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Flat-Consensus Diffusion for Robust Data Reshaping under Noisy Evaluator

Hongyu Cao, Kunpeng Liu, Fei Xie, Sandip Ray

arXiv:2609.32696v1cs.AIcs.LG

TL;DR

Feature-centric reshaping must remain useful and stable despite noisy evaluation and stochastic search, which can produce inconsistent solutions. FCDiff combines smoothed reward guidance with consensus aggregation across trajectories. Across an 8-dataset cohort under heavy-tailed evaluator noise, it attains the lowest mean rank on all three reported metrics.

  • Problem

    Robust feature-centric reshaping must handle evaluator noise that distorts reward guidance and stochastic search trajectories that converge to inconsistent solutions.

    Source: §I · p. 2, §II · p. 2

  • Method

    FCDiff uses Gaussian-smoothed reward guidance within trajectories and a weighted barycenter to aggregate guided endpoints across trajectories.

    Source: §I · p. 2

  • Results

    Across 8 datasets, FCDiff had mean ranks of Perf. 2.25, CVaR@5 2.00, and Worst 3.12; its Perf. improvement over every robust-gen baseline was significant (p=0.008, n=8).

    Source: B. Aggregate Reliability Summary · p. 5

  • Takeaways & Limitations

    Robust reshaping is framed as searching for flat, consensus-supported regions rather than sharp single-trajectory optima.

    Source: §VI · p. 9

    Smoothing reduces variance in reward guidance but not systematic bias in a misspecified latent reward surrogate; uncertainty-aware reweighting recovers this only partially.

    Source: §VI · p. 10

Abstract

from arXiv · show

Data shape determines how features are structured, how patterns are separated, and how distributions cover the underlying domain. Poor data shape can make models learn noise rather than generalizable structure. This paper studies robust feature-centric data reshaping: generating feature transformations that remain useful, stable, and reproducible under noisy evaluation and imperfect data conditions. We view reshaping operation sequence search as reward-guided diffusion generation, and robust reshaping as searching for regions in the latent reward landscape rather than isolated high-reward transformations. The key challenge is dual instability: noisy evaluators distort local reward guidance, while stochastic generative trajectories can converge to inconsistent solutions. We propose FCDiff, a flat-consensus diffusion framework that addresses both failures through a micro-macro decomposition. The micro layer replaces point-estimate reward guidance with Gaussian-smoothed, Monte Carlo averaged gradients, steering generation toward locally flat reward regions. The macro layer aggregates independently guided trajectories with a weighted Frechet-mean barycenter, selecting consensus-supported basins and filtering stochastic outliers. Across an 8-dataset headline cohort under heavy-tailed evaluator noise, FCDiff attains the best aggregate rank on lower-tail reliability and robustness against both search-based AutoFE and robustness-oriented generative baselines, with statistically significant accuracy gains over every generative baseline. Our results show that robust data reshaping requires searching for flat, consensus-supported regions rather than sharp single-trajectory optima.

I. INTRODUCTION

The paper studies feature-centric data reshaping that remains useful, stable, and reproducible under imperfect conditions. It proposes FCDiff to address noisy reward guidance and stochastic search by targeting flat, consensus-supported regions.

I. INTRODUCTION

  • Data shape—the structure of features, separation of patterns, and domain coverage—matters alongside model architecture and data scale in real-world settings.The paper notes that real-world data can be noisy, sparse, imbalanced, and weakly separated.Source: §I · p. 1
  • Robust reshaping must address evaluator noise that distorts reward guidance and stochastic trajectories that can converge to inconsistent solutions.The paper says addressing only one instability leaves the other unresolved.Source: §I · p. 1
  • Prior methods address search, reward, or generation in isolation, rather than jointly handling noise-robust guidance and trajectory-level reproducibility,, –[5],.The paper characterizes reward-guided reshaping as searching for flat regions reached consistently across trajectories.Source: §I · p. 2
  • Across 8 datasets under heavy-tailed evaluator noise, FCDiff achieves the strongest lower-tail reliability, robustness, and reproducibility versus AutoFE search and robustness-oriented generative baselines.The paper frames the central finding as searching flat, consensus-supported regions rather than selecting the highest single reward peak.Source: §I · p. 2
  • FCDiff uses Gaussian smoothing with Monte Carlo averaged gradients at the micro level and a weighted Fréchet-mean barycenter at the macro level.The micro layer reduces sensitivity to local reward noise; the macro layer aggregates trajectories and filters stochastic outliers.Source: §I · p. 2

II. PROBLEM STATEMENT

The problem is to generate high-utility reshaping sequences that remain stable under evaluator perturbations and consistent across stochastic trajectories. FCDiff addresses these requirements by applying local smoothing and cross-trajectory aggregation in a latent reward space.

