Towards a Unified Framework of Optimal Input-Side Dimensional Configuration for Deep CTR Prediction

Chaohua Yang; Fuyuan Lyu; Xing Tang; Dugang Liu; Xiuqiang He; Zhong Ming

cs.IROct 26, 2026

Towards a Unified Framework of Optimal Input-Side Dimensional Configuration for Deep CTR Prediction

Authors: Chaohua Yang, Fuyuan Lyu, Xing Tang, Dugang Liu, Xiuqiang He, Zhong Ming

Organizations: College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China · McGill University, Montreal, Canada · Shenzhen Technology University, Shenzhen, China

Abstract

Deep click-through rate (CTR) prediction has achieved substantial success through increasingly expressive feature interaction architectures. However, predictive performance also depends on how input-side information is configured before interaction modeling. Existing studies have shown that selecting informative samples, features, or embedding units can improve prediction accuracy. Nevertheless, they primarily optimize these selection mechanisms independently along a single input-side dimension, overlooking their shared basic form and the inherent dependencies across input levels, thereby limiting the effectiveness of input-side dimensional configuration. To address this issue, we propose OptIDC, a unified framework for Optimal Input-side Dimensional Configuration in deep CTR prediction. OptIDC jointly learns sample, feature, and embedding-unit level configurations within a unified framework by integrating their corresponding selection mechanisms. To explicitly coordinate selection decisions across different levels, OptIDC further introduces a selection-weighted Optimal Transport mechanism that aligns coarse- and fine-grained selections via transport over finite measures, thereby alleviating cross-level selection conflicts while preserving the semantics of each input level. Moreover, OptIDC is model-agnostic and can be seamlessly integrated into existing CTR models. Extensive experiments on four real-world benchmark datasets demonstrate that OptIDC consistently achieves higher AUC than existing input-side selection methods, validating the effectiveness of unified input-side dimensional configuration.

Figures & tables

Figure 1. Overview of the input-side selection methods for deep CTR prediction. <Figure 1. Fully described in the text.> <A full description of Figure 1 can be found in the second paragraph of Section 1.>

Panel of Figure 2 — Figure 2. (a) A comparison of the performance of different selection methods on the Avazu dataset. (b) The association between selection consistency and model performance on the Avazu dataset. <Figure 2. Fully described in the text.> <A full description of Figure 2 can be found in Section 3.1.>

Figure 3. The architecture of the Optimal Input-side Dimensional Configuration (OptIDC) framework. <Figure 3. Fully described in the text.> <A full description of Figure 3 can be found in Section 4.1.>

Dataset	Model	DNN		DeepFM		DCN		AutoInt		FinalMLP
Dataset	Model	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$
Avazu	Backbone	.7893 $\pm$ .0001	.3757 $\pm$ .0001	.7896 $\pm$ .0004	.3759 $\pm$ .0004	.7893 $\pm$ .0004	.3759 $\pm$ .0004	.7895 $\pm$ .0003	.3755 $\pm$ .0003	.7898 $\pm$ .0004	.3740 $\pm$ .0003
	AutoField	.7840 $\pm$ .0007	.3812 $\pm$ .0007	.7842 $\pm$ .0003	.3809 $\pm$ .0008	.7838 $\pm$ .0006	.3806 $\pm$ .0004	.7838 $\pm$ .0002	.3815 $\pm$ .0005	.7835 $\pm$ .0006	.3812 $\pm$ .0015
	LPFS	.7888 $\pm$ .0007	.3762 $\pm$ .0009	.7896 $\pm$ .0003	.3758 $\pm$ .0003	.7894 $\pm$ .0003	.3758 $\pm$ .0003	.7894 $\pm$ .0004	.3756 $\pm$ .0004	.7898 $\pm$ .0002	.3739 $\pm$ .0001
	OptEmbed	.7884 $\pm$ .0008	.3766 $\pm$ .0009	.7895 $\pm$ .0004	.3756 $\pm$ .0003	.7885 $\pm$ .0007	.3765 $\pm$ .0007	.7884 $\pm$ .0009	.3768 $\pm$ .0010	.7885 $\pm$ .0007	.3757 $\pm$ .0011
	OptFS	.7907 $\pm$ .0002	.3736 $\pm$ .0001	.7915 $\pm$ .0002	.3731 $\pm$ .0001	.7908 $\pm$ .0001	.3735 $\pm$ .0001	.7904 $\pm$ .0003	.3738 $\pm$ .0001	.7916 $\pm$ .0005	.3730 $\pm$ .0003

Table 1. Results on Avazu and Criteo (mean

\pm

standard deviation over five runs with different random seeds), where the best and second best results are marked in bold and underlined, respectively. Note that ∗ indicates a significance level of

p\leq 0.05

based on a two-sample t-test between our method and the best baseline.

