Metadata-Version: 2.4
Name: vdeductive
Version: 0.2.0
Summary: Vibrational Deduction Transformer -- spectral VAE with differentiable graph-wiring generative path
Author-email: Lorenzo Moriondo <tunedconsulting@gmail.com>
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# Vibrational Deduction Transformer (VDT)

A **Spectral-PPCA Variational Autoencoder** whose generative path is mediated by a
learned graph wiring (Laplacian) constrained to the eigenbasis of an ArrowSpace index $$I$$.
Post-training, the model emits a **spectral artefact** that initialises a transformer
with pre-built associative memory.

This architecture is related to NVIB (Nonparametric Variational Information Bottleneck).
It applies pre-built semantic spectral filters and inline memory to a VAE, saving learning
steps by identifying the object of learning via spectral methods.

The feature-space Laplacian $$L_f$$ (as in Graph Wiring) replaces the basis of the latent
space and the prior over mode weights, leaving reparameterisation itself still diagonal
and cheap.

The architecture follows the progression in *The Little Book of Generative AI Foundations*
(Chen, 2026) and is grounded in the VDT paper (Moriondo, 2026):

```
PCA -> Autoencoder -> PPCA -> VAE
 |          |           |       |
Graph     Wiring     Prob.  Spectral-PPCA
Laplacian    AE     Wiring  VDT (this repo)
```

---

## Core Idea

The encoder produces a posterior $$q(z|x)$$ enriched by a lambda-fingerprint from $$L(I)$$.
The decoder maps $$z$$ into a **spectral loading matrix**:

$$
W = U_{1:q} diag(\omega) S
$$

where $$U_{1:q}$$ are the $$q$$ lowest-frequency eigenvectors of the ArrowSpace Laplacian
$$L(I)$$, $$S$$ are learnable loadings in that eigenbasis, and $$\omega$$ are mode weights drawn
from a tau-mode prior. $$W$$ then parametrises a differentiable Laplacian $$L(z)$$, over
which a tau-mode diffusion reconstructs $$x_hat$$ from the embedding table $$E$$.

### Relationship to the Lattice Deduction Transformer (LDT)

The VDT adapts the **deductive, iterative-refinement philosophy** of the
*Lattice Deduction Transformer* (Davis et al., 2026, arXiv:2605.08605) to the
continuous spectral domain. The LDT is a recurrent transformer that approximates
logically sound deduction by projecting its latent state through a discrete lattice
between forward passes; an 800K-parameter LDT achieves 100% accuracy on Sudoku-Extreme
while frontier LLMs score 0%.

The VDT implements the same pattern in four corresponding mechanisms:

| LDT mechanism | VDT implementation | Code location |
|---|---|---|
| Recurrent lattice descent | Discrete damped-wave recurrence `Q_{t+1} = 2Q_t - Q_{t-1} - dt² L_f Q_t - γΔQ + dt² B_t` | `vdeductive/vdeductive.py` `VibrationalStateBlock.forward()` |
| Lattice alpha-projection | Modal projection onto leading eigenvectors `z = mean(Q_K ᵀ U_m)` | `vdeductive/vdeductive.py` `VDT.modal_projection()` |
| Transformer forcing inside recurrence | Self-attention + FFN producing forcing term `B_t` at each wave step | `vdeductive/vdeductive.py` `VibrationalStateBlock` |
| Consistency / validity tracking | Signed density matrix `ρ = ρ_plus − ρ_minus` updated from consecutive wave states | `vdeductive/density.py` `SignedDensityMatrix.update()` |

Where the LDT constrains each recurrent step to remain within a **lattice of logically
consistent states**, the VDT constrains the transformer's value space to remain aligned
with the **spectral geometry of the index** $$I$$. The natural next step toward full parity
with LDT is a *solve loop*: running the recurrent VDT stack at training time to generate
candidate spectral wirings and self-supervising on them, mirroring LDT's on-policy
training via the alpha operator.

