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Controlling Polar Exposure to Delay Memorization in Diffusion Models

Xuanchen Wang, Heng Wang, Weidong Cai

arXiv:2610.02780v1cs.LG

TL;DR

Diffusion models can produce useful samples before detectable copying becomes prevalent, but optimizer geometry can change that quality-to-copy interval. The paper analyzes those memorization clocks and proposes QGD, paired with calibrated checkpoint selection. On CIFAR-10 subsets, QGD preserves Muon’s quality-arrival time while extending the useful interval and reducing copying.

  • Problem

    How update geometry changes the quality-to-copy window remains an open question, despite evidence that diffusion models can reach useful quality before detectable memorization becomes prevalent.

    Source: §1 · pp. 1–2

  • Method

    The paper analyzes random-feature memorization clocks and proposes QGD, which uses a confirmed quality gate and causal copy feedback to limit polar exposure, paired with CBS for calibrated selection from a frozen checkpoint family.

    Source: §1 · p. 2

  • Results

    On 2,000-image CIFAR-10 subsets, QGD preserves Muon’s quality-arrival time, extends the observed generalization window to 8.32× Muon’s, reduces common-checkpoint copying by 75.9%, and achieves final-audit FID 75.56 versus 79.37 for SGD under identical CBS.

    Source: §1 · p. 3

  • Takeaways & Limitations

    The results suggest considering optimizer choice, stopping time, and release calibration jointly; hard switching suppresses copying most strongly, while gradual QGD better preserves quality.

    Source: §1 · p. 2, §6 · p. 10

    The theoretical delay guarantee assumes aligned, fixed features and idealized dynamics; empirical scope is limited, and CBS coverage applies only to the specified detector and threshold.

    Source: §4.3 · p. 7, §6 · p. 10

Abstract

from arXiv · show

Diffusion models can reach useful sample quality before copying training examples, but fast optimization can compress this generalization window by accelerating sample-specific fitting. We investigate this effect through update geometry and propose Quality-Gated De-whitening (QGD), a controller that retains a fast polar-update prefix and progressively restores fixed-gain momentum. Our random-feature analysis separates covariance-controlled, curvature-equalized and amplitude-controlled memorization clocks. Under aligned spectral assumptions, it establishes a finite-exposure condition under which a fixed-gain tail recovers a delay proportional to dataset size. QGD implements this principle with a confirmed quality gate, a bounded decay envelope and causal copy feedback. Immediate switching is the conservative limit; gradual control balances delayed copying against continued quality improvement. We pair QGD with Copy-Budgeted Selection (CBS), which applies simultaneous binomial calibration to a frozen checkpoint family, followed by a fresh evaluation of the released checkpoint. On 2,000-image CIFAR-10 subsets, QGD preserves the polar baseline's quality-arrival time while expanding its useful interval by 8.32x and reducing common-checkpoint copying by 75.9%. With identical calibration and independent quality evaluation, QGD achieves FID 75.56 versus 79.37 for SGD with the same selector. Exposure-matched controls, independent detector audits and transfer to flow matching and dance generation support adaptive exposure control as a practical way to improve the quality-copying tradeoff.

1 INTRODUCTION

The introduction asks how update geometry changes the quality-to-copy window and presents QGD and CBS as complementary controls for training exposure and checkpoint release. Its reported results preserve Muon’s quality-arrival time while widening the useful interval and reducing copying.

