Cross-Day Compatibility of Daily Item Embeddings: An Empirical Study of Alignment, Scale Management, and CTR Adaptation

1 Introduction

• Daily embeddings trained through day t are paired with day t+1 behavior, so multi-day CTR mixes versions whose directions and norms may differ for the same item.Even overlapping rolling windows can yield different coordinate systems while preserving useful within-version relationships.Source: §1 · pp. 1–2
• Related work motivates comparisons of alignment, training continuity, representation geometry, and parameter rescaling in an industrial workflow where the CTR consumer is retrained on mixed versions.Prior examples include orthogonal alignment [5], warm starts and historical regularization [6], structure-preserving incremental recommendation [7], and spherical text embeddings [10].Source: §1 · p. 2
• The study compares 48 configurations, including 32 common-protocol CTR evaluations, across Word2Vec and an item-graph XSimGCL adaptation.Ablations cover initialization, warm starts, transformations, training constraints, and downstream augmentation.Source: §1 · p. 2
• The study asks whether upstream stabilization improves compatibility and CTR, how warm-start scale should be managed, and whether CTR learning adapts to residual version differences.It also examines whether geometric and retrieval metrics help explain effects, and contrasts global state rescaling with per-item output normalization.Source: §1 · p. 2
• Multiple upstream interventions improve compatibility and GAUC, warm starts perform strongly but accumulate scale, and CTR-trained encoders improve directional agreement beyond controls.The section frames these as complementary findings assessed through joint evaluation of trade-offs.Source: §1 · p. 2

2.2.3 Global state rescaling attains the highest observed GAUC

• +4.0% relative GAUC change is the highest observed among 32 CTR configurations for warm_norm, whose day-matched norm change ends at +8.2%.warm_unit reaches +3.1% GAUC, while warm+spherical reaches +3.3% GAUC but has higher LogLoss; warm_norm's paired intervals against warm and warm_unit include zero.Source: Table 1 · p. 3, §2.2.3 · p. 6

2.1.1 Base representations exhibit drift, and retrieval does not determine CTR ordering

• XSimGCL has +76.4% Recall@100 but -0.5% GAUC versus Word2Vec, despite relative cosine and L2 changes of -102.4% and +31.2%.The graph results concern the paper's item–item adaptation; higher co-occurrence recall alone does not justify replacing Word2Vec for this CTR task.Source: Table 1 · p. 3, §2.1.1 · p. 3

2.1.2 Initialization control and alignment both provide positive evidence

• ID-init raises Word2Vec cosine by +51.2% and GAUC by +2.2%; OP raises them by +93.4% and +2.6%, respectively, relative to ordinary Word2Vec.OP raises GAUC in all four representation-family and initialization comparisons, while the cumulative initialization gains cannot be attributed solely to fixed initialization because provenance and parallel optimization also differ.Source: §2.1.2 · pp. 3–4

2.1.3 More flexible matching has distinct geometric and retrieval effects

• +124.9% and +125.4% cosine changes for affine and MLP mappings accompany Recall@100 changes of -58.3% and -62.4%; export-time unit normalization reduces L2 but does not improve GAUC for either tested ID-init+OP pair.In the independently restarted spherical series, ID-init spherical Word2Vec+OP has higher cosine but lower GAUC than unconstrained ID-init Word2Vec+OP.Source: §2.1.3 · p. 4

2.1.4 Geometric trends are informative alongside retrieval and CTR

• Across 17 upstream configurations, cosine has a positive descriptive association with GAUC and L2 a negative one; recall's mixed-configuration association with GAUC is weakly negative.These associations do not establish universal causality; selection still requires GAUC, LogLoss, and retention of behavioral retrieval relationships.Source: §2.1.4 · p. 4

2.2.1 Inherited states yield strong cross-day compatibility

• Warm raises adjacent-day cosine by +127.0% and GAUC by +3.5% versus independent Word2Vec, and the warm family has the highest observed GAUC among daily-version configurations with ordinary DNN training.Figure 1 reports cross-day changes relative to Word2Vec on a fixed held-out cohort.Source: Table 1 · p. 3, §2.2.1 · p. 4, Figure 1 · p. 5

