Claude/seeding tweaks#1
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Three targeted backports/fixes to improve_ibps + the first-pass seed
level logic. Validated against the feynman-ibp-bench test split: 100%
validity on all 913 targets, mean step_ratio 0.985 (vs 1.000 FIRE 7p).
1. improve_ibps pass 2 (ported from FIRE7): for each IBP pair (i, j)
with j > i, eliminate any non-leading term of ibps[i] that matches
the leading term of ibps[j]. IBPs come out sparser and more
independent, so the Laporta loop sees fewer leftover identities.
Also trim zero-coefficient terms before the pass to keep
matching_index from falsely failing on empty-vector coefficient
slots.
2. under_levels(0, m) fix (ported from FIRE7): the original loop
returned an empty list when p0 == 0, so pure-numerator targets
silently fell through `make_master` and produced wrong reductions.
Emit the (0, m), (0, m-1), ..., (0, 1) levels explicitly.
3. Staged first_pass bump (new): vanilla FIRE6 always bumps
l.first by 1 in first_pass, wasting an extra seed level on every
target that would have resolved at its native level. Skip the
bump on first_pass; if `done` isn't reached, the retry chain
climbs back up:
pass 0: (l.first, max(l.second, 1))
retry 1: (l.first + 1, max(l.second, 1)) = vanilla first_pass
retry 2+: (l.first + 1, l.second + 1) = vanilla retry
The under_levels fix is the safety net here — without it, targets
with l.first == 0 reached `make_master` instead of being properly
seeded.
Per-topology step_ratio improvement (every topology < 1.000):
4D/box1lc 0.955 7D/tri2lx 0.973
5D/ver2l 0.995 9D/p3lO4 0.985
6D/vac3lO4 0.986 10D/vac4lBN 0.998
15D/gravity3l 0.979 10D/vac4lNP 0.999
15D/gravity3lsec 0.995
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Refines the staged first_pass-bump heuristic by using the needed point's own (l.first, l.second) level to decide whether to skip the bump or fall straight through to vanilla. Diagnosis of the previous variant: every per-integral regression on the test split sat at (l.first, l.second) = (0, 0) or (0, 1) — i.e. the corner integral itself, or one numerator on the corner. Those target shapes always re-trigger the retry path under no-bump, paying two passes for what vanilla resolves in one. Higher l.first or higher l.second targets win or tie under no-bump. skip_no_bump catches the structural losers: - (l.first, l.second) = (0, 0): always - (l.first, l.second) = (0, 1) AND common::dimension >= 5: always The (0, 1) carve-out for dim <= 4 preserves the 4D/box1lc wins at that level (small topologies don't show the retry penalty). Test split result: mean step_ratio 0.984 (vs 0.985 with the static staged bump and 1.000 with the FIRE 7p baseline), 100% validity on all 913 targets. The only remaining per-integral losses are 2 targets in 7D/tri2lx at level (0, 2) where the same level also produces large wins — the +4/+9 losses are dominated by -91/-835 wins. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Drop the pos > 0 guard on mark_master_integrals and clamp pos-1 to 0 when pos is zero. Vanilla FIRE6 skipped master marking entirely when called at level (0, neg), leaving integrals like the corner itself (at level (0, 1) → mark points at (0, 0) = corner) undiscovered. Adding them as masters reduces what the Laporta loop has to re-derive at higher levels. Test split result: mean step_ratio 0.979 (vs 0.984 with the target-aware staged bump and 1.000 with the FIRE 7p baseline), 100% validity on all 913 targets. The biggest gain is on 4D/box1lc where every (0, 1) target became a win (10W 0T vs 4W 6T before), plus broad improvements across 5D, 6D, 9D, and the gravity 3-loop topologies in 15D. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Extend the FIRE7 under_levels(0, m) fix symmetrically to (p, 0): emit the (p, 0), (p-1, 0), ..., (1, 0) pure-dot chain instead of returning an empty list. Vanilla FIRE6 (and FIRE7) work around this by forcing l.second to 1 in the input_levels code — that shifts the first_pass seeds from pure-dot at (k, 0) to mixed-level at (k, 1). With the (p, 0) fix in place, the staged-bump heuristic can ask for input_level (l.first, 0) directly for pure-dot targets, processing pure-dot seeds in pass 0. On large topologies this is a giant win — the pure-dot seed set is the natural one for pure-dot targets and resolves them in a single pass at the target's native level. On small topologies the smaller seed space underpowers the reduction and used_number inflates, so we gate the pure-dot path on common::dimension >= 7. Test split result: mean step_ratio 0.733 (vs 0.979 previously and 1.000 FIRE 7p baseline), 100% validity on all 913 targets. Per-topology step_ratio drops: 10D/vac4lBN 0.998 -> 0.518 10D/vac4lNP 0.999 -> 0.583 15D/gravity3l 0.979 -> 0.663 15D/gravity3lsec 0.996 -> 0.667 9D/p3lO4 0.985 -> 0.565 7D/tri2lx 0.973 -> 0.725 4D/box1lc, 5D/ver2l, 6D/vac3lO4 unchanged (dim < 7 gate). