Beyond One Epoch: Uncertainty-Weighted Sensitivity Regularization for Recommendation Models

1 INTRODUCTION

• At the second epoch, recommendation models can suffer abrupt out-of-sample deterioration while training loss improves.Prior mitigations reset embedding tables or attenuate row magnitudes.Source: §1 · p. 2
• On the first pass, an example is scored before its label affects model parameters; replay uses embeddings already conditioned on that target.The replay-induced change in the effective objective and optima is termed self-influence asymmetry.Source: §1 · p. 2
• The paper connects its account to the generated-regressor problem, where using an outcome-containing fitted input can make a relationship appear stronger than it is for new examples.When exclusion is impractical, the cited framework calls for propagating input uncertainty through the downstream fit.Source: §1 · p. 2
• UWSR penalizes consumer sensitivity to poorly determined embedding rows, making reliance on uncertain representations costly.The penalty is computed with double backpropagation and regularizes the consumer rather than directly intervening on embeddings.Source: §1 · pp. 2–3
• An exact scalar model and local rowwise analysis identify a mismatch between the consumer rewarded by training examples and the consumer rewarded by fresh examples.An embedding-consumer-update-order intervention empirically tests the hypothesis.Source: §1 · p. 3
• UWSR consistently outperforms single-epoch checkpoints and multi-epoch baselines from state-of-the-art methods across three recommendation datasets.The benchmarks are MovieLens-20M, Amazon Electronics, and Avazu.Source: §1 · p. 3

2 RELATED WORK

• Prior remedies for the one-epoch phenomenon reset embedding tables or attenuate their magnitudes, while standard regularizers such as ℓ2 decay and embedding dropout do not remove the failure.The cited work attributes the failure to distributional shifts in sparse embeddings and rapid network adaptation.Source: §2 · p. 3
• Target-encoding methods use ordered statistics or cross-fitting to exclude an instance's own label, but these frameworks do not address jointly and repeatedly optimized embeddings and consumers.Generated-regressor theory studies downstream consequences of using estimated quantities.Source: §2 · p. 3
• The theoretical framing combines prequential prediction with influence functions, leverage, and covariance-penalty accounts of in-sample optimism.These frameworks characterize consequences of breaking the temporal separation between prediction and observing a target.Source: §2 · p. 3
• UWSR applies input-sensitivity penalties to fitted, information-weighted representations, bridging sensitivity regularization and methods that account for parameter uncertainty.The related methods include curvature- or Fisher-scaled updates and Bayesian uncertainty sampling.Source: §2 · p. 3

3.1 SCALAR MODEL OF THE LEAVE-IN/LEAVE-OUT ASYMMETRY

• As embedding support decreases, the difference between fresh- and replay-optimal consumers and the resulting excess fresh loss both grow.The scalar model fits an entity embedding, holds it fixed, and derives the optimal consumer for in-sample and fresh targets.Source: §3.1 · p. 4

3.2 GENERALIZING TO NEURAL NETWORKS

• The neural analysis models row uncertainty with a Laplace approximation and measures consumer reliance using local logit sensitivity.It considers an active embedding row while holding the remaining embeddings and consumer fixed.Source: §3.2 · p. 5

3.2.1 IMPLICIT PENALIZATION OF UNCERTAIN EMBEDDINGS IN PREQUENTIAL TRAINING

• Prequential training implicitly penalizes downstream sensitivity to poorly informed embedding directions, producing greater excess loss when that sensitivity is high.The local excess risk is derived under first-epoch prequential training.Source: §3.2.1 · pp. 5–6

3.2.2 REPLAY-INDUCED EXPLOITATION OF UNCERTAIN EMBEDDINGS

• Replay encourages reliance on uncertain embeddings because the label-aligned row displacement shifts the logit, creating leave-in optimism that opposes the prequential sensitivity penalty.Rare or low-support rows have the greatest generalized leverage because their information is minimal.Source: §3.2.2 · p. 6

3.3 EMBEDDING-CONSUMER-UPDATE-ORDER INTERVENTION EXPERIMENT

• Embedding-first training increases score sensitivity and worsens validation performance, with the sensitivity inflation strongest for poorly supported rows.The intervention uses two passes per minibatch while matching ordinary training's total updates; consumer-first remains close to ordinary training.Source: §3.3 · pp. 6–7, Figure 2 · p. 7

• UWSR adds a functional regularizer to the dense consumer after the first epoch, restoring the positive inverse-information penalty present during prequential training.The penalty makes sensitivity to poorly determined sparse rows costly while leaving embedding parameters free to be optimized.Source: §4 · p. 7
• The regularizer weights consumer sensitivity by frozen inverse-information estimates computed during epoch one and held fixed in subsequent epochs.This uses the inverse-information geometry maintained by prequential training.Source: §4 · p. 7
• The default row-uncertainty estimate repurposes an adaptive optimizer’s squared-gradient accumulator as an approximation to diagonal Fisher information.It requires no additional computation because the accumulator is already part of ordinary optimizer state.Source: §4 · pp. 7–8
• The sensitivity term is computed with double backpropagation and second-order automatic differentiation.The penalty therefore requires second-order autodifferentiation through the sensitivity calculation.Source: §4 · p. 8

