Interference in mg7: madevent helicity convention, IDWTUP -4, signed-weight fixes

[oliviermattelaer]

Phase 1 of doc/interference_madmatrix_madspace_plan.md.

Where things stood

• madmatrix (CPU) has supported squared split orders since madmatrix: squared split orders, so the interference syntax stops returning the total #125.
• madspace already integrates and unweights signed weights correctly: it keeps a signed and an |w| accumulator per channel, accepts on |w| and restores the sign with copysign.
• Cross sections agree with madevent:
  • p p > u u~ QCD^2==2: −9481(84) vs −9532(63) pb;
  • p p > j j QCD^2==2: 5.283(87)e4 vs 5.263(53)e4 pb.
• What was still wrong for an interference (negative total, signed per-helicity contributions) is fixed here.

Changes

madmatrix: helicity choice.

• The per-event helicity was chosen on the signed running sum over helicities, divided by the signed total. With mixed signs that is not a distribution, so the helicity column of the events was wrong, even though the totals were right. For a Z/γ interference, the per-helicity σ was off by up to 16σ from madevent.
• It now follows madevent: pick helicity i with probability |T_i|/Σ|T| and return sign(T_i)·Σ|T|.
• This is compiled in only when nampso > 1, so every other process compiles exactly as before.
• It is switched on only when the caller gives a random helicity number (umami, i.e. event generation). Systematics re-evaluation, check_sa and fbridge keep the helicity sum ΣT.
• The GPU kernel gets the same rule; see the GPU section below.

Opt-out: interference_helicity. The run card [generation] interference_helicity = "exact" | "summed" controls the helicity choice; the default, "exact", is the madevent convention above.

• "summed" keeps the helicity sum as the weight, which means lower variance; on the heft sample it brings σ_abs from 5.57 back to 4.16 pb.
• The helicities of the interference subprocesses are then written as 9 on every LHE line.
• It reaches the library as the umami parameter interference_helicity_summed, sent only when asked for, because older libraries refuse unknown parameters.

LHE <init>. Negative-weight samples now write IDWTUP = -4, as madevent does, with XMAXUP = σ_abs. Previously it was +3 with XMAXUP = σ. It has to be −4 and not −3: Pythia8 8.317 reads −3 as |XSECUP|·⟨sign⟩.

p p > u u~ QCD^2==2	σ (pb)
mg7	−9635(40)
Pythia8, IDWTUP −3	−6405
Pythia8, IDWTUP −4	−9678(75)

Positive samples are unchanged.

Smaller fixes:

• systematics percentages are measured against |nominal|;
• channel pruning ranks channels by the integral of |w|;
• the MadNIS BufferUnweighter takes the quantile of |w| (see the buffer section below);
• the relative error is printed against |mean|;
• the weight histogram is in units of σ_abs, with a symmetric range for squared-order processes;
• a plot with a negative bin keeps a linear axis;
• the generic xsec acceptance test divides by |reference|, since a negative reference always passed.

Validation

• Per-helicity values. On heft g g > t t~ HIG^2==1 (m_H = 500 GeV), at five fixed points with mixed-sign helicities, the per-helicity values drawn equal Fortran SMATRIXHEL to the grid step, with the same labels and signs.
  • The total cross section is unchanged: −0.405(16) vs −0.402(12) pb.
  • σ_abs goes from 4.16 to 5.57 pb.
• Builds. The d, f, m and scalar builds all compile; the mixed-precision second page is checked too.
• New test_cmd.py::test_standalone_interference_helicity_choice (u u~ > t t~ g QED^2==2). It drives the library through umami via ctypes, and fails with the old choice.
• New test_mg7_interference.py (p p > u u~ QCD^2==2). It checks the cross section against −12253(10) pb, the <init> block and the signed events.
  • The reference comes from three mg7 seeds of 200k events.
  • madevent gives −12340(42) pb with the same settings, 0.7% / 2σ away. That is within the tolerance and was not chased.
• Existing suites:
  • unit: banner, mg7_launch, plots, hwu, systematics_summary;
  • madspace pytest: 1706 passed, 11 skipped;
  • six positive mg7 xsec regression tests (ppjjj, ttx1j) pass.

