wai-quantum 0.3.39: the square's whole space group, a referee in each sector, and guided sampling #188

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dcharlot merged 6 commits from wai-quantum-nqs-pointgroup into main 2026-10-09 02:40:52 -04:00

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dcharlot commented 2026-10-08 10:33:37 -04:00

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wai-quantum 0.3.39. The square lattice's whole space group for neural-quantum-state projection, an exact referee inside each symmetry sector, and guided sampling. Together they take the periodic 4 × 4 J₁–J₂ lattice at J₂ = 0.5 to its ground energy to 1.7·10⁻¹² with a complex α = 1 network in 600 steps. That is on a sector of 107 configurations, against 288 parameters: see Measured.

• Symmetry::square(l, momentum_pi, irrep) — every translation of an l × l torus, each composed with the eight rotations and reflections about a site, in one of their four one-dimensional representations (PointIrrep::{A1, A2, B1, B2}), at momentum 0 or (π, π). Both momenta are left alone by every rotation and reflection, so a point-group character extends to the whole group.
• Symmetry::check() — proves a set of elements a group under composition and its characters ±1 and multiplicative. Without that, Σ_g χ(g) ψ(g·s) projects onto a mixture or onto nothing. ring and torus now refuse a momentum π that their lengths cannot carry.
• SpinModel::exact_ground_energy_in(magnetisation, &Symmetry) — Lanczos on P H P, re-projected after every product so rounding cannot drift into a lower sector. A projected network is now held to its own sector's ground energy. It refuses a set that is not a group, a model the group does not preserve (SpinModel::commutes_with), a flip out of a nonzero magnetisation, and an empty sector.
• Both referees work on the magnetisation sector's own amplitudes rather than all 2ⁿ, with the same start values and the same order of sums. The 22 determinism pins are unchanged.
• CLI and nqs_ground take --point-group a1|a2|b1|b2 and report the exact energy in the projection's sector.
• A projected network starts at ±0.1 (was ±0.01; --init sets it). Near zero, a projected network is nearly the projection of a constant: the uniform superposition, which at zero magnetisation is the ferromagnet's member, an eigenstate whose energy gradient vanishes. Unprojected runs keep ±0.01.
• nqs_ground --exact-final evaluates the trained network over every configuration, separating what training left from what sampling adds.
• VmcConfig::guide samples |ψ|² + guide·|ψ̄|², |ψ̄| the chains' typical amplitude when the batch starts, and weights each sample back by |ψ|² over that, with the error of a weighted mean. Near a node the local energy is a large number over a small one, and |ψ|² visits too rarely for the variance to be measured; the floor visits. Zero (the default) samples |ψ|² exactly as before. Projected networks in the CLI and nqs_ground sample with a guide of 0.1 (--guide sets it).
• No chain starts where the projection vanishes. A configuration fixed by an element of character −1 has no amplitude; every move from it has ratio zero, so a chain started there never left, and its samples fed the estimates the diagonal energy alone. At momentum (π, π) in A₁ on the 4 × 4 lattice a quarter of configurations are such, and a test with 32 chains found one stuck after burn-in. A chain now redraws its start; an unprojected network never does. The sector the 4 × 4 runs below used has no such configurations.
• Acceptance counts proposals. A draw of two parallel spins proposes nothing and no longer counts as a rejection; the moves and the draws are unchanged.

Checked

• Every square space group on 3 × 3 and 4 × 4, at both momenta, in every representation, with and without the flip, closes and multiplies its characters. A character that does not multiply, a set that does not close, and a character other than ±1 are each refused.
• On the 4 × 4 square, a projected network is multiplied by its representation's character under a quarter turn, an axis reflection and a diagonal reflection, and by −1 under a unit translation at (π, π), in all four representations.
• On a 10-site ring, the sector of momentum π and odd parity holds the ground state to 10⁻⁹, and the sector of momentum 0 and even parity lies above it.
• On the periodic 4 × 4 J₁–J₂ lattice at J₂ = J₁/2, the sector even under every rotation and reflection at momentum zero holds the ground state (−8.45792335) to 10⁻⁹; the one odd under a quarter turn lies above it.
• Refusals: open boundaries under ring translations, a flip with nonzero magnetisation, and a σᶻ field under the flip.
• Guided sampling: on a projected 8-site ring, guided estimates agree with enumeration (energy within 5σ, variance within 20 %), and steps repeat bit for bit at any thread count.
• The start: from ±0.01 the projected 8-site ring starts on the ferromagnet (E = n/4, variance below 10⁻³) and is still within 10⁻² of it after 40 steps; from ±0.1 it reaches the ground state to 10⁻³ in 200.

