Computation that keeps presence and absence apart, and collapses to a decision only at the edge — with a genuine, first-class hold.
A visible 0 is not one thing. In binary you never have to decide what 0 means — it's just "not‑1", off, false‑by‑default. Add a third possibility and 0 turns out to be plural: additive identity, false, unknown, null, high‑impedance, ground, abstain, origin. Those are different ideas wearing one glyph, and they don't share a truth table.
uncollapsed takes the middle seriously. It stops storing a single scalar in [-1, +1] and instead keeps two independent non‑negative channels — presence and absence — so four very different states can live behind the same visible 0, and so a decision is a deliberate act at the boundary rather than a default that quietly happens.
the same visible 0, four different inner states
┌────────────┬──────────┬──────────┬──────────────────────────┐
│ void │ presence │ absence │ nothing there │
│ calm │ small │ small │ low-energy balance │
│ conflict │ high │ high │ both poles strong ← ! │
│ lean │ differ │ differ │ a directional tilt │
└────────────┴──────────┴──────────┴──────────────────────────┘
A two-channel net learning noisy XOR — and learning where to abstain. The gold band is HOLD.
📖 Full documentation: https://jfinst1.github.io/uncollapsed/
The whole point of reaching past binary is to get a presence‑zero — a held, positive, central state that actively means something — instead of the absence‑zero binary hands you (a pole, defined by negation, that quietly means "no"). Binary is impatient: every bit is a box already opened. uncollapsed is built to hold the question open and resolve only when there is real force to resolve it — and, crucially, never to default a genuine contradiction to "no".
See docs/theory.md for the full background.
pip install -e ".[dev]" # from a clone
# or, minimal:
pip install -e . # core (numpy only); add [viz] for the plotfrom uncollapsed import UncollapsedField
void = UncollapsedField.void() # nothing there
calm = UncollapsedField(0.18, 0.18) # low-energy centre
conflict = UncollapsedField(0.90, 0.90) # both poles strong
lean = UncollapsedField(0.85, 0.35) # a tilt toward presence
for f in (void, calm, conflict, lean):
m = f.mass()
print(f.icon().glyph(), # all four show "0" or a lean
f"belief={m.belief:.2f} conflict={m.conflict:.2f} void={m.voidness:.2f}",
"->", f.collapse().result.value) # ... but collapse very differentlyA balanced contradiction holds instead of collapsing, and — even under forced pressure — it escalates rather than defaulting to absence. Pressure is recorded, but it is not treated as evidence:
from uncollapsed.field import CollapsePolicy
loaded = UncollapsedField(1.2, 1.2, pressure=1.0, pressure_bias=-1.0)
loaded.collapse(forced=True).result # -> Collapse.ESCALATE (never ABSENCE)
bad = CollapsePolicy(allow_pressure_to_break_ties=True) # you have to *ask* for the bad behaviour
loaded.collapse(policy=bad, forced=True).result # -> Collapse.ABSENCEHidden units carry (presence, absence) all the way through; only the output edge collapses. Synapses use one signed weight whose sign swaps the channels (balanced‑ternary negation), made differentiable.
from uncollapsed.net import train, accuracy, grad_check
print(grad_check()) # ~2e-9: analytical == numerical gradients
net, (_, _, Xte, yte) = train(epochs=3000) # noisy XOR
accuracy(net, Xte, yte) # ~0.99 on UNSEEN noisy points => real learninguncollapsed --demo all
uncollapsed --demo learn --png surface.png
python -m uncollapsed --demo zeroRunning uncollapsed --demo learn:
- Gradient check:
max relative error ≈ 2e-9. The hand‑derived backprop matches numerical gradients — the learning is correct, not hand‑wavy. - Held‑out test accuracy ≈ 0.99 on noisy points the model never saw during training. Ninety‑nine percent on unseen data means it learned the XOR function, not a lookup table over four corners.
- Learned abstention. Trained purely to classify, the net is overconfident — it guesses at the ambiguous centre. Supervise the boundary toward
0.5and it learns to hold exactly where XOR is genuinely undecided, while staying accurate on the clear corners (~0.998).
The gold band below is the region the trained model collapses to HOLD — it abstains precisely along the lines where the answer is undecided. That gold region is presence‑zero, learned from data.
From the two channels (sp = 1 - e^-presence, sa = 1 - e^-absence):
| mass | formula | meaning |
|---|---|---|
belief |
sp (1 - sa) |
evidence only toward presence |
disbelief |
sa (1 - sp) |
evidence only toward absence |
conflict |
sp · sa |
both strong — a loaded contradiction |
voidness |
(1 - sp)(1 - sa) |
both weak — nothing there |
They sum to exactly 1 (the joint distribution of two independent Bernoulli channels). This is subjective‑logic / Dempster–Shafer flavoured, with two corrections that matter:
expectationprojects both conflict and voidness to the base rate, so a fully loaded contradiction reads~0.5, never0.0. A balanced "yes and no" is not secretly a "no".voidnessis high only when both channels are weak, so a confident‑but‑quiet lean isn't mislabelled as mostly void.
- Subjective‑logic‑exact conjunction/disjunction operators in
algebra.py. - Unsupervised abstention — hold driven by the field's own internal conflict, not by labels. (The interesting open problem.)
- Multi‑class / vector‑valued fields.
- A field‑gated readout layer usable as a drop‑in "I'm not ready to answer yet" head.
This is not built in a vacuum. The two‑channel field is closely related to subjective logic (Jøsang's belief/disbelief/uncertainty opinions), Dempster–Shafer evidence theory (belief vs. plausibility, and conflict K), intuitionistic fuzzy sets (membership/non‑membership/hesitation), and three‑valued logics (Kleene, Łukasiewicz). The distinctive commitments here are keeping conflict and voidness first‑class, and treating collapse as an explicit edge operation that can legitimately abstain.
@software{uncollapsed,
author = {Finstad, Jon},
title = {uncollapsed: presence/absence fields and edge collapse with a first-class hold},
year = {2026},
url = {https://github.com/jfinst1/uncollapsed}
}MIT — see LICENSE.