1 INTRODUCTION

  • The paper asks whether update geometry changes the mechanism governing memorization delay while preserving fast initial learning, motivating joint measurement of quality and copying along training trajectories.Prior work found faster learning and memorization with Adam than momentum SGD while retaining dataset-size-dependent delay, and reported learning-rate effects on memorization.Source: §1 · pp. 1–2
  • Random-feature analysis distinguishes covariance-controlled, curvature-equalized, and amplitude-controlled clocks; aligned polar updates can compress delay as fluctuation energy spreads across more directions.This motivates limiting polar exposure after useful population structure is learned, then restoring the small-gradient delay of a fixed-gain tail.Source: §1 · p. 2
  • QGD keeps a fast Muon prefix, starts control after a quality target is confirmed, then uses causal copy feedback to reduce polar exposure within a deterministic envelope while retaining momentum and fixed gain.The envelope bounds subsequent polar exposure, while feedback adapts its allocation to the observed trajectory.Source: §1 · p. 2
  • A sufficient recovery condition is that the fluctuation margin remaining at the gate exceed subsequent polar exposure at the relevant scale; immediate switching is the conservative endpoint, while gradual control retains quality improvement.The experiments compare gradual QGD with a same-gate hard switch and a pilot-fixed gradual schedule at matched exposure.Source: §1 · p. 2
  • CBS calibrates a frozen checkpoint family with simultaneous binomial bounds, selects by development quality among eligible checkpoints or abstains, and uses a separate fresh evaluation of the selected checkpoint.The independent final audit does not change the release decision.Source: §1 · pp. 2–3, Figure 1 · p. 3
  • On 2,000-image CIFAR-10 subsets, QGD preserves Muon’s quality-arrival time, extends the observed generalization window to 8.32× Muon’s, reduces common-checkpoint copying by 75.9%, and achieves final-audit FID 75.56 versus 79.37 for SGD under identical CBS.The evaluation includes matched-exposure controls, component ablations, detector audits, and transfer to flow matching and dance generation.Source: §1 · p. 3

2 RELATED WORK

Related work frames diffusion memorization through prior findings on quality-to-copy timing, optimizer choice, and checkpoint selection. This paper connects those threads to update geometry and a quality-triggered exposure controller.

2 RELATED WORK

  • Diffusion quality and cost vary with objectives, schedules, architectures, guidance, and samplers, while this study fixes these choices within optimizer comparisons using a common pixel-space UNet.Prior work documents training-image reproduction and studies mitigation; this paper examines how optimizer choice shifts detectable-copy onset.Source: §2 · p. 3
  • Prior analyses identified an early quality time and later memorization time, with a dataset-size-dependent window under gradient-based training; this work asks how that window depends on optimization geometry.Related work also studies the transition and linear origins of diffusion behavior across data splits.Source: §2 · p. 3
  • Muon orthogonalizes matrix momentum and is related to spectral-norm steepest descent, while prior work reports altered memorization behavior across optimizers and transitions.The cited optimizer family includes K-FAC, Shampoo, SOAP, and diagonal Adam.Source: §2 · p. 3
  • Unlike existing optimizer transitions and spectral-criterion selection, QGD uses a quality-triggered continuous mixture that limits polar exposure with copy feedback and retains eigenvalue-dependent tail motion.The paper relates this design to diffusion work on early stopping and large-step effects.Source: §2 · p. 4
  • CBS combines detector-based checkpoint selection, exact binomial intervals, development/calibration separation, and Bonferroni correction across a frozen family; adaptive Learn-then-Test is a sequential alternative.The paper also draws on work treating training time as part of the model through mode-dependent learning, early stopping, random features, and supervised memorization dynamics.Source: §2 · p. 4

3 OPTIMIZER GEOMETRY DETERMINES THE MEMORIZATION CLOCK

The random-feature denoiser separates population learning from fitting empirical fluctuations under fixed features and a spectral-separation regime. Comparing gradient flow, exact curvature preconditioning, and polar flow shows how update geometry changes the memorization clock.