---

## The Three-Term ELBO

```
L_VDT = E_q[log p(x | z, W)]
      - KL( q(z)  ||  N(0, I)         )   [isotropic latent KL]
      - KL( q(S)  ||  p(S | I)        )   [spectral-basis KL -- eigenvalue-weighted]
      - KL( q(w)  ||  p(w | tau, L)   )   [tau-mode frequency KL -- Gamma vs Exp(tau*lk)]
```

The ArrowSpace index $$I$$ enters solely through the pre-computed frozen eigenpair
$$(U_{1:q}, L_{1:q})$$ of $$L(I)$$ -- no Laplacian is evaluated or inverted at training time.
Index selection is Bayesian via the ELBO Bayes factor $$exp(L(I1) - L(I2))$$.

---

## Data Flow

```
Input x (B, D)                   Embedding table E (N, D)
    |                                    |
    +-- [lambda-fingerprint from L(I)] --+
    |
    v
+----------------------------------+
|  WiringEncoder                   |
|  VDT attention blocks            |
|  -> (z, mu, log_var, log_a, log_b) |
+----------------------------------+
    |
  (z, mu, log_var)  <- reparameterise
  (log_a, log_b)    -> ModeWeightHead -> q(omega)
    |                     |
    v                     v kl_z ---------------------------+
+------------------------------------------+               |
| SpectralLoadingDecoder                   |               |
|  z, U_{1:q}  ->  W, omega, S, log_var_S  |               |
|  W = U_{1:q} diag(omega) S               |               |
|  log_var_S from independent head         |               |
+------------------------------------------+               |
    |                          |                            |
    |                     log_var_S, S --> kl_S ------------+
    |                                                       |
  W  ->  DifferentiableLaplacian.from_spectral_loading(W, L_base)
    |                                                       |
  L(z)  (B, N, N)                                          |
    |                                                       |
    v                                                       |
+--------------------+      +------------+                 |
|  DiffusionDecoder  | <--- |     E      |                 |
|  TauModeDiffusion  |      +------------+                 |
+--------------------+                                     |
    |                                                       |
  x_hat (B, D)  -->  recon loss -------------------------->+
                      kl_tau (from log_a, log_b) --------->+
                                                            |
                                          VDT ELBO loss <--+
                             (recon + kl_z + kl_S + kl_tau)
```

Post-training, `extract_spectral_artefact()` builds:

$$
A(I) = { W_{hat},  {\omega_{hat_k}},  S_{memory} }
$$

$$S_{memory}$$ is a pre-built outer-product Hopfield matrix keyed on Laplacian eigenvectors
(orthonormal by construction, maximising retrieval SNR) that initialises the transformer's
feed-forward / cross-attention value matrices.

---

## Architecture Modules

| Module | Role |
|--------|------|
| `vdeductive/encoder.py` | `WiringEncoder` -- VDT attention blocks + lambda-fingerprint; `ModeWeightHead` outputs `(log_a, log_b)` for tau-mode prior |
| `vdeductive/vdeductive.py` | `VDTBlock` stack -- multi-head self-attention over graph eigenbasis; computes `rho_p`, `rho_m` density matrices per block |
| `vdeductive/wiring_decoder.py` | `SpectralLoadingDecoder` -- $$z, U_q -> (W, \omega, S, L_z, log_var_S)$$; $$W = U_q diag(\omega) S$$; `log_var_S` from independent head |
| `vdeductive/diffusion_decoder.py` | $$L(z), E -> x_hat$$ via taumode diffusion + MLP refinement |
| `vdeductive/model.py` | `WiringAutoencoder` -- three-term ELBO; `forward()` returns dict `{loss, recon, kl_z, kl_S, kl_tau, x_hat, z, mu, log_var, N_active}`; `extract_spectral_artefact()` |
| `vdeductive/vib_autoencoder.py` | `VibrationalAutoencoder` -- vibrational energy formulation with Rayleigh-Ritz mode selection |
| `vdeductive/laplacian.py` | Differentiable Laplacian builder; `from_spectral_loading(W, L_base)`; `MassMatrix` conditioning |
| `vdeductive/spectral.py` | `spectral_basis_kl`, `tau_mode_kl`, `laplacian_precision_kl`, `build_knn_laplacian`; linalg.eigh offloaded to CPU on MPS |
| `vdeductive/density.py` | Density matrix utilities; positive/negative probability `rho_p`, `rho_m` |
| `vdeductive/spectral_memory.py` | `SpectralAssociativeMemory` -- Hopfield memory pre-built from `A(I)`; delta-rule online updates |
| `vdeductive/stability.py` | Training diagnostics; `spectral_kl_health_check` (6-level hierarchy); `N_active` mode counter |
| `vdeductive/metrics.py` | Evaluation metrics: reconstruction MSE, linear probe accuracy, memory SNR, ELBO Bayes factor |
| `vdeductive/classifier.py` | Downstream node-classification head using frozen `mu` embeddings |
| `vdeductive/dataset.py` | Dataset helpers (MNIST, Cora, PubMed, custom CSV) |
| `vdeductive/device.py` | Device resolution; MPS fallback env-var management |
| `train.py` | Training loop with W&B / CSV logging; `N_active` tracked per epoch |
| `benchmark.py` | Evaluation suite -- 8 metrics + ELBO Bayes factor; auto-selects `mps.yaml` on Apple Silicon |
| `visualise.py` | Visualisation suite for training curves, latent space, and spectral mode shapes |
| `configs/default.yaml` | Full-size hyperparameters (GPU / large RAM) |
| `configs/mps.yaml` | Apple Silicon config: `hidden_dim=32`, `n_layers=2`, `batch_size=4` |
| `configs/mnist.yaml` | MNIST dataset overrides |
| `configs/spectral_demo.yaml` | Spectral generation demo overrides |

