Controlled transport transfer¶

This experiment asks whether one model trained on the controlled 24-node transport graph learns a reusable local operator rather than one fixed network.

The data generator and training policy follow the controlled transport forecast. After training, the weights are frozen and evaluated without retraining on:

32 and 48 nodes
      x
dense fields and four localized pulses
      x
16 recursive forecast steps

DiffusionGRU receives the true, degree-preserving permuted, and self-only topologies for every scope. The node-local LSTM and persistence floor receive no graph. A state digest before and after all evaluations verifies that the trained parameters do not change.

Protocol¶

Revision 8bcce51d853590184996db4d9d54a571cc993052 produced the six DiffusionGRU runs. Revision ca98d4a9d57311d31398b4f0c8ec3bc6708eabe5 produced the three matched LSTM runs after consolidating its four evaluation scopes under one frozen model per seed.

Both models train on 128 eight-step trajectories from host-random seed 20260729 and select a checkpoint on 32 trajectories from seed 20260730. Each training field yields four causal four-snapshot windows and next-step targets. Each transfer scope contains eight independent 20-step trajectories. Dense and pulse transfer fields use seeds 20260861 and 20260862 at 32 nodes, then 20260877 and 20260878 at 48 nodes.

The matched settings are hidden width 8, batch size 64, Adam at 0.01, 30 epochs, validation-RMSE checkpoint selection, and model seeds 0, 1, and 2. DiffusionGRU has 681 parameters; the node-local LSTM has 361.

uv run --locked python -m experiments.run transport_transfer DEV=CPU MODEL=diffusion_gru NODES=all INITIAL=dense SEED=0 EPOCHS=30 HISTORY=4 HORIZON=16 BS=64 HIDDEN=8 LR=0.01

Repeat with INITIAL=pulse and model seeds 1 and 2. The LSTM control evaluates only the two transfer sizes and trains once per model seed:

uv run --locked python -m experiments.run transport_transfer DEV=CPU MODEL=lstm NODES=unseen INITIAL=both SEED=0 EPOCHS=30 HISTORY=4 HORIZON=16 BS=64 HIDDEN=8 LR=0.01

Repeat with model seeds 1 and 2. Every recorded run completed within the runner's unchanged 600-second limit. One exploratory LSTM process that also evaluated the 24-node training size hit that limit under local contention and produced no observation. The frozen protocol omits that irrelevant source-size scope and evaluates both transfer sizes from one training run.

Results¶

The tables report mean RMSE plus sample standard deviation across three model seeds. Persistence is fixed because the transfer fields are fixed.

One step¶

Sixteen-step rollout¶

Step sixteen¶

True-topology DiffusionGRU wins every paired comparison against the permuted graph, self-only graph, LSTM, and persistence in all three seeds. Against the strongest alternative in each scope, its mean rollout-RMSE reduction ranges from 20.1% to 30.4%. The 32- and 48-node scopes agree for both dense and localized initial fields.

Decision¶

The transfer claim required true-topology DiffusionGRU to beat its permuted and self-only controls plus the node-local LSTM on one-step and 16-step rollout RMSE in at least two of three seeds. Both unseen graph sizes had to agree; the 24-node training size could not pass the gate.

The gate passes. One frozen set of local diffusion and recurrent parameters uses the correct sparse topology on graph sizes never seen during training. The positive result is not explained by node count, smooth dense fields, persistence, or a node-local recurrent model.

No new public API is promoted. Graph, DirectedDiffusion, and DiffusionGRU already own the reusable contracts and now have stronger evidence. The synthetic generator, pulse policy, graph-family construction, scope selectors, state digest, recursive evaluation, and training loop remain research-only. Sequential evaluation is sufficient, so the experiment does not justify batching different graphs.

Limits¶

The source and target graphs come from one synthetic graph family and share one deterministic, noiseless, fully observed transport law. The generator and DirectedDiffusion express the same known local operator independently. Node semantics, coefficients, feature count, sampling interval, and topology type do not change. The LSTM is a graph-free control, not a parameter-matched architecture ablation.

This proves controlled size transfer, not transfer across cities, physical systems, or process regimes. More experiments on this generator would mostly measure an already identified operator. The next model-quality stage should retain these controls on a real physical sensor network with missingness, exogenous context, and measured topology.