τ? keep v6 · CASCADE
the cascade & the confidence trap · v6

THE CASCADE

v5 needed a regime cue to route. v6 asks: skip it. Run Dave's cheap silo first; escalate to the plain expert only when the silo is unsure — its own confidence is the router, no cue. Does it work? Only when the silo is calibrated — uncertain exactly when it's wrong. Two tasks prove the point: when it holds, you route the hard cases to plain for free; when it doesn't, the silo is confidently wrong and the cascade is blind.

The mechanism

Cheap first, escalate only when unsure

Every example runs the cheap silo (K²=16 attention pairs). If the silo's top-class probability clears a threshold τ, keep its answer. If not, escalate to the order-aware plain expert (+N²=64 pairs). The routing signal is the silo's own confidence — no regime cue, no learned router. The catch: confidence only tells you when to escalate if the silo is uncertain on the examples it gets wrong.

input no cue CHEAP SILO K²=16 pairs conf ≥ τ ? sure? yes · keep done · 16 pairs total no · escalate PLAIN EXPERT +N²=64 → 80 total
The held-out results · seed 0

Same cascade, two tasks — calibration decides

Both tasks are cue-free and differ only in whether the hard regime is legible in the content. Read each card: the three accuracy bars (silo alone / plain alone / the cascade), the acc-vs-compute curve (the cascade swept over τ, between the silo and plain points), and the two diagnostics — ECE (miscalibration; lower is better) and conf-AUC (does confidence predict correctness; 0.5 = blind).

Reading the diagnostics

Why calibration is the whole game

ECE — expected calibration error

Average gap between how confident the silo is and how often it's right, over confidence bins. A calibrated model has ECE ≈ 0. The entangled silo (0.12) is confidently wrong on the order examples — high confidence, low accuracy. The telegraphed silo (0.05) knows what it doesn't know.

conf-AUC — does confidence predict correctness

AUROC of the silo's confidence as a detector of "this answer is right." 0.5 = blind (confidence tells you nothing). Entangled 0.59 is near-blind; telegraphed 0.90 ranks right-above-wrong. A cascade routes on this number — so it inherits exactly the silo's (mis)calibration.

The colophon

What's real — and what it isn't

What's real

Both experts are genuinely trained from scratch (numpy Adam); selftest.py gradient-checks the hand-written backprop (< 1e-5) and asserts the core finding — the telegraphed silo really is better-calibrated (AUC 0.90 vs 0.59) and the cue-free cascade really closes ~100% of the silo→plain gap at 29% less compute than plain. Reproducible at seed 0 with python train.py.

What it isn't

A constructed contrast, not a claim about real data — the two tasks are built to isolate calibration; real workloads sit somewhere between. It is not "cascades beat routers": the cue-free cascade only matches plain when the regime is legible in the content. When it isn't (entangled), no cue-free method helps — the honest sequel to v5's catch. Tiny models, one seed, synthetic.

SOURCE · github.com/DavidWise01/transformer-silo-v6 · model.py (encoder + two experts + cascade + ECE/AUC, gradient-checked) · tasks.py (entangled + telegraphed, cue-free) · train.py → results.json · selftest.py. The hexalogy: build (v1) · measure (v2) · train one silo (v3) · two in parallel (v4) · route with a cue (v5) · route on confidence (v6).