---

## Quickstart

```bash
uv pip install -e ".[dev]"

# Training -- config is auto-selected for your device:
#   MPS (Apple Silicon) -> configs/mps.yaml   (small model, batch=4)
#   otherwise           -> configs/default.yaml
uv run train.py --dataset cora

# Override config or batch size explicitly:
uv run train.py --config configs/default.yaml --dataset cora
uv run train.py --config configs/mps.yaml --dataset cora --batch-size 8

# Benchmark -- auto-selects mps.yaml on Apple Silicon:
uv run benchmark.py --dataset cora --output data/Cora/results/

# Benchmark with explicit config or batch override:
uv run benchmark.py --dataset cora --output data/Cora/results/ --config configs/default.yaml
uv run benchmark.py --dataset cora --output data/Cora/results/ --batch-size 16
```

or:

```bash
# editable dev install (recommended for active work)
pip install -e ".[dev,ogb,wandb]"

# or regular install from PyPI once published
pip install "vdeductive[ogb]"

# then run from any directory
vdeductive-train --config configs/mps.yaml --dataset cora
vdeductive-train --config configs/mps_arxiv.yaml --dataset ogbn-arxiv
```

### Apple Silicon (MPS) notes

- Set `PYTORCH_ENABLE_MPS_FALLBACK=1` before running (the scripts print a reminder if not set).
- All `linalg.eigh` calls are offloaded to CPU explicitly in `vdeductive/spectral.py`.
- `configs/mps.yaml` keeps `hidden_dim=32` and `batch_size=4` to avoid the ~28 GiB MHA
  activation tensor that the full config produces on Cora (`N=2708`).
- The `MassMatrix` conditioning warning (`ratio > 100`) is benign on regular / k-NN graphs;
  set `mass_clip=1e3` in the config to suppress it (see `docs/04-stability.md` S7).

---

## Evaluation Metrics

| Metric | What it measures |
|--------|-----------------| 
| Reconstruction MSE | Quality of `x_hat` recovered through the wiring path |
| `kl_z` | Standard isotropic KL regularisation of latent `z` |
| `kl_S` | Spectral alignment of loadings with ArrowSpace index `I` |
| `kl_tau` | Effective frequency band selection via tau-mode prior |
| `N_active` | Mean number of modes with `E[omega_k] > 0.01` per batch (logged to CSV) |
| `memory_snr` | Retrieval quality of `SpectralAssociativeMemory` (key orthogonality) |
| `elbo_bayes_factor` | `exp(L(I1) - L(I2))` -- comparison of competing ArrowSpace indices |
| `linear_probe_acc` | Discriminative quality of frozen latent `mu` |