Measured

Periodic 4 × 4 J₁–J₂ at J₂ = 0.5 (exact −8.45792335; the next state in its sector is 13 % higher). A complex α = 1 network, 600 steps of 1000 samples, its energy then taken over every configuration:

projection, even parity	start	relative error
translations	±0.01	1.87·10⁻²
translations	±0.1	1.90·10⁻²
space group, A₁	±0.01	2.09·10⁻²
space group, A₁	±0.1	1.27·10⁻³
space group, A₁	±0.3	1.09·10⁻³
space group, A₁, guided 0.1	±0.1	1.7·10⁻¹²
space group, A₁, guided 1	±0.1	1.2·10⁻¹²

Unguided from ±0.1, 2000 steps reach 4.60·10⁻⁴, and α = 2 reaches 6.91·10⁻⁴ in 600. Guided, the variance over every configuration is below 4·10⁻¹¹.

The sector is small: 107 configurations up to its symmetries, against the network's 288 parameters. Reaching it to rounding says the training finds what the network can hold, not how it does where the sector is larger than the network. Unprojected, the guide changes nothing (2.78·10⁻² over every configuration, the documented ~3 %).

On the 8-site ring (every configuration enumerated, 200 steps), the start alone moves the result from 2.8·10⁻² (±0.01) to 2.6·10⁻⁴ (±0.1) and 5·10⁻⁷ (±0.3).

The sampled variance is not the variance, and the sampled energy is not a bound. The ±0.01 space-group run reported 1.4·10⁻² from its final 8000 samples; over every configuration its variance is 0.55. 89 % of that sits in two configurations related by symmetry, each of probability 2.6·10⁻⁶ (expected 0.02 times in 8000 samples), where the local energy is 310 from the mean: amplitudes near a node.

• Not the chains: thinning tenfold reported 1.9·10⁻²; 64 000 samples hit one of the two and reported 1.55.
• The ±0.1 network is the same: 97 % of its variance sits in configurations whose probabilities total 2.4·10⁻³.
• Across both networks and three samplings, every sampled energy came out below the enumerated one (by at most 4·10⁻⁴ relative): the unsampled tail lies above the mean.

A guide brings a spread tail into view, not a needle. On the ±0.1 network, guided sampled variances came within 5 % of the exact one at every floor from 0.01 to 1, four seeds each; unguided seeds gave 0.11 to 2.0 times it. The ±0.01 network's variance sits in two configurations of 12 870, which no 8000 samples visit reliably: guided seeds still gave 0.1 to 2.3 times it.

The reported acceptance now counts proposals only (a draw of two parallel spins proposes nothing; it was counted as a rejection). Moves and draws are unchanged, so every trajectory is the same bits.

The translation-only run repeats an earlier run's trajectory bit for bit at a different thread count, and its sampled final estimate is the documented 1.7 %.

Gates

• cargo test --release --features full --lib quantum_nqs: 19 passed. The new tests take at most 22 s in debug under a loaded host.
• --locked resolves in all five lockfiles that pin wai-quantum (wai-quantum, wai-quantum-serve, wai-rs, wai-web, wai-pack).
• cargo test --release --features full --test bit_identity: 22 passed, digests unchanged.
• clippy (--lib --tests --examples): clean in the module and the example.
• scripts/check-comparative-prose.sh, scripts/check-no-vanity-metrics.sh: clean.

