Montevideo delayed edges¶

This record asks whether the real directed stop graph carries causal signal beyond the selected seasonal floor.

Decision¶

At tinygrad revision 6ea7d366, delayed residuals on real edges fail the frozen promotion gate.

The real graph selects a one-hour lag. It improves validation RMSE by only 0.000062 while worsening MAE, and both structural controls achieve lower validation RMSE. On test, the real graph worsens both MAE and RMSE relative to the seasonal floor.

Tinymesh retains the experiment and negative result. It adds no edge-field primitive, recurrent architecture, or public API.

Question¶

The selected baseline predicts one value for each node and ordered hour-of-week phase. Subtracting it leaves a node residual field:

target[v,t] - seasonal[v,t] = residual[v,t]

residual[u,t-lag] -- real edges u -> v -- incoming mean --> signal[v,t,lag]

prediction[v,t] = seasonal[v,t] + alpha * signal[v,t,lag]

For every structure and lag, one global scalar minimizes training squared residual error:

alpha = sum(signal * residual) / sum(signal**2)

A zero denominator gives alpha = 0. There is no node, edge, or phase-specific coefficient.

Controls¶

The lag set is fixed at {1, 2, 3, 6, 12, 24} hours. The same fit and validation selection run on:

real       original directed edges, original node fields
reverse    every directed edge reversed, original node fields
permuted   original edges, node fields shifted left by one node index

The reverse control tests edge direction. The cyclic field control preserves the graph, tensor shapes, value distribution, and temporal order while breaking stop identity.

Each structure selects minimum validation RMSE, then MAE, then the smaller lag. All three choices are frozen before test metrics are computed.

Candidate evidence¶

CPU candidate values are below. Metal differs only in the last digits of some coefficients and block reductions; rounded metrics, selections, and the gate are unchanged.

Bold rows are selected by RMSE, not by MAE.

Selected test¶

Isolated nodes receive a zero spatial residual, so their prediction remains the seasonal floor. Metrics retain all 675 nodes.

Gate¶

Each split is divided into three contiguous blocks. Real edges must improve both overall metrics and each metric in at least two blocks against every comparator.

The tiny validation RMSE movement is neither metric-consistent nor structure-specific. It reverses on test.

Sparse path¶

Graph.sum folds the 743 time rows into feature width and reduces the complete field with one csr_sum call per structure:

value buffer          [675, 743]
forward row pointer   [676]
forward column        [690]
transpose row pointer [676]
transpose column      [690]

Each graph sum owns 2 * (676 + 690) = 2,732 device int32 topology values. UOp inspection finds one sparse call and no [675,675] topology carrier. The experiment uses node fields of shape [743,675,1], not dense node-pair state.

An independent host implementation matches incoming means, the closed-form coefficient, predictions, and metrics on a small directed periodic fixture. Boundary tests prove lagged predictions read only earlier rows; perturbing test rows leaves every fit, validation metric, and selected lag unchanged.

Reference boundary¶

PyG's MessagePassing surface separates messages from target aggregation. This experiment needs only the existing Tinymesh composition Graph.sum(field) / in_degree; it does not justify another abstraction. PyG Temporal's DCRNN motivates directional diffusion; this stage tests its simplest identifiable component before adding recurrent complexity.

TorchGeo and TerraTorch remain reference-only because no raster adapter, geospatial sampler, backbone, neck, or head participates in this test. No PyTorch, NumPy, or geo runtime is added.

Meaning¶

This result rejects one narrow claim: an unweighted incoming mean of delayed stop residuals is not a useful next-hour correction on this month of data.

It does not prove that graphs or spatiotemporal graph neural networks are irrelevant. Route identity, within-hour travel time, bus trajectories, service frequency, traffic, weather, mobile-agent attachment, learned edge state, and more observations are absent. Those facts could define a different graph signal. They do not justify adding speculative Tinymesh machinery before a caller demonstrates it.

Reproduce¶

DEV=CPU uv run --locked python -m unittest tests.test_montevideo_delayed_edges
DEV=METAL uv run --locked python -m unittest tests.test_montevideo_delayed_edges
uv run --locked python -m experiments.run montevideo_delayed_edges DEV=CPU
uv run --locked python -m experiments.run montevideo_delayed_edges DEV=METAL