• The evaluation covers MovieLens-20M, AmazonElectronics, and Avazu, with hyperparameters selected on validation data and test data held out from selection.Four-epoch training is used unless otherwise noted, and multi-epoch methods receive four times the one-epoch baseline’s gradient steps.Source: §5 · p. 8
• UWSR consistently improves test performance across all datasets over naive replay, one-epoch checkpoints, and state-of-the-art methods.The evaluation reports raw BCE and AUC, with AUC as the primary metric.Source: §5 · p. 8
• UWSR maintains low logit sensitivity and improves validation loss beyond one epoch without directly restraining embedding norms.The active embedding norms remain free to grow.Source: §5 · p. 8

• UWSR uses double backpropagation weighted by frozen inverse row information to constrain target sensitivity on poorly determined rows.The approach avoids direct interventions on embeddings.Source: §6 · p. 8
• The rowwise analysis assumes independent embedding updates and does not model cross-row interactions.The formulation also considers fixed-window replay; continual learning would require dynamically updating row information matrices.Source: §6 · p. 8
• Further work is needed to measure the intervention’s contribution relative to other factors driving overall multi-epoch degradation.The intervention shows that within-minibatch self-inclusion is sufficient to trigger target-sensitivity escalation.Source: §6 · p. 9

• The authors report that they reviewed all AI-assisted content and take responsibility for it.Source: AI USE DISCLOSURE · p. 9

REPRODUCIBILITY STATEMENT

• Datasets and model architectures are publicly available, with preprocessing, experimental setup, and hyperparameter configurations documented.The statement says source code for the algorithms and training pipelines will be made publicly available upon publication.Source: REPRODUCIBILITY STATEMENT · p. 9

ETHICS STATEMENT

• The work reports no human subjects, personally identifiable information, sensitive topics, or immediate ethical concerns, and uses standard public datasets.The authors report no direct risks of negative societal impact from the specific algorithms and results.Source: ETHICS STATEMENT · p. 9

B.1 METHOD DETAILS

• UWSR uses a row-wise AdaGrad-style cumulative gradient-energy statistic to scale downstream sensitivity by estimated embedding-row uncertainty.The statistic is reused in a dual role: the optimizer scales updates by its inverse square root, while UWSR weights sensitivity by its inverse.Source: §B.1 · pp. 13–14
• The row-uncertainty weights use table-level shrinkage and are frozen after the first pass; inactive rows receive no additional accumulated information.The accumulator has no exponential decay or bias correction.Source: §B.1 · p. 13
• Realized- and conditional-score-moment variants have nearly identical computational cost and closely agree in Table 2.The penalty requires second-order autodifferentiation through the row score sensitivity.Source: §B.1 · p. 14

B.2 UWSR TRAINING PROCEDURE

• The training procedure accumulates row statistics during the first epoch, then adds a sensitivity penalty to the BCE objective on later epochs.The algorithm freezes normalized row weights after the first pass.Source: §B.2 · p. 14

B.3 ALTERNATIVE Σ CONSTRUCTIONS

• The expected-Fisher alternative uses occurrence-level conditional score moments, while the uniform ablation removes row- and table-specific uncertainty weighting.The uniform penalty is related to double backpropagation and input-Jacobian regularization.Source: §B.3 · p. 15

C DATASET DETAILS

• MovieLens-20M uses timestamp-sorted contiguous windows to predict ratings of at least four stars across 20,000,263 ratings.The monitoring window includes approximately 85% unseen users and 17% unseen items.Source: C DATASET DETAILS · p. 15
• Amazon Electronics uses 2,608,764 binary training examples and user, item, category, and truncated history features.Monitoring users and items all occur in training.Source: C DATASET DETAILS · p. 15
• Avazu uses 40,428,967 binary click examples across 22 categorical fields, with evaluation-time unseen rates reaching 34.6% in some fields.The official training file provides 28,300,276 examples.Source: C DATASET DETAILS · p. 15

D MODEL, TRAINING AND HYPERPARAMETER DETAILS

• Sparse tables use 32-dimensional embeddings, and the shared consumer is a WuKong-inspired interaction model with residual blocks, factorization heads, and a SiLU output network.The sparse tables are zero-initialized, with symmetry broken by the interaction block’s linear projection path.Source: D MODEL, TRAINING AND HYPERPARAMETER… · p. 15
• Table 4 reports paired epoch-four test-set changes averaged over five seeds, with two-sided 95% t-intervals against one-pass Adam checkpoints.Positive values denote improvements.Source: Table 4 · p. 16

E VALIDATION RESULTS AND ADDITIONAL COMPARISONS

• Table 3 reports epoch-four validation ΔBCE (%) against the corresponding one-pass model, with positive values denoting improvement.Source: Table 3 · p. 16

F ACCUMULATOR GRANULARITY ABLATION

• Table 5 is an Amazon Electronics accumulator-granularity ablation after four epochs using seed 7; both variants select λ = 0.03 on validation.Auxiliary-state counts exclude model parameters and optimizer state.Source: Table 5 · p. 16

G ARCHITECTURE RESULTS

• Table 6 compares Amazon validation results across WuKong, DCNv2, and AutoInt using ΔBCE relative to each architecture’s one-pass baseline.Source: Table 6 · p. 17

H COMPUTATIONAL COST

• Paired computational-cost arms show later-pass ratios of 1.16 and 1.20 and end-to-end ratios of 1.12 and 1.14.The table defines overhead relative to four-pass naive replay; later-pass step time is relative to one naive replay step.Source: H COMPUTATIONAL COST · p. 17, Table 7 · p. 17