3 OPTIMIZER GEOMETRY DETERMINES THE MEMORIZATION CLOCK

  • The random-feature denoiser uses fixed features and a least-squares readout whose empirical optimum is decomposed into population structure and empirical fluctuation under spectral separation.The regime places population energy at order-one covariance eigenvalues and fluctuation energy at smaller ones.Source: §3 · p. 4
  • The analysis tracks population prediction error and progress toward empirical fluctuation, defining memorization in aligned disjoint channels as the covariance-weighted fitted fraction that reaches one at the empirical optimum.The toy quality and memorization clocks order structure and fluctuation learning; the neural protocol instead uses a shared sample-quality target.Source: §3 · p. 4
  • Gradient flow retains covariance-dependent fitting rates and has memorization time Θ(n) under the stated eigenvalue scaling and bounded population/fluctuation cross energy, whereas exact curvature preconditioning equalizes rates and has half-fluctuation time log 2.In the disjoint-channel case, the preconditioned straight trajectory need not reach the quality gate.Source: §3 · p. 4
  • In aligned polar flow, coefficient travel depends on fluctuation amplitudes and rank rather than positive covariance eigenvalues, so spreading fluctuation energy across more directions shortens the polar clock.This motivates a polar prefix followed by restoration of small-eigenvalue delay.Source: §3 · pp. 4–5
  • Across six dataset sizes and two noise levels, gradient-flow memorization slopes are 1.00/1.05 versus Muon’s 0.20/0.18 at d = 64, with 21.14×/29.72× window narrowing at n = 512.At d = 16, Muon’s slopes rise to 0.60/0.65; the ordering persists under tanh and noise-draw changes, while exact preconditioning misses quality for n ≤64.Source: §3 · p. 5

4 EXPOSURE-CONTROLLED TRAINING AND CALIBRATED RELEASE

The section separates development-time training control from post-training release assessment, then specifies a quality-gated optimizer transition and calibrated checkpoint selection.

4.1 SEPARATE DEVELOPMENT, CALIBRATION AND EVALUATION

  • Five paired trajectories use shared training conditions, confirmed development probes, calibration on frozen checkpoints, and a separate final evaluation bank.The protocol distinguishes the clocks used for training control from release calibration and final assessment.Source: §4.1 · p. 5

4.2 OUR TRAINING METHOD: QUALITY-GATED DE-WHITENING

  • QGD keeps the full Muon update until the quality target is confirmed, then reduces polar updates through causal copy feedback within a bounded exposure envelope.The post-gate mixture preserves momentum and fixed gain without subsequent RMS normalization.Source: §4.2 · pp. 5–6
  • Under aligned assumptions, finite polar exposure with a positive remaining fluctuation margin gives a memorization delay proportional to dataset size.For fixed threshold, covariance Θ(n^-1), fixed gain, bounded gate time, and uniformly positive margin, the theorem gives τθ = Θ(n).Source: §4.2 · p. 6
  • Immediate switching is the conservative zero-additional-exposure endpoint, while gradual control retains quality improvement as copying is delayed relative to continued polar training.The same-gate hard switch reaches the fluctuation threshold no later than the gradual polar-transition path under the aligned assumptions.Source: §4.2 · p. 6

4.3 OUR SELECTION RULE: COPY-BUDGETED SELECTION

  • CBS calibrates detector-flag rates on fresh inputs for a frozen checkpoint family, then selects the lowest-development-FID checkpoint meeting quality and copy-budget criteria or abstains.It uses simultaneous binomial calibration across candidates.Source: §4.3 · p. 6
  • CBS bounds release with a detector-budget violation only for the declared detector and generation distribution; its guarantee excludes undetected copying and population FID.A further fresh bank evaluates the selected checkpoint without changing its identity.Source: §4.3 · p. 7

5 EXPERIMENTS AND RESULTS

Across matched trajectories, QGD preserves Muon’s quality-arrival time while delaying copying, and its benefit also appears in calibrated checkpoint release and transfer evaluations. The experiments compare exposure controls, selection rules, and independent audits to assess quality and copying together.

5.1 QUALITY AND COPYING ALONG MATCHED TRAJECTORIES

  • 8.32× larger useful interval, independent common-step FID improving from 81.3 to 77.8, and copying falling by 75.9% at n = 2,000.QGD preserves Muon’s quality-arrival time; the hard switch suppresses copying more strongly while QGD retains stronger quality.Source: §5.1 · p. 7, Figure 2 · p. 8

5.2 EXPOSURE RECOVERY AND CONTROLLER COMPONENTS

  • With fixed gain, the finite-mixture copy time rises from 20.85 to 148.49 as n grows from 64 to 512, versus time 4 for continued polar flow.The residual margin is 0.165 across tested sizes; hard switching delays copying further, while gradual mixture fits the remaining population component earlier.Source: §5.2 · p. 7
  • Matched-exposure controls test when exposure is spent: the pilot-fixed open-loop schedule has comparable mean exposure to QGD, while paired trajectories let feedback adapt decay and shutoff.Hard switching has lower copying and longer delay; QGD improves common-step quality. Removing the gate sacrifices the shared fast prefix.Source: §5.2 · p. 8