🤖 Generated with Claude Code

## What wai-quantum 0.3.39. The square lattice's whole space group for neural-quantum-state projection, an exact referee inside each symmetry sector, and guided sampling. Together they take the periodic 4 × 4 J₁–J₂ lattice at `J₂ = 0.5` to its ground energy to `1.7·10⁻¹²` with a complex `α = 1` network in 600 steps. That is on a sector of 107 configurations, against 288 parameters: see Measured. - **`Symmetry::square(l, momentum_pi, irrep)`** — every translation of an `l × l` torus, each composed with the eight rotations and reflections about a site, in one of their four one-dimensional representations (`PointIrrep::{A1, A2, B1, B2}`), at momentum 0 or (π, π). Both momenta are left alone by every rotation and reflection, so a point-group character extends to the whole group. - **`Symmetry::check()`** — proves a set of elements a group under composition and its characters `±1` and multiplicative. Without that, `Σ_g χ(g) ψ(g·s)` projects onto a mixture or onto nothing. `ring` and `torus` now refuse a momentum π that their lengths cannot carry. - **`SpinModel::exact_ground_energy_in(magnetisation, &Symmetry)`** — Lanczos on `P H P`, re-projected after every product so rounding cannot drift into a lower sector. A projected network is now held to its own sector's ground energy. It refuses a set that is not a group, a model the group does not preserve (`SpinModel::commutes_with`), a flip out of a nonzero magnetisation, and an empty sector. - **Both referees work on the magnetisation sector's own amplitudes** rather than all `2ⁿ`, with the same start values and the same order of sums. The 22 determinism pins are unchanged. - **CLI and `nqs_ground`** take `--point-group a1|a2|b1|b2` and report the exact energy in the projection's sector. - **A projected network starts at `±0.1`** (was `±0.01`; `--init` sets it). Near zero, a projected network is nearly the projection of a constant: the uniform superposition, which at zero magnetisation is the ferromagnet's member, an eigenstate whose energy gradient vanishes. Unprojected runs keep `±0.01`. - **`nqs_ground --exact-final`** evaluates the trained network over every configuration, separating what training left from what sampling adds. - **`VmcConfig::guide`** samples `|ψ|² + guide·|ψ̄|²`, `|ψ̄|` the chains' typical amplitude when the batch starts, and weights each sample back by `|ψ|²` over that, with the error of a weighted mean. Near a node the local energy is a large number over a small one, and `|ψ|²` visits too rarely for the variance to be measured; the floor visits. Zero (the default) samples `|ψ|²` exactly as before. Projected networks in the CLI and `nqs_ground` sample with a guide of 0.1 (`--guide` sets it). - **No chain starts where the projection vanishes.** A configuration fixed by an element of character −1 has no amplitude; every move from it has ratio zero, so a chain started there never left, and its samples fed the estimates the diagonal energy alone. At momentum (π, π) in A₁ on the 4 × 4 lattice a quarter of configurations are such, and a test with 32 chains found one stuck after burn-in. A chain now redraws its start; an unprojected network never does. The sector the 4 × 4 runs below used has no such configurations. - **Acceptance counts proposals.** A draw of two parallel spins proposes nothing and no longer counts as a rejection; the moves and the draws are unchanged. ## Checked - Every square space group on 3 × 3 and 4 × 4, at both momenta, in every representation, with and without the flip, closes and multiplies its characters. A character that does not multiply, a set that does not close, and a character other than `±1` are each refused. - On the 4 × 4 square, a projected network is multiplied by its representation's character under a quarter turn, an axis reflection and a diagonal reflection, and by −1 under a unit translation at (π, π), in all four representations. - On a 10-site ring, the sector of momentum π and odd parity holds the ground state to `10⁻⁹`, and the sector of momentum 0 and even parity lies above it. - On the periodic 4 × 4 J₁–J₂ lattice at `J₂ = J₁/2`, the sector even under every rotation and reflection at momentum zero holds the ground state (`−8.45792335`) to `10⁻⁹`; the one odd under a quarter turn lies above it. - Refusals: open boundaries under ring translations, a flip with nonzero magnetisation, and a `σᶻ` field under the flip. - Guided sampling: on a projected 8-site ring, guided estimates agree with enumeration (energy within 5σ, variance within 20 %), and steps repeat bit for bit at any thread count. - The start: from `±0.01` the projected 8-site ring starts on the ferromagnet (`E = n/4`, variance below `10⁻³`) and is still within `10⁻²` of it after 40 steps; from `±0.1` it reaches the ground state to `10⁻³` in 200. ## Measured Periodic 4 × 4 J₁–J₂ at `J₂ = 0.5` (exact `−8.45792335`; the next state in its sector is 13 % higher). A complex `α = 1` network, 600 steps of 1000 samples, its energy then taken over every configuration: | projection, even parity | start | relative error | |---|---|---| | translations | ±0.01 | 1.87·10⁻² | | translations | ±0.1 | 1.90·10⁻² | | space group, A₁ | ±0.01 | 2.09·10⁻² | | space group, A₁ | ±0.1 | 1.27·10⁻³ | | space group, A₁ | ±0.3 | 1.09·10⁻³ | | space group, A₁, **guided 0.1** | ±0.1 | **1.7·10⁻¹²** | | space group, A₁, **guided 1** | ±0.1 | **1.2·10⁻¹²** | Unguided from ±0.1, 2000 steps reach 4.60·10⁻⁴, and `α = 2` reaches 6.91·10⁻⁴ in 600. Guided, the variance over every configuration is below 4·10⁻¹¹. **The sector is small**: 107 configurations up to its symmetries, against the network's 288 parameters. Reaching it to rounding says the training finds what the network can hold, not how it does where the sector is larger than the network. Unprojected, the guide changes nothing (2.78·10⁻² over every configuration, the documented ~3 %). On the 8-site ring (every configuration enumerated, 200 steps), the start alone moves the result from 2.8·10⁻² (`±0.01`) to 2.6·10⁻⁴ (`±0.1`) and 5·10⁻⁷ (`±0.3`). **The sampled variance is not the variance, and the sampled energy is not a bound.** The `±0.01` space-group run reported 1.4·10⁻² from its final 8000 samples; over every configuration its variance is 0.55. 89 % of that sits in two configurations related by symmetry, each of probability 2.6·10⁻⁶ (expected 0.02 times in 8000 samples), where the local energy is 310 from the mean: amplitudes near a node. - Not the chains: thinning tenfold reported 1.9·10⁻²; 64 000 samples hit one of the two and reported 1.55. - The `±0.1` network is the same: 97 % of its variance sits in configurations whose probabilities total 2.4·10⁻³. - Across both networks and three samplings, every sampled energy came out *below* the enumerated one (by at most 4·10⁻⁴ relative): the unsampled tail lies above the mean. **A guide brings a spread tail into view, not a needle.** On the `±0.1` network, guided sampled variances came within 5 % of the exact one at every floor from 0.01 to 1, four seeds each; unguided seeds gave 0.11 to 2.0 times it. The `±0.01` network's variance sits in two configurations of 12 870, which no 8000 samples visit reliably: guided seeds still gave 0.1 to 2.3 times it. The reported acceptance now counts proposals only (a draw of two parallel spins proposes nothing; it was counted as a rejection). Moves and draws are unchanged, so every trajectory is the same bits. The translation-only run repeats an earlier run's trajectory bit for bit at a different thread count, and its sampled final estimate is the documented 1.7 %. ## Gates - `cargo test --release --features full --lib quantum_nqs`: 19 passed. The new tests take at most 22 s in debug under a loaded host. - `--locked` resolves in all five lockfiles that pin wai-quantum (wai-quantum, wai-quantum-serve, wai-rs, wai-web, wai-pack). - `cargo test --release --features full --test bit_identity`: 22 passed, digests unchanged. - clippy (`--lib --tests --examples`): clean in the module and the example. - `scripts/check-comparative-prose.sh`, `scripts/check-no-vanity-metrics.sh`: clean. 🤖 Generated with [Claude Code](https://claude.com/claude-code)