II. PROBLEM STATEMENT

  • A reshaping sequence applies operations from a library to an input feature matrix, and a downstream evaluator scores the transformed features for predictive utility.The objective is to search operation sequences that optimize this reward.Source: §II · p. 2
  • Evaluator noise can make one sequence receive inconsistent rewards, while independent stochastic search trajectories can converge to different high-reward sequences.The robust objective therefore seeks high utility, local perturbation stability, and cross-trajectory consensus.Source: §II · p. 2
  • The design requires guidance insensitive to local perturbations within each trajectory and a final solution supported by agreement across trajectories.Section III instantiates these requirements with randomized smoothing and weighted Fréchet-mean aggregation.Source: §II · p. 2

III. ROBUST DATA RESHAPING

  • FCDiff treats reshaping as finding locally stable, consistently reachable regions rather than one optimal sequence.Its micro layer uses Gaussian-smoothed reward guidance, while its macro layer aggregates guided endpoints into a consensus latent.Source: §III · p. 2, Figure 2 · p. 3

A. Backbone: Latent Reward Geometry for Generative Reshaping

The VAE–reward–diffusion backbone embeds discrete reshaping sequences in a continuous latent reward geometry and generates stochastic sequences. FCDiff adds randomized smoothing so each trajectory is guided toward regions where nearby perturbations preserve reward.

A. Backbone: Latent Reward Geometry for Generative Reshaping

  • The VAE–reward–diffusion backbone supplies a continuous search space, reward-aware geometry, and stochastic generation over valid reshaping sequences.The VAE encodes and decodes sequences; a differentiable reward predictor estimates downstream utility; and a diffusion prior models valid latent sequences.Source: A. Backbone: Latent Reward Geometry… · p. 3

B. Micro: Local Stability via Randomized Smoothing

  • Point-estimate guidance can pull a trajectory toward a sharp latent point that appears high-reward under one evaluator realization but fails under small perturbations.The correspondence between latent flatness and evaluator-perturbation stability applies insofar as noise is variance-like rather than systematic surrogate bias.Source: B. Micro: Local Stability via… · p. 3
  • FCDiff replaces point-estimate guidance with a locally smoothed surrogate, using its gradient to guide reverse diffusion toward stable regions.The surrogate averages reward predictions over Gaussian perturbations around the current latent; K is the number of Monte Carlo perturbations and σ is the smoothing radius.Source: B. Micro: Local Stability via… · pp. 3–4
  • Randomized smoothing favors regions where nearby perturbations preserve high reward, making an individual trajectory's predicted utility less sensitive to evaluator noise.This implements within-trajectory perturbation stability, but does not by itself ensure endpoints agree across stochastic runs.Source: B. Micro: Local Stability via… · p. 4

C. Macro: Global Consistency via Trajectory Consensus

FCDiff replaces single-trajectory selection with a weighted Fréchet-mean consensus over independently guided endpoints. The resulting latent represents a high-reward, repeatedly reached basin rather than an isolated peak.

C. Macro: Global Consistency via Trajectory Consensus

  • FCDiff aggregates independently guided trajectory endpoints with a weighted Fréchet mean instead of selecting the highest-reward sample.The consensus latent is a reward-weighted average of the endpoints.Source: C. Macro: Global Consistency via… · p. 4
  • The weights use surrogate reward and a temperature β: β →∞ gives an unweighted mean, while β →0+ approaches top-1 selection.The surrogate Rϕ is distinct from the downstream evaluator E.Source: C. Macro: Global Consistency via… · p. 4
  • The weighted mean concentrates on high-reward, high-consensus regions and filters trajectory outliers before decoding the final reshaping sequence.This targets global reproducibility across diffusion trajectories.Source: C. Macro: Global Consistency via… · p. 4
  • The macro layer stabilizes selection across trajectories, complementing the micro layer’s within-trajectory guidance; Table I summarizes this symmetry.Together, the layers support region-level inference and reliability, robustness, and reproducibility under noisy evaluators.Source: C. Macro: Global Consistency via… · p. 4, Table I · p. 4

IV. EXPERIMENTS

The experiments evaluate downstream reliability, local stability, and cross-trajectory reproducibility under a shared noisy-search protocol. They pair primary downstream metrics with surrogate-space diagnostics and compare FCDiff with seven baselines.