5.3 VALID SELECTION UNDER A COPYING BUDGET

  • At tighter copy budgets, family search can retain candidates missed by single preselection; at looser budgets, margin preselection can approach full-search quality with fewer outputs.The selector choice depends on the archive and budget; calibration cost is considered alongside quality and release availability.Source: §5.3 · p. 8, Table 3 · p. 9, §5.4 · p. 9

5.5 INDEPENDENT AUDITS AND TRANSFER

  • Across flow matching and dance generation, QGD improves the joint quality–copying tradeoff against continued polar training, while conservative alternatives retain lower copying in some settings.Dance quality separates beat synchrony, kinetic-feature distribution quality, and diversity; audits use task-specific quality measures and fresh copying outputs.Source: §5.5 · p. 9, Table 5 · p. 10

5.4 INDEPENDENT QUALITY OF RELEASED CHECKPOINTS

  • FID 75.56 for QGD versus 79.37 for conservative SGD under identical CBS allocation and independent final audit.All methods use a 200k archive; the comparison holds the release policy fixed.Source: §5.4 · p. 8, Table 4 · p. 10

6 DISCUSSION AND CONCLUSION

The discussion links update geometry and finite polar exposure to the quality-to-copy interval, and argues that optimizer choice, stopping time, and release calibration belong in a joint design decision. The authors qualify this conclusion by the theory’s assumptions, empirical scope, detector dependence, and evaluation costs.

6 DISCUSSION AND CONCLUSION

  • Finite polar exposure suffices to recover a spectral delay, while hard switching suppresses copying most and gradual QGD better preserves quality.Matched-exposure controls isolate feedback’s value from exposure reduction alone.Source: §6 · p. 10
  • Optimizer choice, stopping time, and release calibration should be considered jointly rather than as separate design decisions.Calibration shows when a larger checkpoint family justifies its additional cost.Source: §6 · p. 10
  • The theoretical guarantee assumes aligned, fixed features and idealized updates; empirical effects may change beyond the limited architectures, datasets, and optimizer families studied.CBS coverage is limited to the specified copy detector and threshold, and probe cadence and family size affect generation and calibration cost.Source: §6 · p. 10

A LINEAR-MODEL DEFINITIONS AND COMPLETE CLOCK STATEMENTS

The random-feature model defines population prediction error and empirical memorization along trajectories, then compares their clocks under gradient, curvature-preconditioned, and aligned polar flows. The resulting delays depend on different spectral or coefficient-distance quantities, with practical Muon requiring separate experimental checks.

Model and clocks

  • The model uses fixed random features, with W_emp the minimum-norm training readout and W_pop the population-objective readout.Its two trajectory metrics are population prediction distance and projection onto the empirical component absent from the population readout.Source: A LINEAR-MODEL DEFINITIONS AND… · p. 15
  • The quality clock uses a relative-to-own-minimum threshold only for qualifying cells, while the memorization clock is the first half-threshold crossing.A positive floor makes the quality level attainable; censored records are excluded from exact-value slope fits.Source: A LINEAR-MODEL DEFINITIONS AND… · p. 15

Gradient-flow clock

  • When fluctuation eigenvalues scale as n^-1 and normalized cross energy stays below 1/4, gradient flow has memorization time Θ(n).Modes with order-one eigenvalues approach their empirical coefficients on an O(1) timescale; discrete gradient descent reproduces the flow’s memorization slopes within 0.01.Source: A LINEAR-MODEL DEFINITIONS AND… · p. 16

Curvature-preconditioned clock

  • Exact curvature preconditioning equalizes mode rates, giving W_t = (1 − e^-t)W_emp and no direct eigenvalue-rate dependence.The straight trajectory need not meet the generalization criterion, in which case τ_gen and R are undefined.Source: A LINEAR-MODEL DEFINITIONS AND… · p. 16

Polar-flow clock

  • Aligned polar flow makes coefficient-arrival times independent of positive covariance eigenvalues, with τ_mem = s/(2η) when fluctuation singular values equal s.For fluctuation rank r and bounded singular-value ratio, the delay scales as √(n/r) under the stated energy assumptions.Source: A LINEAR-MODEL DEFINITIONS AND… · p. 16