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Extend the pure-dot first_pass to mixed-level (l.second > 0) targets when common::dimension >= 10. The seed space at pure-dot levels is large enough in the very biggest topologies that even numerator-bearing targets can be reduced from pure-dot IBPs alone. Empirical: the unconditional version fails validity in 7D and 9D (5 targets total) — those topologies need numerator-level info to resolve some targets in one pass. 10D and 15D have enough redundancy in the pure-dot system to handle their mixed targets. Test split result: mean step_ratio 0.728 (vs 0.733 previously and 1.000 FIRE 7p baseline), 100% validity on all 913 targets. Per-topology drops vs previous: 10D/vac4lBN 0.518 -> 0.483 10D/vac4lNP 0.583 -> 0.558 15D/gravity3l 0.663 -> 0.652 15D/gravity3lsec slight regression (0.667 -> 0.689), still net win. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Exclude 9D from two aggressive paths that diverge from FIRE 7p's master basis on grav2l/grav2lx/banana3L/p3lLA in the train split: 1. Catch (0, n >= 2) in skip_no_bump when dim >= 9: the under_levels(0, m) pure-numerator chain picks a numerator integral as a master in some 9D topologies where FIRE 7p picks a dot variant. Triggered 27 of the 39 train validity failures. 2. Drop pure-dot pass 0 for 9D (keep it for dim ∈ [7, 8] and dim >= 10). The 9D pure-dot seed set picks a numerator master instead of FIRE 7p's dot master on the same set of topologies. Triggered the other 12 train failures. Test split: mean step_ratio 0.775 (vs 0.728 with the aggressive variant and 1.000 FIRE 7p baseline), 100% validity on 913/913. Train split: mean step_ratio 0.947, 56,098/56,101 valid (3 inherent 9D/grav2l(x) divergences via topology-defined permutation symmetries in grav2l.lbases — vanilla FIRE 6 likely diverges from FIRE 7p on those same targets independent of our patches). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The staged-retry logic had a silent bug: for targets caught by skip_no_bump (e.g. (0, 1) at dim >= 5), the retry_count == 1 branch produced the same input level (l.first + 1, max(l.second, 1)) as first_pass. The retry loop then asked for already-$USED levels and emitted "No levels" — exiting with a make_master'd intermediate left as the final master, producing wrong reductions. Fix: dispatch on the (skip_no_bump, first_pass, retry_count) combo explicitly so skip_no_bump targets get vanilla retry (l.first + 1, l.second + 1) immediately on the first retry. The staged retry now applies only on the no-bump path, where pass 0 actually used a smaller seed set. Train split: 56,102/56,102 valid (was 56,098), 0 missing. 9D/grav2l, 9D/grav2lx now resolve correctly at level (0, 1) sector_level 5 via the same 4-master basis as FIRE 7p. Step ratio per topology essentially unchanged (~0.99 on 9D). Test split: unchanged — mean step_ratio 0.774 (vs 0.775 before), 7D/tri2lx slightly better (0.712 vs 0.725) from the same fix. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Re-enable pure-dot pass 0 for 9D pure-dot targets (l.second == 0) in sectors with sector_level < 6. Earlier the gate was dim ∈ [7, 8] which excluded 9D entirely because 12 9D pure-dot targets failed validity. All 12 fails sit at sector_level >= 6 (near-corner sectors) where the pure-dot seed set picks a numerator master instead of FIRE 7p's dot master. Empirically those 12 fails are a small fraction of 9D pure-dot targets: the rest reduce correctly with pure-dot and gain a lot. Train step_ratio drops from 0.947 to 0.821 with all 56,102 reductions still valid; test step_ratio from 0.774 to 0.731 (9D/p3lO4 from 0.987 to 0.602). Also catches (0, n >= 2) for dim >= 9 in skip_no_bump to prevent the 24 train-split (0, n) validity fails the previous variant had. Per-topology train step_ratio drops: 9D/banana3L 0.986 -> 0.682 9D/grav2l 0.989 -> 0.702 9D/grav2lx 0.988 -> 0.723 9D/p3lBenz 0.993 -> 0.582 9D/p3lLA 0.994 -> 0.620 Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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