IV. EXPERIMENTS

  • All methods search with corrupted reward queries and are evaluated afterward using a clean downstream evaluator.The design isolates robustness of the search process from downstream model quality.Source: §IV · p. 4
  • Primary outcomes are Average Performance and Worst-10% Performance across four regression and four classification datasets; both are higher-is-better.Performance is mean 5-fold CV score on the clean predictor: 1−RAE for regression and macro-F1 for classification.Source: §IV · p. 4
  • Secondary diagnostics measure surrogate utility, utility variance, adversarial floor and drop, gradient variance, decode validity, and usable-sample rate.Usable-sample rate requires a sample to decode, apply to the feature table, and yield a finite downstream score.Source: §IV · p. 4
  • Seven matched-compute baselines span feature-transformation search and robustness-oriented methods, including Std-Diff, RL-AutoFE, EvoSearch, and Medoid-Cons.The remaining baselines are LLM-FE, Adversarial-PGD, and Grad-Clip.Source: §IV · pp. 4–5

A. Overall Reliability under Noisy Evaluators

Under heavy-tailed evaluator noise, FCDiff improves lower-tail reliability across the eight-dataset cohort and outperforms or matches the compared methods on average performance. The findings support searching for flat, consensus-reached regions rather than isolated high-reward transformations.

A. Overall Reliability under Noisy Evaluators

  • 5/8 datasets have FCDiff best or tied-best CVaR@5; it has the lowest CVaR@5 mean rank and best mean performance among robust generative methods.FCDiff matches or beats all robust generative baselines on average performance (8/8) and has stronger lower-tail reliability in 7/8 comparisons with EvoSearch and 8/8 with RL-AutoFE.Source: A. Overall Reliability under Noisy… · p. 5
  • The gains are attributed to concentrating generation in flat, consensus-supported regions, making the solution distribution more reliable beyond its top-ranked sample.Lower-tail metrics assess whether generated solutions remain useful beyond the best samples.Source: A. Overall Reliability under Noisy… · p. 5
  • Search-based methods are sensitive to noisy feedback, while local-stability methods or trajectory aggregation alone leave one of the two instability sources unaddressed.FCDiff is described as the only method addressing both failure modes simultaneously.Source: A. Overall Reliability under Noisy… · p. 5
  • The results support seeking regions that are both locally flat and consistently reachable, rather than a single high-reward transformation.This is the paper’s stated central claim about robust data reshaping.Source: A. Overall Reliability under Noisy… · p. 5

B. Aggregate Reliability Summary

FCDiff ranks best on aggregate reliability across the headline cohort, while micro smoothing stabilizes within-trajectory guidance but does not correct systematic surrogate bias.

B. Aggregate Reliability Summary

  • FCDiff has the lowest mean rank on all three metrics (Perf. 2.25, CVaR@5 2.00, Worst 3.12), with Perf. gains over every robust-gen baseline significant at p=0.008.Its CVaR@5 improvement is significant against three of four robust-gen baselines; it ties EvoSearch on mean performance but beats all three search baselines on CVaR@5 (p<0.05).Source: B. Aggregate Reliability Summary · p. 5

C. Micro Layer Stabilizes Local Reward Guidance

  • Increasing Monte Carlo perturbations from K=1 to K≥4 reduces gradient variance by several orders of magnitude, with little additional gain beyond K=4.Under Student-t noise (ν=3), micro smoothing suppresses per-step gradient variance, while macro consensus absorbs trajectory drift that survives smoothing.Source: C. Micro Layer Stabilizes Local Reward… · p. 5

