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fix(neural): make the ESN forecaster actually forecast - #962
While working on #959 I found that the trained ESN forecast no better than the series mean, whatever the reservoir scaling. The training data is fine: training_pipeline.ex already groups outcomes by pattern and orders them by fixed_at, which was the Known Gap 5 drift. The faults are in the readout:
Train/predict mismatch.solve_ridge/2 fits a linear map, but compute_output/3 passed it through a sigmoid that the fit never saw. A correct linear estimate of 0.5 came out as 0.62, and every forecast was squeezed toward the middle.
No bias. The slot commented "+1 for bias" held the input value. There was no constant feature.
The "ridge regression" did not converge. It ran 200 epochs of SGD at lr 5e-4 and stopped far short of the minimum.
The fix
All in lib/neural/echo_state_network.ex:
Features:[state..., input, 1.0]. The input lets the readout fall back to persistence, and the constant gives a real bias.
Solve: closed-form ridge, (XᵀX + λI′)w = Xᵀy with the bias unpenalised, solved by Gaussian elimination with partial pivoting. The system is (reservoir + 2) square, so 82×82 by default. Training also runs faster than the SGD did (31 s vs 43 s for the evaluation below).
Output: the linear readout, clamped to [0, 1]. Consumers such as the blackboard's predicted_next treat it as a confidence. The untrained fallback is unchanged.
Persistence stores only an ESN summary, so there are no saved weights to migrate.
Measured
One-step MSE on held-out data: the last 200 of 600 steps, 80-node reservoir, seeds 1–3. "Persistence" means predicting next = current, the baseline a forecaster has to beat. "Confidence" is a running success rate whose true success probability drops from 0.9 to 0.5 halfway through, the shape the training pipeline produces.
series
mean
persistence
old ESN
new ESN
smooth
3.6e-2
9.9e-4
3.6e-2
1.4e-4 – 1.9e-4
memory
2.2e-2
1.4e-3
3.3e-2
6.8e-4
confidence
3.3e-2
1.4e-6
4.5e-3
1.6e-6 – 1.7e-6
The new ESN beats persistence by 7× and 2× on the two oscillating series and ties it on the confidence series, which is so smooth that persistence is near-optimal. Removing the reservoir, leaving only input and bias, falls back to roughly persistence, so the reservoir is contributing.
A decision this re-opens
#959 scaled the reservoir to ‖W‖∞ = 0.95 because that guarantee is provable, and at the time accuracy could not decide the question. Now it can. Rescaling the same reservoir to spectral radius 0.95 gives a further 2–3× improvement: smooth 4.8e-5–5.0e-5, memory 2.9e-4–3.2e-4, against 1.4e-4–1.9e-4 and 6.8e-4 with the row-sum scaling. The cost is the stability guarantee and the clean Lean target. This PR does not change the scaling; it is your call.
Tests
test/neural_test.exs:
A constant series (0.3) is forecast as itself (±1e-3).
Forecasts on the 100 held-out points beat persistence by at least 2× on a smooth series. The reservoir is warmed on the 200 training points first, and only held-out forecasts are scored (CodeRabbit caught an earlier version that also scored training points).
Forecasts stay inside [0, 1] on a square wave.
The first two fail on the old readout: on the held-out points it lost to persistence by 47× (esn_mse=0.0439, persistence_mse=0.00094). The third passes on both, since the old sigmoid also bounded the output; it guards the new clamp.
Checks
mix test: 2079 tests, 1 failure, 242 excluded. The failure is rsr_conformance_test.exs:195, which also fails on clean main and is unrelated.
mix format --check-formatted and mix compile --warnings-as-errors are clean.
The trained ESN predicted no better than the series mean. Three defects in
the readout:
- Train/predict mismatch. solve_ridge/2 fits a linear map, but
compute_output/3 passed the result through a sigmoid the fit never saw, so
a correct estimate of 0.5 came out as 0.62 and every forecast was squeezed
towards the middle. Apply the linear readout and clamp to [0, 1].
- No bias. The "+1 for bias" slot held the input value; there was no
constant feature. Features are now [state..., input, 1.0].
- The "ridge regression" was 200 epochs of SGD at lr 5e-4, far short of the
minimum. Replace it with the closed-form solve of (XᵀX + λI')w = Xᵀy
(bias unpenalised) by Gaussian elimination with partial pivoting.
One-step MSE on held-out data (last 200 of 600 steps, 80-node reservoir,
seeds 1-3; baselines: series mean, and persistence "next = current"):
series mean persistence old ESN new ESN
smooth 3.6e-2 9.9e-4 3.6e-2 1.4e-4 - 1.9e-4
memory 2.2e-2 1.4e-3 3.3e-2 6.8e-4
confidence 3.3e-2 1.4e-6 4.5e-3 1.6e-6 - 1.7e-6
Tests: a constant series is forecast as itself; held-out forecasts beat
persistence by 2x; forecasts stay in [0, 1]. The first two fail on the old
readout (it lost to persistence by 42x).
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_0165rGu3tsKmJtevmrdMVyfJ
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lib/neural/echo_state_network.ex
test/neural_test.exs
📝 Summary
Summary by CodeRabbit
Improvements
Forecasts are now kept within the range from 0 to 1, making them suitable for values such as probabilities.