---

## Flagship Demo -- Spectral Graph Generation

Standard VAEs decode $$z$$ into flat feature vectors. The VDT decodes $$z$$ into a
*graph wiring* -- a Laplacian -- whose eigenvalues are vibrational modes of the system
(cf. Rayleigh's *Theory of Sound*). The latent space directly encodes spectral geometry,
enabling **entropy-controlled generation**: sample novel wirings whose Laplacian spectrum
matches a target entropy level.

```bash
# Train on synthetic spring-network graphs and run all evaluations
uv run demos/spectral_generation_demo.py --n-graphs 400 --epochs 60

# Interactive pluot + static visualisations
uv run demos/visualise_spectral_demo.py --results results/spectral_demo
```

Outputs written to `results/spectral_demo/`:

| File | Content |
|------|---------|
| `spectral_demo_results.csv` | Per-sample spectral entropy + Frobenius distance to nearest training Laplacian |
| `entropy_control_results.csv` | Entropy-targeting experiment: target vs best error vs match rate |
| `training_log.csv` | Epoch-level ELBO, reconstruction MSE, KL terms, N_active |
| `figures/training_curves.png` | Loss component curves |
| `figures/entropy_distribution.png` | Dataset vs generated spectral entropy histogram |
| `figures/spectral_distance.png` | Distribution of nearest-neighbour spectral distances |
| `figures/latent_entropy.png` | PCA-2D latent space coloured by spectral entropy |
| `figures/mode_shapes.png` | First 4 vibrational mode shapes of a sample spring network |
| `figures/entropy_target_error.png` | Entropy targeting precision across entropy range |
| `figures/pluot_manifest.json` | Load in [pluot](https://github.com/keller-mark/pluot) for interactive view |

---

## Full Training and Visualisation

```bash
uv run train.py --config configs/default.yaml --epochs 50
uv run visualise.py --mode training --checkpoint checkpoints/ \
    --dataset data/Cora/processed/ --output data/Cora/output
```

---

## Config Priority in `benchmark.py` and `train.py`

Both scripts resolve the config and batch size in the same order:

1. `--config <path>` CLI flag (explicit override)
2. Auto-select `configs/mps.yaml` when device resolves to `mps` (no flag needed)
3. Fall back to `configs/default.yaml`

Batch size resolves as:

1. `--batch-size <n>` CLI flag
2. `cfg['training']['mps_batch_size']` when device is `mps`
3. `cfg['training']['batch_size']`
4. Fallback: `4`

---

## Connection to ArrowSpace

`vdeductive/laplacian.py` mirrors `ArrowSpaceBuilder.build()` logic from
[pyarrowspace](https://github.com/tuned-org-uk/pyarrowspace) as a differentiable
PyTorch layer so gradients flow through `L(z)`.

The ArrowSpace index `I` determines the frozen eigenpair `(U_{1:q}, L_{1:q})` that
parametrises both the loading-matrix prior and the tau-mode frequency prior.
Index selection is made Bayesian via the ELBO Bayes factor.

---

## Documentation

| File | Content |
|------|---------|
| [`docs/README.md`](docs/README.md) | Concept tree, document map, implementation sequence |
| [`docs/00-architecture.md`](docs/00-architecture.md) | Full architecture reference: modules, ELBO, data flow |
| [`docs/01-references.md`](docs/01-references.md) | Bibliography and related work |
| [`docs/03-branching.md`](docs/03-branching.md) | Six algorithm tracks and option compatibility |
| [`docs/04-stability.md`](docs/04-stability.md) | Stability hierarchy and diagnostics |

---

## References

- **Davis, L., Haller, L., Alfarano, A., and Santolucito, M.** (2026).
  *Lattice Deduction Transformers.* arXiv:2605.08605.
  <https://arxiv.org/abs/2605.08605> — primary architectural inspiration for the
  recurrent deductive refinement loop in `vdeductive/vdeductive.py`.
- *The Little Book of Generative AI Foundations*, T. Chen, 2026
- VDT paper (Moriondo, 2026) -- ArrowSpace / Graph Wiring
- ArrowSpace technical report (Moriondo, 2026) -- see `docs/01-references.md`
- Rayleigh, *Theory of Sound*, vol. 1 -- vibrational mode decomposition