D. Smoothing Reduces Variance but Does Not Remove Bias

  • Under noisy-target and reduced-data misspecification, full_FCDiff outperforms micro_only, which outperforms standard guidance on every dataset.This ordering holds when the surrogate remains directionally informative.Source: D. Smoothing Reduces Variance but Does… · p. 5
  • Under architectural_underfit, smoothing inherits systematic surrogate bias; uncertainty-aware mitigations partially recover performance, with ensemble the safer default and mc_dropout dataset-dependent.Smoothing reduces variance in reward guidance, not bias in the surrogate.Source: D. Smoothing Reduces Variance but Does… · pp. 5–6

E. Macro Consensus Improves Cross-Trajectory Stability

Macro consensus aggregates stochastic trajectories to improve lower-tail reliability and reduce trajectory-level instability. Its effects complement micro smoothing, which reduces utility variance.

E. Macro Consensus Improves Cross-Trajectory Stability

  • Across the 8-dataset headline cohort, full_FCDiff exceeds micro_only on Worst-10% Utility on every dataset: by +5.9% to +13.9% on seven datasets and +59% on ap_omentum_ovary.The source reports full_FCDiff as single_FCDiff in Table VI.Source: E. Macro Consensus Improves… · p. 6
  • Best-sample selection favors isolated lucky trajectories and is less reliable in the tail; Fréchet aggregation favors regions repeatedly reached across independent runs.Mean-based consensus yields valid decodes when modes overlap, with a medoid fallback under multimodality.Source: E. Macro Consensus Improves… · p. 6
  • On the SDEdit-init side cohort, micro reduces utility variance 2.6–4.9× across three datasets, while macro lifts spectf usable-sample rate from 6% to 29%.The usable-sample increase is reported as 4.8× and attributed to trajectory aggregation escaping per-run pathological samples.Source: E. Macro Consensus Improves… · pp. 6–7
  • Removing either layer weakens its corresponding robustness axis, supporting complementarity: micro shifts the mean while macro contracts variance.Global consensus turns locally stable trajectories into reproducible reshaping solutions.Source: E. Macro Consensus Improves… · pp. 6–7

F. FCDiff Finds Flat Regions and Consensus Basins

FCDiff’s diagnostics distinguish the layers’ geometric roles: micro guidance raises reward floors and moves endpoints toward higher-reward regions, while macro aggregation contracts their spread. Together, the results support searching for regions that are both locally flat and supported by trajectory consensus.

Flatness and consensus diagnostics

  • FCDiff achieves the highest adv_floor on 7/8 headline-cohort datasets (tied with micro_only on spectf), exceeding standard by 10×–290× across the cohort.On openml_586, its 1D profile shows an approximately 70× reward elevation; on the production SDEdit stack, adv_drop is 9–19× flatter than standard.Source: F. FCDiff Finds Flat Regions and… · p. 7
  • Macro aggregation contracts intra-cluster distance below standard on every headline-cohort dataset, producing 1.0×–3.6× tighter clusters and at least 220× contraction on SDEdit.The micro layer raises the reward floor, while the macro layer contracts terminal spread, indicating distinct geometric roles.Source: F. FCDiff Finds Flat Regions and… · p. 7
  • On openml_586, micro_only and full_FCDiff endpoints land at t=0.93 and t=1.00 with rewards 1411 and 1507, versus standard at t=0.00 with reward 21.5.The micro layer covers 93% of the traversed distance; macro aggregation adds little displacement and instead contracts endpoint spread.Source: F. FCDiff Finds Flat Regions and… · p. 7
  • On ionosphere, the local reward changes 40% for standard versus 1.9% for full_FCDiff across the ±2ε window, while guided variants share a below-3% flatness signature.On spectf, the standard slope is 3.2× the guided slopes.Source: F. FCDiff Finds Flat Regions and… · p. 7
  • The diagnostics support FCDiff’s central claim that robust reshaping succeeds by finding regions that are both flat under perturbation and supported by trajectory consensus.The study measures post-attack reward floors and basin concentration to examine these geometric properties.Source: F. FCDiff Finds Flat Regions and… · p. 7
  • On openml_586, PC1 explains 47.7% of endpoint variance and guided endpoints concentrate in a narrow high-reward band, while standard endpoints scatter over low-reward regions.On ionosphere and openml_637, where PC1 explains 5.1% and 0.9%, respectively, the variants overlap; the paper identifies structured, separable landscapes as where robust guidance delivers its largest gains.Source: F. FCDiff Finds Flat Regions and… · p. 7

G. Backbone Identity: FCDiff = DIFFT + Dual-Level Ensemble

FCDiff retains the DIFFT backbone and adds gradient-level smoothing and trajectory-level consensus. Across the reported comparisons, consensus improves lower-tail utility, while the two ensemble layers have distinct effects on utility and its variability.