MadNIS buffer

BufferUnweighter, the partial unweighting of the MadNIS replay buffer, accepts on |w| but took its maximum weight from the quantile of the signed weights.

Synthetic batches. It now has a Python binding and madspace/tests/test_buffer_unweighter.py. The table gives the fraction of events kept:

batch	signed quantile (old)	|w| quantile (new)
all positive	28.5%	28.5%
all negative	100% (no unweighting at all)	28.5%
mostly negative, short positive tail	94%	< 50%

The all-negative and mixed tests fail on the old code. The buffer stayed unbiased either way, because the rescaled adaptive_prob holds for any maximum weight.

Effect on training. It is not measurable on our samples. With MadNIS forced on for 4000 batches, the buffers reach capacity within about 1200 batches either way:

process	RSD, signed	RSD, |w|
p p > u u~ QCD^2==2	0.1081	0.1085
heft g g > t t~ HIG^2==1	0.0886	0.0880

With the default card the buffer is never used: buffer_skip_batches equals train_batches, both 1000.

GPU (phase 4): validated on CUDA (manneback)

The GPU backend refused nampso > 1 at compile time. It now follows the CPU implementation:

• calculate_jamps keeps njampso = ncolor × nampso jamps. DeviceAccessJamp and every device jamp buffer use njampso as the plane length, so nothing changes without split orders.
• color_sum_kernel pairs the jamps over all ordered pairs of amplitude orders, as color_sum_cpu_splitorders does.
• sqSoIndex and chosenSqso are generated __device__ constexpr, which is an empty macro on CPU.
• The runtime cuBLAS colour sum is refused for split orders.
• add_and_select_hel uses the madevent helicity convention, behind the same flag as on CPU.
• GPU umami's helicity filtering now uses the per-helicity jamp buffer as scratch.

Validation on CUDA. Run 37917456030, on an NVIDIA A10 through the vmadgraph runner. This branch includes claude/vmadgraph-parallel-tasks-7fe363.

check	result
u u~ > u u~ QED^2==2	−5.5828746494657217e−02, against Fortran −5.5828746494657265e−02 (8.7e−16)
QED=0+2+4 against QED^2<=4	1.6e−16
FPTYPE=m	8.5e−9
umami helicity choice	11 of 16 points with mixed signs, as on CPU
mg7 p p > u u~ QCD^2==2	−12248(109) pb, IDWTUP −4, 4191 of 5000 events negative

Pre-existing GPU bug, fixed here. The first run found it. A process whose couplings are all flavour couplings, with none depending on α_s, declared zero-sized coupling arrays, which nvcc refuses in device code. One example is u u~ > u u~ QED^2==4 with flavour grouping. This was not specific to split orders.

lemaitre4 (HIP) has not been run yet.

CI job. The new interference job of gpu_runner_ci.yml (.github/gpu_ci/interference_gpu.sh and interference_checks.py) runs on "Run workflow" on manneback and lemaitre4. It is off on pushes to main until validated. It checks:

• standalone u u~ > u u~: the Fortran interference, the QED=0+2+4 sum rule, and FPTYPE=m;
• the helicity choice through umami, using device memory;
• mg7 p p > u u~ QCD^2==2 against the CPU reference.

On a CPU backend the script passes every check.

Not in this PR

• α_s power of the kept squared orders (phase 2): today qcd_power = -1 forces the systematics to re-evaluate the matrix element.
• [treextree] on mg7, which needs Interference processes: [LIxtree=QCD] and [treextree] left/right syntax #243.
• Massive-leg helicities in mg7 are lab-frame helicities, since there is no me_frame boost on main, while madevent's are partonic-CM ones. This predates this PR.