dcharlot added 2 commits 2026-10-08 10:33:37 -04:00

wai-quantum: the square's whole space group, and a referee in each sector ... 6ec74bd9dc

Symmetry::square projects onto the translations of an l × l torus with
the eight rotations and reflections, in one of their four
one-dimensional representations (PointIrrep), at momentum 0 or (π, π).
Symmetry::check proves a set of elements a group and its characters
multiplicative; ring and torus now refuse a momentum π their lengths
cannot carry.

SpinModel::exact_ground_energy_in is Lanczos on P H P, re-projected
after every product, so a projected network is held to its own
sector's ground energy. It refuses a set that is not a group, a model
the group does not preserve (commutes_with), and a flip out of a
nonzero magnetisation. Both referees now work on the magnetisation
sector's own amplitudes rather than all 2^n, with the same start and
the same order of sums.

The CLI and nqs_ground take --point-group a1|a2|b1|b2 and report the
exact energy in the projection's sector.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

wai-quantum 0.3.39: a projected network starts off the ferromagnet ... 1b2afe0c7d

A projected network whose parameters start near zero is nearly the
projection of a constant: the uniform superposition, which at zero
magnetisation is the ferromagnet's member, an eigenstate whose energy
gradient vanishes. On the 8-site ring a ±0.01 start ends 2.8e-2 above
the ground state after 200 enumerated steps, ±0.1 ends 2.6e-4 above.
On the periodic 4 × 4 J1-J2 lattice at J2 = 0.5 the space group from
±0.01 ended at 2.09e-2 and from ±0.1 at 1.27e-3 (600 steps, energies
over every configuration); translations alone ended at 1.9e-2 from
either. Projected networks in the CLI and nqs_ground now start at
±0.1; --init sets it.

nqs_ground --exact-final evaluates the trained network over every
configuration. The sampled variance of the ±0.01 space-group run was
1.4e-2; its variance over every configuration is 0.55.

