METR-LA local diffusion¶

True directed transport beats both matched controls on every declared metric in seeds 0 and 1. The earlier self-only DiffusionGRU still has lower MAE and RMSE than this factorized model. The result isolates a repeatable topology signal; it does not improve the best forecaster or add a public API.

Factorization¶

At each five-minute step:

                         +--> local GRU --> local residual --------+
x[t] -------------------+                                         |
                         |                                         v
                         +--> directed diffusion               forecast
                                  |                                ^
                         [forward - x, reverse - x]                 |
                                  |                                |
                             spatial GRU --> spatial residual -- tanh(gate[H])
                                                                   |
persistence -------------------------------------------------------+

The forecast is:

persistence + local residual + tanh(gate[h]) * spatial residual

The horizon gate starts at exactly zero. The residual head also starts the local readout at zero, so the complete model initially equals causal persistence. The local path receives no graph input.

The transported field keeps direction explicit:

[forward(x) - x, reverse(x) - x]

Self-only diffusion makes this field exactly zero. True and permuted affinity therefore differ only through transported information, while every model keeps the same node-local path and parameter shapes.

Sparse work¶

Each period performs one forward and one reverse sparse sum. Twelve history steps therefore require 24 sparse calls, half the calls of the entangled DiffusionGRU. Topology storage remains O(N + E) and no node-by-node, node-edge, or product space-time adjacency is materialized.

Controls¶

true       directed METR-LA affinity
permuted   one fixed isomorphic node relabeling with aligned affinity
self       self edges with unit affinity

Features, target windows, initialization, optimizer, loss, checkpoint policy, and budget remain matched. Model test stays closed.

The frozen validation protocol uses:

head=residual   loss=mae        hidden=32
epochs=3        batch=512       learning_rate=0.001
checkpoint=each epoch

True topology advances only if it beats both controls on overall RMSE and 30/60-minute RMSE without exceeding self-only overall MAE in at least two of three matched seeds. Stop once that gate is satisfied or impossible.

Validation result¶

Values are mean ± sample standard deviation across seeds 0 and 1:

Across two seeds, two metrics, and two controls, true transport wins all eight paired overall comparisons. Its mean MAE is 0.45% lower than permuted and 0.84% lower than self-only; its mean RMSE is 0.62% and 0.85% lower.

Mean validation RMSE shows the topology signal at every reported horizon:

True transport beats both controls at 30 and 60 minutes in each seed, satisfies the declared gate twice, and stops the protocol before seed 2.

Incumbent comparison¶

Passing a topology-identification gate is not the same as improving the model:

The earlier self-only model dominates the factorized model: its MAE is 1.73% lower and its RMSE is 0.44% lower. Factorization improves MAE by 0.30% relative to the earlier true graph model but worsens RMSE by 1.35%.

Every factorized curve is still improving at epoch 3. The frozen comparison proves the topology signal at that budget; it does not establish converged or equal-time model quality.

Decision¶

topology identification   pass
predictive improvement    fail against incumbent
public API promotion      no
model test                closed

The next experiment should first compare models at a bounded plateau or equal execution budget. If the local floor still degrades, train and freeze the incumbent local forecast before fitting a zero-gated transport residual to its errors. Do not add dynamic edges, node identity, or learned adjacency yet.

Ownership¶

DirectedDiffusion remains the public spatial primitive. Root subtraction and direction concatenation stay direct tensor composition in the experiment. The local cell, readouts, and horizon gate also remain experiment-owned because the model does not improve the incumbent. This separation follows the motivation of D2STGNN, not an implementation claim of paper parity.

Reproduce¶

The matched Metal comparison used:

uv run --locked python -m experiments.run metr_la_local_diffusion DEV=METAL EPOCHS=3 MODEL=true HEAD=residual LOSS=mae SEED=0 BS=512 HIDDEN=32 LR=0.001 CHECKPOINT_EVERY=1
uv run --locked python -m experiments.run metr_la_local_diffusion DEV=METAL EPOCHS=3 MODEL=permuted HEAD=residual LOSS=mae SEED=0 BS=512 HIDDEN=32 LR=0.001 CHECKPOINT_EVERY=1
uv run --locked python -m experiments.run metr_la_local_diffusion DEV=METAL EPOCHS=3 MODEL=self HEAD=residual LOSS=mae SEED=0 BS=512 HIDDEN=32 LR=0.001 CHECKPOINT_EVERY=1
uv run --locked python -m experiments.run metr_la_local_diffusion DEV=METAL EPOCHS=3 MODEL=true HEAD=residual LOSS=mae SEED=1 BS=512 HIDDEN=32 LR=0.001 CHECKPOINT_EVERY=1
uv run --locked python -m experiments.run metr_la_local_diffusion DEV=METAL EPOCHS=3 MODEL=permuted HEAD=residual LOSS=mae SEED=1 BS=512 HIDDEN=32 LR=0.001 CHECKPOINT_EVERY=1
uv run --locked python -m experiments.run metr_la_local_diffusion DEV=METAL EPOCHS=3 MODEL=self HEAD=residual LOSS=mae SEED=1 BS=512 HIDDEN=32 LR=0.001 CHECKPOINT_EVERY=1

All runs use revision b62ca7c6, record evaluate_test=false and test=null, and finish inside the fixed 600-second bound.