Latent Knowledge Before Behaviour
Ongoing research. This is an experimental result from active work, not a settled conclusion. The numbers are what we measured and the method is described so you can judge it, but the programme is still running and later experiments may revise what it means. More about this programme.
EXPLORATORY. Not a preregistered study. Local CPU, 10 training runs, no GPU, no cost.
Program v2 tier 2, item F2. Decisive computation: . Output: analysis/decode_probe.py. Reproduce with analysis/decode_probe.jsonpython analysis/decode_probe.py in about twelve minutes on a throttled laptop CPU.
The question
Every signal this program has found is coincident with the transition, or worse. The geometry peak lands at the transition under AdamW and 243 steps after it under SGD (D8). No early-trajectory metric ranks final outcomes (K1). Every controller idea in Bucket C needs something that arrives first, and nothing did.
F2 looks in a different place. At each point in training, fit a linear probe from the model's hidden state to the token it is supposed to emit, and compare that probe's accuracy against the model's own.
The probe is the same function class as the output head, a linear map from final_norm to the vocabulary. So this is not asking whether some clever decoder can extract the answer. It asks whether an optimally fitted version of the readout the model already has would beat the one it has learned. If yes, the information is present and the head has not yet learned to read it.
Kill test: decodability and behavioural accuracy rise simultaneously within measurement resolution across ten seeds.
Result: the kill test fails, decisively
| Quantity | Value |
|---|---|
| Probe reaches 50% at step | 59.3 |
| Model reaches 50% at step | 82.7 |
| Lead | +23.5 steps [+22.1, +24.9] |
| Runs with a lead above the 5-step resolution | 10 / 10 |
| Largest probe-minus-model gap | +0.2071 [+0.1975, +0.2167] at step 28 |
The information is linearly present in the hidden state roughly 23 steps before the model can act on it, on a transition that lands around step 83. That is about 28% of the way to the event, and it is the first genuinely leading signal in this program.
It is not an artifact of the threshold
The 50% crossing was chosen before looking. The lead survives every level tested, and is positive in all ten runs at every one:
| Crossing level | Lead (steps) | SD |
|---|---|---|
| 20% | +24.6 | 1.9 |
| 30% | +35.6 | 3.1 |
| 40% | +39.2 | 3.8 |
| 50% | +23.5 | 1.9 |
| 60% | +14.9 | 0.7 |
| 70% | +13.4 | 0.9 |
| 80% | +13.6 | 1.7 |
| 90% | +17.5 | 3.3 |
The controls hold
- Shuffled-label control:
0.0315, against a chance level of0.0312. A probe of this capacity extracts nothing from noise, so the measured decodability is not fitting artefact. - Instrument check: the probe matches the model at the end in 10 of 10 runs (
0.9923against0.9917). This is the load-bearing control, for the reason below.
The correction that changes everything about this record
The first version of this pilot returned the opposite verdict, and it was wrong.
| First version | Corrected | |
|---|---|---|
| Lead | +1.5 steps [-0.0, +3.0] | +23.5 steps [+22.1, +24.9] |
| Runs with a resolvable lead | 1 / 10 | 10 / 10 |
| Verdict | killed | leading indicator |
Nothing about the models changed. The entire verdict flipped on probe strength, through two independent weaknesses:
- The probe was the wrong estimator. Closed-form ridge regression onto one-hot targets is a weak classifier at high accuracy. It ended training at
0.9303while the model reached0.9917: an optimally fitted readout losing to a trained one by 6 points, which is not possible if the probe is doing its job. It was replaced with a cross-entropy-fitted linear classifier, using the ridge solution as its starting point. - The probe was sample-limited. With 512 sequences it fits 1,568 parameters on 3,328 rows and under-fits badly. Raising the fitting set to ~26,000 scored positions closed the remaining gap.
Crucially, the weakness biased the answer toward the null. The under-powered probe was overtaken by the model before the 50% crossing, so its crossing was delayed by its own incapacity, and the measured lead collapsed toward zero. A weak instrument does not produce noise here; it produces a confident, wrong negative.
Standing rule adopted from this. A null result from a probe is a statement about the probe until the probe is validated against a known-achievable target. Every probe in this project must now clear an instrument check, for a readout probe, matching the trained readout at convergence , and that check must be reported alongside the result.
This is the second time in program v2 that a measurement, not a model, produced the headline: D6 found that the post-peak fall was a property of the measuring frame. Both were caught by asking what the instrument could and could not do, rather than by re-examining the data.
An observation worth carrying to F3
At step 1, before any meaningful training, the probe already reads 0.1761 against the model's 0.0368, about 5.6x chance. A substantial part of the answer is linearly present in an almost untrained recurrent state.
That is the echo-state hypothesis (F3) appearing unbidden: random recurrent dynamics already carry usable information about the lagged token, and part of what training does is learn to read what was largely already there rather than to create it. F3 should be run next, and this pilot has already given it a nonzero prior.
What this changes for the program
- The central obstacle is partially removed. Program v2's constraint table records that the transition signal is coincident, not leading. That remains true of the geometry signal. It is now false in general: a decode-probe gap leads by 23 steps.
- Bucket C's gate is half-satisfied. The gate requires D3 answering "smooth" and one of F2 / F1 / E4 producing a usable timing signal. F2 has produced one, so D3 is now the sole remaining gate and its priority rises accordingly.
- The signal is usable online. The probe needs labels, and during training the labels are in hand. Fitting it is one linear solve plus a short refinement, negligible against a training step.
- A4's non-oracle version becomes possible. The transition kick needed to act before the transition and had no way to know when that was. It now has a candidate.
Limits
- One architecture (
tiny-gru), one task, one width (48), one optimizer (AdamW). D8 showed that timing claims in this project can belong to the optimizer rather than to learning, so F2 under SGD is a required follow-up before anything is built on it. - The lead is measured between two accuracy curves crossing a level. It is not yet demonstrated that the gap predicts the transition step across seeds, with transitions spanning only ~10 steps here there is little variance to correlate against, the same limitation that made A9 unanswerable. Establishing predictive power needs the wider transition spread that a learning-rate or width sweep would give.
- 23 steps is a real lead but a short one. Whether it is enough to act on is A4's question, not this one.