A test holds the trap: from ±0.01 the projected 8-site ring starts on
the ferromagnet and is still there after 40 steps; from ±0.1 it reaches
the ground state to 1e-3 in 200.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

dcharlot added 1 commit 2026-10-08 11:39:16 -04:00

wai-quantum: the sampled variance misses a tail near the nodes ... 7dd6fc1710

Measured on the trained 4 × 4 networks with every configuration
enumerated: 89 % of the ±0.01 network's variance (0.55; sampled
1.4e-2) sits in two configurations of probability 2.6e-6 each, where
the local energy is 310 from the mean. Thinning tenfold does not find
it; 64 000 samples hit one and report 1.55. For the ±0.1 network 97 %
of the variance sits in configurations whose probabilities total
2.4e-3. Every sampled energy came out below the enumerated one, by at
most 4e-4 relative. The docs had put it down to the chains; it is the
tail.

Acceptance now counts proposals: a draw of two parallel spins
proposes nothing and was being counted as a rejection. Moves and
draws are unchanged, so every trajectory is the same bits.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

dcharlot added 1 commit 2026-10-08 11:39:40 -04:00

wai-quantum: the 4 × 4 space group after 2000 steps, and at α = 2 ... 01b4cbac38

From ±0.1 a complex α = 1 network reaches 4.60e-4 in 2000 steps, and
α = 2 reaches 6.91e-4 in 600; both energies over every configuration.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

dcharlot added 1 commit 2026-10-08 11:52:50 -04:00

wai-quantum: no chain starts where the projection vanishes ... 9ddd8eb7c1

A configuration fixed by a group element of character −1 has no
amplitude in the sector. Every move from it has ratio zero, so a chain
started there never left, and each of its samples fed the estimates
the diagonal energy alone. At momentum (π, π) in A1 a quarter of the
4 × 4 lattice's configurations are such; a test with 32 chains found
one stuck after burn-in. A chain now draws its start again until the
amplitude is finite. An unprojected network never redraws, and the
sector the documented 4 × 4 runs used has no such configurations.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

dcharlot added 1 commit 2026-10-08 12:59:19 -04:00

wai-quantum: guided sampling, and the 4 × 4 space group to rounding ... 0d59375329

VmcConfig::guide samples |ψ|² + guide·|ψ̄|² instead of |ψ|², |ψ̄| the
chains' typical amplitude when the batch starts, and weights each
sample back by |ψ|² over that; the error is then that of a weighted
mean. Near a node of the network the local energy is a large number
over a small one and |ψ|² visits too rarely for the variance to be
measured; the floor visits. Zero, the default, samples |ψ|² as before:
every pin and documented unguided figure is unchanged.

On the trained 4 × 4 J1-J2 networks, enumerated: the ±0.1 network's
guided variance came within 5 % of the exact one at every floor from
0.01 to 1, four seeds each (unguided seeds: 0.11 to 2.0 times it). The
±0.01 network's variance sits in two configurations of 12 870, which
no 8000 samples visit reliably; guided seeds still gave 0.1 to 2.3
times it.

Trained guided at 0.1 or 1, the same complex α = 1 space-group
network, start and 600 steps reach the ground energy to 1.7e-12 and
1.2e-12 (unguided: 1.27e-3), variance below 4e-11. The sector holds
107 configurations up to symmetry against 288 parameters; the docs say
so. Unprojected, the guide changes nothing (2.78e-2). Projected
networks in the CLI and nqs_ground now sample with a guide of 0.1.

A test holds guided estimates to enumeration on a projected 8-site
ring (energy within 5σ, variance within 20 %) and bit-identity across
thread counts.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

dcharlot changed title from wai-quantum 0.3.39: the square's whole space group, a referee in each sector, and a start off the ferromagnet to wai-quantum 0.3.39: the square's whole space group, a referee in each sector, and guided sampling 2026-10-08 12:59:34 -04:00

dcharlot merged commit 80b26b2883 into main 2026-10-09 02:40:52 -04:00

dcharlot referenced this pull request from a commit 2026-10-09 02:40:54 -04:00

Merge pull request 'wai-quantum 0.3.39: the square's whole space group, a referee in each sector, and guided sampling' (#188) from wai-quantum-nqs-pointgroup into main

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