2.2.2 High directional agreement coexists with accumulated scale

• Warm's day-matched norm change grows from +41.8% on Day 1 to +102.5% on Day 8, while its one- and seven-day L2 changes are -80.3% and -3.9%.At a seven-day lag, warm has a total squared-L2 change of -20.6%; the angular and norm-difference terms decompose squared distance, not causal training effects, and the angular term also depends on norms.Source: Figure 1 · p. 5, §2.2.2 · p. 6

2.3.1 Trained encoders achieve the highest directional agreement for most methods

• The CTR-trained encoder has the highest cross-day cosine for four of six upstream methods; for Word2Vec+OP, train-to-test cosine exceeds untrained and SVD controls by 10.8 and 4.0 percentage points.For warm_norm and ID-init spherical Word2Vec+OP, trained train-to-test cosine ranks third and second, respectively, within 3.6 percentage points of each method's maximum.Source: §2.3.1 · pp. 6–7, Table 2 · p. 7

• Augmentation has no consistent benefit across representations: strength-0.5 noise raises GAUC in three of seven pairs, while both all-history comparisons lower it.Source: §2.3.2 · p. 7
• For Word2Vec+OP, noise strength 0.5 maximizes test GAUC, but validation BCE favors strength 1.0.Source: §2.3.2 · p. 7
• Fixed training versions improve GAUC only for Word2Vec+OP among three tested pairs, and also change information timing and coverage.These comparisons support representation-specific selection rather than default noise or history expansion.Source: §2.3.2 · p. 7

3.1 Data, embedding versions, and temporal pairing

• Proprietary behavioral sequences produce daily embeddings, while logged ad impressions and clicks supply CTR training and evaluation data.Embedding windows overlap; catalogs contain at least one million items, and retrieval uses a fixed common candidate set. CTR extracts contain at least one million training and test examples, exclude two service-defined request categories, and label exposed items.Source: §3.1 · p. 7, Table 3 · p. 7

3.2 Systematic ablations and comparison design

• Ablations add, remove, or combine components within a base representation or DNN input protocol; the inventory is not a full factorial design.The interventions span initialization, inheritance, transformations, training constraints, regularization, and augmentation; reused artifacts and small pilots are not independent replications.Source: §3.2 · p. 8, Table 4 · p. 8

3.3 Inherited state and scale management

• Warm variants inherit item and context states, while warm_unit normalizes exported item vectors and warm_norm rescales both tables after each day.Global rescaling uses the full-vocabulary mean item norm and a reference initialization mean, preserving directions and relative norms; warm+spherical instead enforces unit-norm states during training.Source: §3.3 · pp. 8–9

3.4 Joint evaluation metrics

• Evaluation combines same-item cross-day cosine and L2, co-occurrence Recall@100, request-macro GAUC, and LogLoss, reporting changes relative to Word2Vec.Recall uses eligible Day 9 targets and a fixed common candidate set; GAUC averages within-request AUC across requests with both labels, while LogLoss averages eligible-row prediction loss, and both are offline measures.Source: §3.4 · p. 9

3.5 CTR model and training

• A shared item encoder maps fixed precomputed embeddings from all dates to a lower-dimensional space for geometry analysis.The trained encoder is compared with an untrained same-architecture encoder and same-dimension projections; relevant comparisons retain labels, feature processing, and evaluation rules.Source: §3.5 · pp. 9–10

3.6 Temporal trajectories and encoder diagnostics

• Temporal diagnostics compare a held-out item cohort across eight dates and 28 date pairs, averaging squared-L2 decompositions and lag summaries.Encoder diagnostics reuse six saved upstream/CTR pairs and compare fixed mappings across dates, including random projection, SVD, untrained, and trained encoders; outputs are evaluated without additional normalization.Source: §3.6 · p. 10

3.7 Paired uncertainty

• Paired GAUC uncertainty uses 20,000 request-level bootstrap resamples and percentile 95% intervals.Intervals are conditional on the saved models and one test day.Source: §3.7 · p. 10