Times (sec)	Backbone	OptEmbed	OptFS	AutoDim	AutoDenoise	OptIDC
Train (Total)	1069	3378	1301	2613	2481	2575
Train (Batch)	0.0847	0.0930	0.0902	0.1880	0.0989	0.1032
Inference	0.0034	0.0042	0.0040	0.0124	0.0040	0.0041

Table 2. Training and inference time on the Avazu dataset.

Dataset	Method	DNN		DeepFM		DCN		AutoInt		FinalMLP
Dataset	Method	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$
Avazu	AOP	0.7912	0.3731	0.7916	0.3731	0.7911	0.3735	0.7911	0.3734	0.7920	0.3727
	DSFS	0.7911	0.3736	0.7917	0.3732	0.7914	0.3734	0.7911	0.3737	0.7925	0.3728
	DSFS+OT	0.7915	0.3733	0.7919	0.3731	0.7921	0.3728	0.7916	0.3734	0.7926	0.3725
	DSES	0.7913	0.3738	0.7920	0.3729	0.7912	0.3734	0.7913	0.3732	0.7920	0.3731
	DSES+OT	0.7915	0.3738	0.7921	0.3729	0.7917	0.3732	0.7923	0.3727	0.7921	0.3729

Table 3. Ablation analysis of our method on the Avazu dataset, with the best results marked in bold.

Figure 4. Model size of OptIDC and baselines on four datasets. <Figure 4. Fully described in the text.> <A full description of Figure 4 can be found in Section 5.4.>

Panel of Figure 5 — Figure 5. Analysis of cost matrix design in OT coordination and different coordination methods on the Avazu dataset. <Figure 5. Fully described in the text.> <A full description of Figure 5 can be found in Section 5.5.>

Figure 6. Selection consistency evaluation of OptIDC on the Avazu and Criteo datasets. <Figure 6. Fully described in the text.> <A full description of Figure 6 can be found in Section 5.6.>

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Avazu	Criteo	ML1M	AliCCP
#Train	32,343,174	36,672,494	800,167	38,070,670
#Validation	4,042,897	4,584,061	100,021	4,229,235
#Test	4,042,896	4,584,062	100,021	43,016,614
#Field	24	39	7	18
#Feature	4,428,306	6,780,406	13,240	1,283,107

Appendix

Table 4. Dataset statistics.

Dataset	Model	DNN		DeepFM		DCN		AutoInt		FinalMLP
Dataset	Model	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$
ML1M	Backbone	.8151 $\pm$ .0001	.5192 $\pm$ .0007	.8147 $\pm$ .0006	.5201 $\pm$ .0015	.8148 $\pm$ .0004	.5199 $\pm$ .0013	.8148 $\pm$ .0004	.5205 $\pm$ .0020	.8138 $\pm$ .0003	.5236 $\pm$ .0017
	AutoField	.8137 $\pm$ .0006	.5211 $\pm$ .0010	.8137 $\pm$ .0003	.5212 $\pm$ .0003	.8141 $\pm$ .0002	.5206 $\pm$ .0012	.8137 $\pm$ .0003	.5209 $\pm$ .0016	.8137 $\pm$ .0002	.5225 $\pm$ .0011
	LPFS	.8154 $\pm$ .0006	.5181 $\pm$ .0004	.8158 $\pm$ .0005	.5194 $\pm$ .0014	.8157 $\pm$ .0004	.5177 $\pm$ .0006	.8153 $\pm$ .0007	.5184 $\pm$ .0010	.8136 $\pm$ .0008	.5227 $\pm$ .0007
	OptEmbed	.8156 $\pm$ .0004	.5188 $\pm$ .0007	.8155 $\pm$ .0006	.5188 $\pm$ .0009	.8158 $\pm$ .0004	.5176 $\pm$ .0007	.8159 $\pm$ .0004	.5177 $\pm$ .0011	.8142 $\pm$ .0010	.5209 $\pm$ .0012
	OptFS	.8161 $\pm$ .0002	.5178 $\pm$ .0004	.8163 $\pm$ .0003	.5173 $\pm$ .0004	.8164 $\pm$ .0001	.5171 $\pm$ .0003	.8161 $\pm$ .0004	.5173 $\pm$ .0007	.8156 $\pm$ .0003	.5194 $\pm$ .0013

