Candidate-dependent residual routing trades top-of-list accuracy for recall in sequential recommendation
Authors: Han Chen, Yingrui Li
Organizations: Department of Computer Science, The University of Texas at Austin, Austin, Texas, United States · Unaffiliated, Fairfax, Virginia, United States
Candidate-dependent routing lets a sequential recommender weight a user's past behaviors differently for each item it scores. We test whether this flexibility helps by adding a small residual routing module to a self-attentive baseline, in two versions that differ only in what sets the routing weights: the user's history representation or the candidate item's embedding. Across five paired seeds on the REES46 cosmetics-shop dataset, with matched training for all three models, candidate-dependent routing leaves the primary metric, normalized discounted cumulative gain at cutoff ten (NDCG@10), essentially unchanged (mean relative change +0.003%). Secondary and exploratory analyses show that this flat average hides two effects that cancel. The candidate-dependent model places more relevant items in its top ten (recall +1.81%) but ranks the first one lower (mean reciprocal rank -1.09%), and most of its new hits land at positions six to ten. Its gains come from queries with at least one target among the user's last 50 events, while queries whose targets all lie outside that window get worse. In this form, candidate-dependent routing trades accuracy at the top of the list for recall further down.
Figures & tables
Figure 1: Scoring with the residual routing module. (A) The baseline (B) scores every candidate against the same history representation h . (B) The two routed models use the same residual form and differ only in the routing vector that weights the behavior-stream means: the history representation for user-dependent routing (U) and the candidate embedding for candidate-dependent routing (C). In both, the residual term still depends on the candidate. The scalar α starts at zero, and all parameters are trained.
Seed
B
U
C
C/B −1 (%)
2026100601
0.343049
0.344798
0.343869
+0.2391
2026100602
0.344962
0.343568
0.342639
-0.6734
2026100603
0.346149
0.346769
0.346484
+0.0968
2026100604
0.343179
0.345101
0.345436
+0.6578
2026100605
0.345625
0.347483
0.344564
-0.3068
Table 1: Normalized discounted cumulative gain at cutoff ten (NDCG@10) for each of the five paired seeds at epoch 12. B, baseline; U, user-dependent routing; C, candidate-dependent routing. Values are query means weighted to the stratum proportions of the test partition. Relative changes are computed before rounding.
Figure 2: Effect of candidate-dependent routing on NDCG@10, overall and by query type. (A) Relative change for the candidate-dependent model (C) against the baseline (B) in each of the five seeds, with their mean. The one-sided 95% confidence bound (+0.49%) lies below the +1% margin set in advance. (B) Mean paired relative change in each stratum (exploratory). A query is all-novel if none of its targets appears in its history (at most 50 earlier events), all-repeat if all of them do, and mixed otherwise. Percentages beside the stratum names are shares of the test population; each stratum contributes 1,536 evaluated queries. Lines run from zero to each estimate and are not confidence intervals.
Metric @10
B
U
C
C/B −1 (%)
Seeds favoring C
NDCG
0.344592
0.345544
0.344598
+0.003
3/5
Recall
0.429810
0.434808
0.437542
+1.806
5/5
Hit rate
0.449208
0.454164
0.456819
+1.701
5/5
MRR
0.329954
0.328900
0.326372
-1.085
0/5
Table 2: Ranking metrics at cutoff ten. B, baseline; U, user-dependent routing; C, candidate-dependent routing; NDCG, normalized discounted cumulative gain; MRR, mean reciprocal rank. Model means average the five seed-level weighted means, and relative changes average the five paired changes. NDCG@10 is the primary metric; the others are secondary. Supplemental Tables S3 and S4 give seed-level results at cutoffs 10 and 20.
Position
Baseline B
Candidate C
C − B
1
0.266793
0.257033
-0.009761
2
0.029430
0.034616
+0.005186
3
0.014428
0.017917
+0.003489
4–10
0.033942
0.035034
+0.001092
Total
0.344592
0.344598
+0.000006
Table 3: Contribution of each rank position to NDCG@10 (exploratory). Each entry is the weighted mean over queries of the discounted gain from a target at that position, divided by the query’s ideal discounted cumulative gain, then averaged over the five seeds (absolute NDCG scale). The columns sum to the model means, so the C − B column sums to the difference in means, not to the mean paired relative change.
Figure 3: Candidate-dependent routing and cross-stream attention in the earlier Transformer models. Points are relative changes in NDCG@10 between seed-averaged model means; bars are exploratory 95% bootstrap intervals that resample users and paired seeds. Candidate-dependent routing starts the routing token from the candidate embedding instead of a history summary, with streams unable to attend to one another directly. Cross-stream attention lets the streams attend to one another in the candidate-dependent model. On REES46, both models in the routing comparison were retrained, and the cross-stream comparison pairs a retrained model with an original one.
