Selective Test-Time Compute Scaling for Click-Through Rate Prediction via Uncertainty-Triggered Feature Path Exploration

CTR models estimate click probabilities from sparse categorical fields such as user profiles and item attributes. WDL, DeepFM, DCN, and xDeepFM improved memorization and low- to high-order interactions; later gating and attention methods introduced dynamic feature selection. However, industrial values typically follow a power-law frequency distribution. Tail embeddings may be poorly trained or statistically close to random initialization. The paper therefore asks whether post-training inference can selectively compensate for reliability differences that training-time architecture design cannot observe per request.

Given a frozen model Fθ and complete feature set F_full, the task is to estimate P(y|F_full) without updating parameters, adding trainable parameters, or accessing training labels. A near-zero logit may indicate epistemic uncertainty or genuine aleatoric ambiguity near a 50% click probability. Marginal feature frequency also fails when individually common values form a novel interaction. Uniform multi-path inference wastes compute on easy cases and can repeatedly sample unreliable features.

• ��Frequency prior: a Count-Min Sketch-inspired structure stores approximate training counts and applies saturation normalization with η. •Dual-signal uncertainty: model confidence from |logit|/γ is combined with attribution-weighted frequency, targeting both decision-boundary ambiguity and sparse representation knowledge. •Selective exploration: all instances are filtered, but only uncertain ones receive K(x)=floor(Kmaxu(x)) additional paths. •Consistency aggregation: path predictions are weighted by mutual agreement rather than averaged blindly.

• ��Initial inference: run the frozen CTR backbone on F_full to obtain logit(x).
• ��Attribution: backpropagate to each embedding and compute attr(fi)=||∇ei logit(x)||2; only input gradients are retained.
• ��Frequency index: maintain L hash tables per field, take the minimum estimated count, and normalize as min(cnt(fi),η)/η.
• ��Uncertainty: compute s_model=min(|logit|/γ,1), attribution-weighted s_freq, then u=1-[αs_model+(1−α)s_freq].
• ��Filtering and exploration: retain features above offline field thresholds τi. For uncertain inputs, sample diverse subsets using reliability and attribution strength.
• ��Aggregation: combine path predictions with consistency weights; confident inputs return the filtered prediction directly.

The evaluation covers four datasets and three backbone architectures, comparing UTTSI with training-phase CTR models and feature-selection baselines. The supplied text does not name the datasets or report individual AUC, Logloss, split, or baseline values, so those details cannot be reconstructed. The reported setup uses γ equal to the 95th percentile of validation-set absolute logits; Kmax controls the maximum exploration depth. Input-gradient attribution costs approximately 0.5–1 forward pass. A separate seven-day online A/B test evaluates production impact.

The paper reports consistent and statistically significant gains across all four datasets and three backbones, suggesting that UTTSI is not tied to one architecture. The most specific online result is a 5.3% relative CTR improvement with p<0.01. Average inference cost is approximately 2.8× the base model, while parallel execution keeps worst-case latency at a single-forward-pass level. Confident examples skip exploration entirely, supporting the claim that uncertainty-aware allocation is more efficient than applying a fixed number of random paths to every request.

UTTSI can wrap existing CTR services for advertising, e-commerce, feed recommendation, and search ranking, especially where categorical features are long-tailed and retraining is expensive. Deployment requires a frequency index, a differentiable path to input embeddings, and calibrated α, γ, field thresholds, and Kmax. The expected operational pattern is fast inference for well-supported requests and deeper exploration for sparse or boundary cases, with an average cost near 2.8×.

The framework assumes differentiable backbones, accessible embeddings, and sufficiently stable training-frequency statistics. Marginal frequency may miss novel high-order interactions, while gradients add computation and may be noisy. Random path construction introduces throughput and engineering complexity. The supplied text lacks complete offline tables, dataset identities, detailed ablations, and confidence intervals, preventing precise attribution of gains to filtering, uncertainty estimation, or aggregation. Future work should study interaction-aware priors, forward-only attribution, dynamic SLO-aware scheduling, calibration, fairness, and distribution drift.