> Status: Mechanism note. The example run did not pass the 5-year gate > (rolling 30-day average Sharpe), so the numbers below illustrate the > vector → return summary → position map. They are not a performance claim.

Question

Does an STT (statistical) model “predict price,” or does it ask: when a similar past pattern showed up, how were next-day returns distributed — and turn that into a position?

This post explains the second path with figures.

One-line summary

1. An encoder maps a recent OHLC window into a vector z. 2. Training windows’ z values are clustered into groups (default 32). 3. Each group stores next-day return mean, dispersion (std), and count. 4. Position is tanh(mean / (std + ε)) clipped to [-1, 1]; too-few samples → 0. 5. At inference: new window → z → nearest group → that group’s stored position.

Figure 1. STT does not forecast prices directly. It looks up a past next-day return summary attached to a pattern address z.

Example run contract

The current recommended preset sparse_v1 also uses 10%/10% train/test. The earlier first-wave design used 30%/30%.

What “probability” is actually stored

Intuitively we want “the distribution of next-day returns given this vector.” The artifact does not keep the full histogram.

Per group it stores:

• mean_ret — mean next-day return of member windows
• std_ret — dispersion of those returns
• count — sample size
• position — precomputed [-1, 1] action from the summary
• centroids — group centers for nearest-neighbor lookup

So “looking at a probability distribution” really means: summarize samples at train time, then look up the summary table at runtime.

Figure 2. X = group mean next-day return (%), Y = std (%), color = stored position, point size = count. Higher mean and lower dispersion tend to push toward a stronger long position.

Largest |position| groups in this run:

A positive mean with a large std yields a smaller score, and thus a smaller tanh position.

Visualizing the stored summary

The curves below are normal approximations drawn from stored mean/std. They are not rebuilt empirical histograms.

Figure 3. Group 12 sits to the right with a=+0.75. Group 26 is also positive but has only five samples. Group 0 is near zero mean and near-zero position.

The point is not that the model samples a full distribution each day. It is that groups differ in location and width, and those differences drive position size.

What tanh does

score = mean_ret / (std_ret + eps)
a = 0                  if count < min_count
a = clip(tanh(score), -1, 1)   otherwise

score asks how large the mean is relative to dispersion. tanh soft-clips that score into [-1, 1] so the model does not jump straight to full long/short. Groups with fewer than min_count (here 5) samples are forced to flat (0).

Figure 4. The curve is tanh(score). Colored points are groups with enough samples; gray crosses are forced to zero. Points on the curve mean the stored position matches the formula.

Figure 5. All 32 groups sorted by position. In this example 18 are nonzero and 14 are zero for insufficient samples. Spreading 170 train windows across 32 bins naturally leaves some bins thin.

What happens at inference

For a new decision day:

1. Build the same OHLC window. 2. Encode to z. 3. Pick the nearest stored centroid. 4. Emit that group’s stored position as the target.

Runtime does not re-estimate the return distribution. It reads the lookup table frozen at training time.

What this post does not claim

• That this example run is deployable (it failed the 5Y gate).
• That the normal approximation is the true next-day return law.
• That a 10% random train split is optimal (adjacent-window leakage and thin

samples are known risks).

• That STT beats IQL (separate contracts: STT uses real prices only; IQL trains

the policy on synthetic transitions).

Reproduce

trading/agents/runs/stt_waves/sparse_v1/stt_franceschi_v1_btcusdt_20260727_135008/

# key files
return_groups.json   # mean_ret, std_ret, count, position, centroids
stt_meta.json        # window, train/test fractions, split indices

The position formula matches fit_return_groups in trading/agents/statistical/return_table.py.

Next

• Re-encode train windows and overlay empirical histograms on the normal

approximation

• Compare position dispersion across backbones and windows (32/64/128)
• Repeat the same figures only on STT candidates that pass the 5Y gate