4.1 Joint evaluation identifies useful stabilization

• Joint evaluation supports stabilization for multi-version CTR, but stronger geometric matching can coincide with retrieval loss or lower GAUC.Geometry diagnoses drift; retrieval and CTR indicate whether a changed representation remains useful.Source: §4.1 · p. 10

4.2 Global scale management and inherited optimization

• Recall changes from -2.3% to +15.9% cannot come from final common output rescaling alone, and warm+spherical does not surpass warm_norm in GAUC or LogLoss.The comparison also changes the loss, optimization settings, and initial contexts, so training-time unit norms alone do not establish the best observed CTR.Source: §4.2 · p. 11

4.3 CTR learning provides a further adaptation stage

• CTR-trained encoders further alleviate residual directional drift, with same-dimensional controls supporting an additional contribution from task learning.Learning is assessed primarily through cosine; raw L2 is auxiliary because an unscaled lower-dimensional random projection can shorten fixed difference vectors without learned alignment.Source: §4.3 · p. 11

4.4 Practical recommendations and online evaluation

• OP is a practical initial baseline when an existing daily Word2Vec pipeline prioritizes limited code changes and low operational overhead.Warm_norm can be evaluated against OP through online A/B testing, weighing offline gains against the cost of retaining and recovering daily embedding tables and vocabulary.Source: §4.4 · p. 11

4.5 Scope and limitations

• Inference is bounded by one industrial setting and main window, mostly one run per configuration, test-informed later choices, and offline-only predictive results.The exploratory paired intervals have no multiple-comparison or selection adjustment; encoder rankings are descriptive point estimates, and the bootstrap omits retraining variability and within-user request dependence.Source: §4.5 · p. 11

5 Conclusion

• Across two representation pipelines, initialization control, post-hoc alignment, and warm starts can improve compatibility and downstream prediction, with benefits and trade-offs assessed jointly.The study identifies geometry, behavioral retrieval, and CTR as complementary evaluation dimensions.Source: §5 · p. 12
• Global state rescaling limits warm-start norm growth and attains the highest observed GAUC, supporting its prioritization in the studied inherited-training workflow.The authors distinguish this from per-item output normalization and recommend separate assessment of the two approaches.Source: §5 · p. 12
• Trained encoders achieve the highest cross-day cosine for four of six upstream methods, supporting complementary roles for upstream stabilization and downstream task learning.Practical choices also depend on the cost of maintaining daily states and versions.Source: §5 · p. 12

A Complete Experimental Inventory

• Small parallel pilots use their own matched asynchronous Word2Vec references and are not comparable to the main evaluation; all observed results use relative percentage changes defined in Section 3.4.Geometry uses Day 7–8 and norm uses Day 8.Source: A Complete Experimental Inventory · p. 14
• The inventory covers 48 configurations, and its metrics are reported as relative percentage changes from Word2Vec (0%), except pilot rows use matched pilot baselines.The inventory also marks missing measurements with dashes.Source: Table 5 · p. 14, A Complete Experimental Inventory · p. 14
• The listed metric columns are Cosine, L2, Norm, Recall, GAUC, and LL.W2V means Word2Vec, and ID means ID-init.Source: A Complete Experimental Inventory · pp. 14–15

E. Fixed training input

• The table lists synchronous W2V prototype 1s with -84.9 and prototype 2s with -58.4; the rows are configurations 47 and 48, respectively.Source: E. Fixed training input · p. 15

A.1 Timing scope

• Timing records include recorded I/O for embeddings, reuse base times for OP without measured OP/unit overhead, and use a separate two-run timing reference for Word2Vec.Graph means cover seven days; ID-init Word2Vec and warm chains cover eight days, while independently restarted spherical training covers Day 8 and temporal pilots cover two days.Source: §A.1 · p. 15
• DNN timing includes validation where recorded, and shared artifacts add no training; differing epochs, I/O, and hardware preclude controlled throughput comparisons.Source: §A.1 · p. 15

B.1 Base representations

• The graph baseline is a study-specific weighted item–item adaptation of XSimGCL that combines neighborhood aggregation and contrastive learning with embedding perturbations.Its construction and objective differ from the original recommendation model; a common positive rescaling sets its exported median norm to a reference scale without unit-normalizing individual vectors.Source: §B.1 · p. 15

