cross-entropy quality bound. The orchestrator runs panels sequentially in-process (single GPT-2 instance amortized across panels); users wanting concurrency shard at the CLI invocation level.

from polygram import EpochCompressor

epoch = EpochCompressor(
    sae_checkpoint="sae.safetensors",
    prompts=prompts,
    layer=10,
    coverage_target=0.95,
    cosine_threshold=0.30,
    n_visits_per_feature=3,
    max_iterations=5,
    quality_delta_multiplier=2.0,
)
result = epoch.run("sae.epoch.safetensors")
result.report.to_json("epoch_report.json")
print(result.report.convergence_reason)  # 'stable_clusters' | 'max_iterations' | ...

Convergence: cluster-set fingerprint stable across two consecutive iterations. Hard cap on iterations and a relative quality bound (delta_k ≤ multiplier × delta_1) prevent runaway compression. CLI wrapper: polygram compress-epoch .... Worked example: examples/compress_epoch_validated.py. See docs/research/compression-epoch-design.md for the rationale.

Development

pip install -e ".[dev,plot]"
pytest

Relationship to Q-Orca

Polygram does not define a new file format. It generates standard Q-Orca .q.orca.md files (matching the style of examples/larql-animals-interference.q.orca.md from q-orca-lang) and uses Q-Orca for verification, simulation, and the analytic Gram helper compute_concept_gram_mps.

License

Apache-2.0.