Appendix

Table 5. Results on ML1M and AliCCP (mean

\pm

standard deviation over five runs with different random seeds), where the best and second best results are marked in bold and underlined, respectively. Note that ∗ indicates a significance level of

p\leq 0.05

based on a two-sample t-test between our method and the best baseline.

Figure 7. Comparison of sample retention ratio and embedding retention ratio between OptIDC and baselines on the Avazu dataset. <Figure 7. Fully described in the text.> <A full description of Figure 7 can be found in Appendix C.4.>

Dataset	Method	DNN		DeepFM		DCN		AutoInt		FinalMLP
Dataset	Method	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$	AUC $\uparrow$	LogLoss $\downarrow$
Criteo	AOP	0.8106	0.4407	0.8104	0.4409	0.8107	0.4406	0.8103	0.4417	0.8108	0.4410
	DSFS	0.8109	0.4408	0.8106	0.4410	0.8110	0.4406	0.8109	0.4409	0.8109	0.4408
	DSFS+OT	0.8110	0.4406	0.8107	0.4409	0.8112	0.4405	0.8110	0.4408	0.8111	0.4405
	DSES	0.8108	0.4407	0.8107	0.4409	0.8109	0.4408	0.8109	0.4406	0.8110	0.4408
	DSES+OT	0.8109	0.4407	0.8108	0.4408	0.8110	0.4407	0.8110	0.4405	0.8112	0.4404

Appendix

Table 6. Ablation analysis of our method on the Criteo dataset, with the best results marked in bold.

Figure 8. Sensitivity analysis of key parameters is performed on the Avazu dataset. <Figure 8. Fully described in the text.> <A full description of Figure 8 can be found in Appendix C.5.>

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Click-through rate (CTR) prediction estimates which ads or items users will click to improve ranking, recommendation, and advertising decisions.

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Beyond Interaction Capacity: Estimator Scaling with Recursive Models for CTR Prediction

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Georgia Institute of Technology · Google Research

Feature Interaction Modeling Ensemble Learning CTR Prediction

Open paper AskPDF arXiv

Click-Through Rate prediction, a core task in recommendation and advertising systems, relies on modeling interactions among sparse categorical features. Explicit cross networks are a central paradigm for CTR prediction, and recent progress has largely come from increasing the interaction capacity of a single predictor through deeper cross networks and more expressive cross operators. We revisit whether continually increasing interaction capacity remains the most effective way to improve predictive performance, and find that its benefits quickly exhibit diminishing returns even as capacity continues to grow. This motivates a complementary scaling direction that we call estimator scaling, where additional resources are used to incorporate multiple related estimators rather than only enlarging a single predictor. Through theoretical analysis, we show that the gains from estimator scaling are governed by the amount of non-shared predictive variation available across estimators. However, exploiting this variation naively can be expensive: independently trained models provide substantial estimator diversity but require deployment cost to grow with ensemble size. This motivates a parameter-efficient realization of estimator scaling that can incorporate diversity from multiple estimator sources without maintaining multiple full models. Building on this view, we introduce RECursive Averaged Predictor (RECAP), a parameter-efficient recursive CTR model that operationalizes estimator scaling at three levels: distillation across independently trained models, exponential moving averaging over training trajectories, and aggregation over inference-time routes within a weight-shared recursive backbone. Experiments across multiple benchmarks establish new state-of-the-art predictive performance on standard benchmarks, while placing the RECAP on a favorable performance-parameter Pareto frontier.

Abstract

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