B.2 Initialization and inherited states

• ID-init gives each item a deterministic initial state based on its namespace and key, while warm starts inherit prior-day item and context tables and reinitialize missing context states.ID-init vectors remain trainable, and warm_unit changes only exported vectors while warm_norm inherits globally rescaled states.Source: §B.2 · p. 16

B.3 Alignment and scale management

• OP fits an orthogonal map from anchor directions and applies it to full vectors, whereas affine and MLP alternatives fit unconstrained maps by squared-error matching.OP preserves within-version inner products, norms, and cosine rankings; its fitting anchors are disjoint from the evaluation cohort, and the first day is unchanged.Source: §B.3 · p. 16
• Output unit normalization removes per-item norms after training, whereas warm_norm rescales both inherited tables by a common factor and affects subsequent training.warm_norm retains relative item norms.Source: §B.3 · p. 16

B.4 Spherical training constraint

• The spherical SGNS variant constrains item and context vectors to unit norm during training, changing optimization rather than merely normalizing exported vectors.warm+spherical inherits prior-day item directions but uses fresh unit-norm contexts, so its comparison with ordinary warm does not isolate one operation.Source: §B.4 · p. 16

B.5 Temporal regularization

• Both temporal pilots restart with ID-init and encourage agreement with frozen preceding-day directions for common items, while new items receive no historical term.The graph variant adds a cosine-distance penalty; the Word2Vec variant alternates SGNS updates with directional blending that preserves current norms, and the pilots use different optimization procedures and short-pilot scope.Source: §B.5 · p. 16

B.6 Downstream augmentation and version selection

• Residual-noise augmentation samples signed, normalized adjacent-day embedding differences from a same-method training-period reservoir for eligible inputs.Validation and test inputs remain unperturbed, and noisy inputs are not renormalized; historical augmentation substitutes earlier versions or expands rows across versions while retaining labels and other features.Source: §B.6 · p. 16
• Fixed-version training uses a designated later embedding version for earlier exposures, changing information timing and coverage while leaving validation and test mappings unchanged.Partial historical replacement retains one input per row and falls back to the original when history is unavailable.Source: §B.6 · p. 17

B.7 Repeatability scope

• Single-worker Word2Vec and ID-init XSimGCL were bitwise repeatable in the tested environment, but parallel Word2Vec retained scheduling variability.Synchronous prototypes also changed sampling and optimization, and repeatability was checked only in small pilots using a separate same-day retrieval protocol.Source: §B.7 · p. 17

B.8 Dimension and encoder controls

• Random orthogonal projection and uncentered SVD map to the encoder’s output dimension, while the untrained encoder uses a fresh fixed initialization of the trained encoder architecture.SVD uses training dates only, with equal date and within-date item weights, no labels or held-out dates, and no whitening; the trained encoder uses a validation-selected checkpoint.Source: §B.8 · p. 17

B.9 Warm-start temporal diagnostics

• The warm_norm scale target uses the full evolving vocabulary, distinct from the fixed cohort used for temporal diagnostics.Section 3.6 defines the fixed-cohort lag averages and squared-distance decomposition.Source: §B.9 · p. 17

C Complete Encoder Controls

• Tables 6–7 retain 180 geometry values across six methods, five representations, three date scopes, and two metrics, with transformed outputs sharing an output dimension and no extra normalization.Table 6 reports cosine changes and Table 7 reports L2 changes, each using original Word2Vec input as a common 0% baseline.Source: C Complete Encoder Controls · p. 17, Table 6 · p. 18, Table 7 · p. 18

D Paired Statistical Analysis

• Table 8 reports differences in Word2Vec-relative GAUC change, with pointwise 95% paired-bootstrap intervals; positive differences favor the method on the right.Source: Table 8 · p. 19
• Each bootstrap resample uses matched requests for both models, and intervals are conditional on saved models and one test day.Source: D Paired Statistical Analysis · p. 19
• The exploratory intervals do not cover retraining or other test dates and include no multiple-comparison or selection adjustment.Source: D Paired Statistical Analysis · p. 19