Practical update geometry

  • Practical Muon adds momentum, approximate orthogonalization, and evolving features, so its behavior is tested experimentally rather than established by the exact-flow propositions.Tempered orthogonalization controls update direction by interpolating normalized momentum and its polar factor at matched per-layer RMS; monotonic window compression is empirical, not a theorem.Source: A LINEAR-MODEL DEFINITIONS AND… · p. 16

B PROOFS OF THE THREE OPTIMIZER CLOCKS

The proofs explain how covariance rates, curvature equalization, and coefficient travel produce distinct memorization clocks. They also qualify the polar rank scaling and distinguish exact-flow conclusions from practical update interventions.

Gradient-flow proof

  • In the eigenbasis of Kn, gradient-flow columns decouple; modes with eigenvalues bounded away from zero approach their empirical coefficients at an O(1) exponential rate, while population prediction-error bounds additionally require controlling fluctuations and their interaction with population covariance K.Source: B PROOFS OF THE THREE OPTIMIZER CLOCKS · p. 17

Curvature-preconditioning proof

  • Curvature preconditioning reduces the flow to a straight path toward W_emp, whose memorization crossing is log(2(1 + c_n)) when c_n > −1/2.If c_n ≤ −1/2, the threshold is already met at zero; the path may never enter the defined generalization phase.Source: B PROOFS OF THE THREE OPTIMIZER CLOCKS · p. 17

Polar-flow proof

  • Aligned polar flow clips each channel coefficient at its target, producing a memorization-time bound independent of positive curvature.With fluctuation rank proportional to n and bounded singular-value ratio, the bound gives Θ(√(n/r)); interpreting r as total update rank requires comparable ranks.Source: B PROOFS OF THE THREE OPTIMIZER CLOCKS · pp. 17–18

Three-clock comparison

  • For common fluctuation covariance and singular value, the three clocks scale respectively as n, 1, and n/r for gradient, curvature-preconditioned, and polar flow.The finite-range rank family is nearly flat when n ≪ r and approaches a square-root regime when n ≫ r; at fixed rank, changing amplitude alters the prefactor, not the asymptotic exponent.Source: B PROOFS OF THE THREE OPTIMIZER CLOCKS · p. 18

Practical intervention caveat

  • Tempering and finite Newton–Schulz depth are empirical interventions because general matrix singular vectors need not align with covariance eigenvectors, and monotonic crossing times do not follow.The comparison fixes update RMS and reports observed responses rather than asserting a monotonicity theorem.Source: B PROOFS OF THE THREE OPTIMIZER CLOCKS · p. 18

C CONTROLLER AND CHECKPOINT-SELECTION PROOFS

The controller proof bounds post-gate polar exposure to recover a dataset-size delay under aligned spectral conditions, while checkpoint certification controls detected-copy probability for a frozen family. The statements have explicit quality and deployment scope limits.

Exposure envelope

  • The exponential envelope bounds total post-gate polar exposure even when copy feedback never activates.The envelope also omits practical momentum and approximate Newton–Schulz orthogonalization.Source: C CONTROLLER AND CHECKPOINT-SELECTION… · p. 19

Finite-exposure controller proof

  • Finite post-gate polar exposure with positive remaining fluctuation margin gives a pathwise Θ(n) memorization delay under the stated uniform conditions.The bound applies to measurable coefficient schedules, including causal copy-feedback schedules; a fixed positive polar floor retains amplitude-controlled arrival instead.Source: C CONTROLLER AND CHECKPOINT-SELECTION… · p. 19

Heterogeneous-channel extension

  • For heterogeneous fluctuation channels, the linear-in-n delay holds when their spectral values lie in [c/n, C/n] and Proposition 1’s other uniform conditions hold.The unequal-channel result requires its stated margin and rate conditions; it reduces to Proposition 1 when amplitudes and curvature are equal.Source: C CONTROLLER AND CHECKPOINT-SELECTION… · pp. 19–20