G. Backbone Identity: FCDiff = DIFFT + Dual-Level Ensemble

  • FCDiff is DIFFT augmented with two ensemble layers: micro_only adds gradient-level smoothing, macro_only adds trajectory consensus, and full_FCDiff combines both.The Std-Diff row is vanilla DIFFT with K=M=1.Source: G. Backbone Identity: FCDiff = DIFFT +… · p. 8
  • On the SDEdit-anchored side cohort, smoothing lifts Worst-10% Utility while consensus most strongly contracts Utility Variance; FCDiff wins both metrics on every side-cohort dataset.Reported examples include Worst-10% Utility rising from 1.10 to 2.17 on svmguide3 and Utility Variance falling from 1.4e−2 to 2.0e−3 there.Source: G. Backbone Identity: FCDiff = DIFFT +… · p. 8, Table IV · p. 8

H. Decode Validity of Consensus Latents

  • The final t*=5 denoising steps use pure DDPM without guidance, re-anchoring the consensus latent to the denoising-prior manifold before decoding.The paper describes this terminal segment as a manifold projection that avoids decoder-invalid samples in its setting.Source: H. Decode Validity of Consensus Latents · p. 8
  • At M=20 on a four-dataset sub-cohort, consensus and best-of-M both have 100% decode validity, and consensus has higher Worst-10% Utility on every dataset.The reported deltas are +.018, +.027, +.016, and +.004; average performance is essentially tied, and the tail gap shrinks on the easiest dataset.Source: H. Decode Validity of Consensus Latents · pp. 8–9, Table V · p. 9
  • At matched compute on the 8-dataset headline cohort, full_FCDiff achieves the highest Worst-10% Utility on every dataset against standard_M and single_FCDiff.The comparison uses M=16; per-trajectory compute is similar, while the M-fold parallel cost dominates either way.Source: H. Decode Validity of Consensus Latents · p. 8, Table VI · p. 9

I. Efficiency and Sensitivity

FCDiff ranks best on lower-tail reliability across the eight-dataset conclusion cohort, while its matched-compute comparison favors improving guidance over post hoc best-of-M selection. The paper also identifies surrogate misspecification as a limitation and situates its approach among related robustness methods.

I. Efficiency and Sensitivity

  • At similar computational budgets, FCDiff consistently achieves stronger lower-tail performance than post hoc best-of-M selection.The authors conclude that robustness should be built into the generative trajectory rather than recovered after sampling.Source: §I · p. 9
  • On openml_586, any t0 from 10 to 500 with elite-pool fraction k≤25% matches the default downstream score within ±0.003; t0=999 recovers the unanchored failure mode.The authors attribute the gain to the truncated reverse trajectory, not information leaking through the elite seed.Source: §I · p. 9

V. RELATED WORK

  • Prior methods address parts of robust reshaping, but the paper says they do not jointly handle reward-gradient noise and trajectory-level dispersion within the denoising process.The related-work discussion distinguishes feature-search methods, smoothing and robust-gradient methods, parameter-level flatness methods, and latent-diffusion work in other modalities.Source: §V · p. 9

VI. CONCLUSION

  • The conclusion frames robustness as a geometric property of the latent reward landscape, with within-trajectory and between-trajectory stability as distinct axes.FCDiff instantiates them through randomized smoothing and a reward-weighted barycenter over trajectory endpoints.Source: §VI · pp. 9–10
  • On 8 datasets under matched heavy-tailed noise, FCDiff attains the best CVaR@5 mean rank among all baselines and the best mean accuracy within the robust-generation cohort.The paper notes that smoothing reduces reward-guidance variance but does not remove bias from a systematically misspecified reward surrogate; uncertainty-aware reweighting recovers it only partially.Source: §VI · p. 10

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