Training now accounts for both the current input and the network’s internal state, improving forecasts on tested constant and held-out data.
The ESN readout now uses reservoir state, current input, and a bias. Training fits readout weights with closed-form ridge regression instead of gradient descent. Trained predictions are clamped to [0, 1]. Three tests cover constant-series prediction, held-out forecasting, and prediction bounds.
Changes: ESN Readout
Layer / File(s)
Summary
Readout feature construction lib/neural/echo_state_network.ex
The initial readout weight vector and training data now use reservoir state, current input, and a bias feature.
Readout fitting and prediction lib/neural/echo_state_network.ex, test/neural_test.exs
Training uses closed-form ridge regression with an unpenalised bias and Gaussian elimination with partial pivoting. Trained predictions use the shared feature vector and are clamped to [0, 1]. Tests check constant-series prediction, held-out forecasting against a persistence baseline, and prediction bounds.
sequenceDiagram
participant ESN as EchoStateNetwork
participant Features as features/2
participant Ridge as solve_ridge/2
participant Gaussian as gaussian_solve/2
ESN->>Features: Build training feature vectors
ESN->>Ridge: Fit readout weights
Ridge->>Gaussian: Solve ridge system
Gaussian-->>Ridge: Return weights
ESN->>Features: Build prediction feature vector
ESN->>ESN: Apply readout and clamp prediction
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Merge Risk: Low · previous review a6eab
The forecasting test may pass despite weak held-out predictions. Correct its evaluation window to make the reported improvement reliable; the remaining merge risk is bounded.
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The title clearly and concisely describes the main change: fixing ESN forecasting behaviour.
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The pull request description directly explains the ESN readout changes, regression solver, prediction clamp, tests, and measured results. It matches the changeset.
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Inline comments:
Review comments at @test/neural_test.exs:
- Line 113: Update the persistence comparison around EchoStateNetwork.step to
warm the reservoir on train, then generate predictions only for the remaining
100 held-out points. Calculate both MSE values from those held-out predictions
so training-series predictions are excluded.
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The test stepped through all 300 points, so accuracy_report/1 (last 200
predictions) included training points 101-200. Warm the reservoir on the
training series, clear the prediction history, and score only the 100
held-out points. Still fails against the old readout (47x worse than
persistence there).
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_0165rGu3tsKmJtevmrdMVyfJ
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What was wrong
While working on #959 I found that the trained ESN forecast no better than the series mean, whatever the reservoir scaling. The training data is fine:
training_pipeline.exalready groups outcomes bypatternand orders them byfixed_at, which was the Known Gap 5 drift. The faults are in the readout:solve_ridge/2fits a linear map, butcompute_output/3passed it through a sigmoid that the fit never saw. A correct linear estimate of 0.5 came out as 0.62, and every forecast was squeezed toward the middle.The fix
All in
lib/neural/echo_state_network.ex:[state..., input, 1.0]. The input lets the readout fall back to persistence, and the constant gives a real bias.(XᵀX + λI′)w = Xᵀywith the bias unpenalised, solved by Gaussian elimination with partial pivoting. The system is (reservoir + 2) square, so 82×82 by default. Training also runs faster than the SGD did (31 s vs 43 s for the evaluation below).predicted_nexttreat it as a confidence. The untrained fallback is unchanged.Persistence stores only an ESN summary, so there are no saved weights to migrate.
Measured
One-step MSE on held-out data: the last 200 of 600 steps, 80-node reservoir, seeds 1–3. "Persistence" means predicting next = current, the baseline a forecaster has to beat. "Confidence" is a running success rate whose true success probability drops from 0.9 to 0.5 halfway through, the shape the training pipeline produces.
The new ESN beats persistence by 7× and 2× on the two oscillating series and ties it on the confidence series, which is so smooth that persistence is near-optimal. Removing the reservoir, leaving only input and bias, falls back to roughly persistence, so the reservoir is contributing.
A decision this re-opens
#959 scaled the reservoir to ‖W‖∞ = 0.95 because that guarantee is provable, and at the time accuracy could not decide the question. Now it can. Rescaling the same reservoir to spectral radius 0.95 gives a further 2–3× improvement: smooth 4.8e-5–5.0e-5, memory 2.9e-4–3.2e-4, against 1.4e-4–1.9e-4 and 6.8e-4 with the row-sum scaling. The cost is the stability guarantee and the clean Lean target. This PR does not change the scaling; it is your call.
Tests
test/neural_test.exs:The first two fail on the old readout: on the held-out points it lost to persistence by 47× (
esn_mse=0.0439,persistence_mse=0.00094). The third passes on both, since the old sigmoid also bounded the output; it guards the new clamp.Checks
mix test: 2079 tests, 1 failure, 242 excluded. The failure isrsr_conformance_test.exs:195, which also fails on clean main and is unrelated.mix format --check-formattedandmix compile --warnings-as-errorsare clean.🤖 Generated with Claude Code
https://claude.ai/code/session_0165rGu3tsKmJtevmrdMVyfJ