Checkpoint-selection proof

  • For a fixed checkpoint family and independent iid certification inputs, simultaneous binomial bounds control the chance of releasing a candidate whose detected-copy probability exceeds budget.The union bound does not require independence across candidates.Source: C CONTROLLER AND CHECKPOINT-SELECTION… · p. 20

Certificate scope

  • The certificate covers the frozen detector, released weights, reference set, sampler, and conditioning distribution, not undetected semantic copying, unseen deployment distributions, or population FID.After certification results are revealed, newly trained adaptive checkpoints need fresh independent samples or a separately justified sequential method.Source: C CONTROLLER AND CHECKPOINT-SELECTION… · p. 20

D HARD-SWITCH ORDERING AND AN EXPOSURE DESIGN RULE

The aligned comparison shows that same-gate hard switching maximizes fluctuation delay, while a finite-exposure mixture retains dataset-size scaling under a positive-margin condition. Random-feature diagnostics compare optimizer window ratios, and matched-RMS controls isolate update direction and orthogonalization depth.

D HARD-SWITCH ORDERING AND AN EXPOSURE DESIGN RULE

  • Under the equal-channel assumptions, same-gate hard switching maximizes aligned delay, and finite exposure retains delay when the remaining fluctuation margin exceeds subsequent polar exposure.The comparison holds up to threshold arrival; Proposition 1 bounds the delay retained by a finite-exposure mixture relative to hard switching.Source: D HARD-SWITCH ORDERING AND AN EXPOSURE… · p. 20
  • The finite mixture’s post-gate delay has log–log slope 0.986, versus 0.038 for excess exposure, 0.111 for a positive floor, and zero for always-polar flow.The hard-switch post-gate delay is exactly n log(3/2); the asymptotic linear claim follows from the uniform positive margin and fixed gain, not the finite-range fit alone.Source: Table 6 · p. 21, D HARD-SWITCH ORDERING AND AN EXPOSURE… · p. 21
  • At n = 256 and t = 4, finite-mixture risk is 0.05471 versus 0.06997 for hard switching, but hard switching later reaches lower minimum full risk, 0.03506 versus 0.05346.The gradual transition therefore improves early utility in this diagnostic without being uniformly optimal.Source: D HARD-SWITCH ORDERING AND AN EXPOSURE… · p. 22, Figure 3 · p. 22

E BACKGROUND RANDOM-FEATURE DIAGNOSTICS

  • At d = 64, ReLU Muon-minus-gradient-flow window-slope gaps are −0.75 and −0.82, compared with −0.35 and −0.35 at d = 16.For tanh, the corresponding d = 64 gaps are −0.79 and −0.81; differences are paired on the same draw and size support.Source: E BACKGROUND RANDOM-FEATURE DIAGNOSTICS · p. 24

F DIRECTIONAL INTERVENTIONS AT MATCHED MAGNITUDE

E BACKGROUND RANDOM-FEATURE DIAGNOSTICS

G IMPLEMENTATION AND EVALUATION PROTOCOL

The protocol uses paired CIFAR-10 trajectories, fixed model and optimizer settings, and staged development, calibration, and independent audit data. Fresh detector audits and controller controls distinguish detector dependence and schedule choices, while paired aggregation accounts for censoring and calibration variability.

G IMPLEMENTATION AND EVALUATION PROTOCOL

  • Five paired CIFAR-10 initializations share data order, training noise, and initialization within each pair, with no augmentation in the primary study.The 6.47M-parameter DDPM-style UNet uses fixed released weights, sampler, and generation distribution before certification.Source: G IMPLEMENTATION AND EVALUATION PROTOCOL · pp. 25–26
  • Quality and copy events are confirmed at a subsequent probe before control begins, and final audit or calibration results never guide the controller.Development FID uses fixed latent inputs; the released checkpoint’s final FID is measured on a separate 50,000-output bank.Source: G IMPLEMENTATION AND EVALUATION PROTOCOL · p. 26

H INDEPENDENT DETECTOR AUDITS

  • The independent SSCD audit uses fresh outputs after the pixel-controlled trajectory is frozen, testing detector dependence without establishing sensitivity to all forms of copying.The detector-specific rates quantify only the declared rule’s outputs under the fixed certification specification.Source: H INDEPENDENT DETECTOR AUDITS · p. 26, Table 15 · p. 27

I CONTROLLER CONTROLS AND PAIRED UNCERTAINTY

  • The same-gate hard switch shares QGD’s prefix, momentum, and gain, while the open-loop control uses a pilot-fixed gradual schedule with matched aggregate exposure.Paired summaries preserve censoring limits; Table 17 gives the complete controller comparison and Table 18 varies controller settings and probe cadence.Source: I CONTROLLER CONTROLS AND PAIRED… · p. 27, Table 17 · p. 28, Table 18 · p. 28
  • Checkpoint-selection quality averages released decisions within each trajectory before summarizing the five trajectory means, separating trajectory variation from calibration-bank variability.Conditional-on-release quality averages do not change the denominator for release or joint-error frequencies.Source: I CONTROLLER CONTROLS AND PAIRED… · pp. 27–28

J FROZEN-FAMILY CALIBRATION AND SELECTOR COMPARISON

CBS calibrates a frozen checkpoint family with simultaneous binomial bounds, selects by development quality among eligible certified checkpoints, and may abstain. Its guarantee concerns joint release and detector-budget violation, while archive construction and calibration add to end-to-end cost.

J FROZEN-FAMILY CALIBRATION AND SELECTOR COMPARISON

  • CBS applies per-candidate error δ/M bounds to a frozen eligible family, then selects the checkpoint with best development FID among certified candidates.The family includes searched seeds, hyperparameters, averaging choices, and sampler configurations; the certificate does not cover post-calibration selection across methods.Source: J FROZEN-FAMILY CALIBRATION AND… · pp. 28–29
  • The fixed-sequence comparator orders eligible checkpoints using development information and stops at the first failed level-δ test; stopping is essential to validity.Unlike CBS’s simultaneous bounds, the order affects fixed-sequence power but not validity.Source: J FROZEN-FAMILY CALIBRATION AND… · p. 29
  • CBS’s guarantee covers the joint event of release and detector-budget violation, not violation conditional on release or population FID.A model revision requires fresh calibration or a separately justified sequential procedure.Source: J FROZEN-FAMILY CALIBRATION AND… · p. 29

K COMPUTATION AND PRACTICAL COST

  • The 200k archive cost accounting includes 500k CBS calibration outputs and a separate 50k-output final quality audit.Development quality generation and feature extraction cost 90 seconds, with the copy check adding 5 seconds on shared samples.Source: K COMPUTATION AND PRACTICAL COST · p. 29, Table 22 · p. 30
  • A smaller checkpoint family reduces calibration outputs but also leaves fewer choices for selection.The selector comparison reports both quality or availability and the number of generated calibration outputs.Source: K COMPUTATION AND PRACTICAL COST · p. 30

L TRANSFER METRICS AND GENERATION SETTINGS

Transfer evaluations apply QGD settings to image flow matching and music-conditioned AIST++ motion, with fixed methods and evaluation protocols. Motion quality is measured across beat alignment, kinetic-feature distribution, and diversity, while copying audits concern a declared coarse descriptor.

L TRANSFER METRICS AND GENERATION SETTINGS

  • The image-flow comparison uses the same UNet and small CIFAR-10 subset, with 50 uniform Heun sampling steps and a predeclared development FID target of 89.1.The flow observation horizon is 220k updates, and final quality uses an independent image-audit protocol.Source: L TRANSFER METRICS AND GENERATION… · p. 30
  • AIST++ motion evaluation uses a 4M-parameter pose generator and split-by-recording groups, with beat alignment compared against a predeclared threshold of 0.270.Kinetic-feature FID and diversity are separate measures; diversity targets the held-out reference scale rather than unbounded increase.Source: L TRANSFER METRICS AND GENERATION… · p. 30, Table 23 · p. 31
  • The pose-copying flag uses nearest-neighbor ratios in standardized kinetic-feature space and does not certify the absence of semantic or frame-level copying.The joint motion evaluation is designed so high beat alignment cannot conceal repetitive or unrealistic motion.Source: L TRANSFER METRICS AND GENERATION… · p. 30

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