Dataset
Training
Validation
Test
Catalog items
REES46
1,761,398
423,081
507,957
40,749
RetailRocket
787,209
246,408
299,730
225,101
KuaiSAR-small
1,013,508
185,227
205,745
1,151,617
Table S1: Processed query counts and ranking catalog sizes. Counts precede selection of the evaluation cohorts. The catalog contains training target items and excludes reserved tokens.
Seed
C − B
C − U
U − B
C/U −1 (%)
U/B −1 (%)
2026100601
+0.00082011
-0.00092968
+0.00174979
-0.2696
+0.5101
2026100602
-0.00232286
-0.00092863
-0.00139423
-0.2703
-0.4042
2026100603
+0.00033500
-0.00028591
+0.00062090
-0.0824
+0.1794
2026100604
+0.00225743
+0.00033504
+0.00192240
+0.0971
+0.5602
2026100605
-0.00106033
-0.00291821
+0.00185788
-0.8398
+0.5375
Table S2: Paired NDCG@10 contrasts for all five seeds. Absolute differences use the NDCG scale; relative differences are percentages. C/B is the primary contrast; C/U and U/B are descriptive.
Model / seed
NDCG@10
Recall@10
MRR@10
Hit rate@10
B / 2026100601
0.343049
0.425816
0.329085
0.445334
B / 2026100602
0.344962
0.429973
0.330582
0.449318
B / 2026100603
0.346149
0.434908
0.330473
0.454692
B / 2026100604
0.343179
0.426366
0.328928
0.445636
B / 2026100605
0.345625
0.431984
0.330703
0.451058
U / 2026100601
0.344798
0.438126
0.327147
0.457117
Table S3: Weighted query metrics at cutoff 10 for every epoch-12 checkpoint in the paired experiment. B denotes the baseline, U user-dependent routing and C candidate-dependent routing.
Model / seed
NDCG@20
Recall@20
MRR@20
Hit rate@20
B / 2026100601
0.359525
0.490730
0.333617
0.509691
B / 2026100602
0.359072
0.486571
0.334577
0.507937
B / 2026100603
0.360277
0.491965
0.334308
0.511388
B / 2026100604
0.358354
0.487403
0.333085
0.506862
B / 2026100605
0.359533
0.488003
0.334495
0.507147
U / 2026100601
0.357951
0.490254
0.330795
0.509644
Table S4: Weighted query metrics at cutoff 20 for every epoch-12 checkpoint. These outcomes are descriptive secondary measures.
Contrast
Metric
Mean difference
Relative (%)
Positive seeds
C/B
NDCG@10
+0.000006
+0.003
3/5
C/B
Recall@10
+0.007732
+1.806
5/5
C/B
Hit rate@10
+0.007611
+1.701
5/5
C/B
MRR@10
-0.003582
-1.085
0/5
C/U
NDCG@10
-0.000945
-0.273
1/5
C/U
Recall@10
+0.002734
+0.632
5/5
Table S5: Overall descriptive contrasts at cutoff 10. Relative effects are the mean of five paired seed ratios, not ratios of the model means. A positive seed favors the numerator model.
Stratum
Contrast
Mean difference
Relative (%)
Positive seeds
all-novel
C/B
-0.005092
-7.186
0/5
all-novel
C/U
-0.002650
-3.792
0/5
all-novel
U/B
-0.002442
-3.430
1/5
all-repeat
C/B
+0.004879
+0.764
5/5
all-repeat
C/U
+0.000517
+0.082
3/5
all-repeat
U/B
+0.004362
+0.682
5/5
Table S6: Exploratory NDCG@10 contrasts within repeat strata. Novelty is defined against the retained history of at most 50 strictly prior events. Relative effects average the five paired seed ratios. Positive seeds favor the first model in each contrast.
Model / seed
Train (min)
Train peak (MiB)
Evaluate (s)
Eval. peak (MiB)
B / 2026100601
55.37
540.4
31.74
130.1
B / 2026100602
50.52
540.4
28.23
130.1
B / 2026100603
67.86
540.4
33.44
130.1
B / 2026100604
54.84
540.4
32.04
130.1
B / 2026100605
47.05
540.4
29.22
130.1
U / 2026100601
52.21
551.3
37.63
140.2
Table S7: Observed training and evaluation costs. Peak memory is allocated GPU tensor memory. Scheduling and device contention differed among runs, so timing differences cannot be attributed solely to the models.
Model / seed
Epoch 1
Epoch 2
Epoch 3
Epoch 4
Epoch 5
Epoch 6
B / 2026100601
3.1383
2.2913
1.7979
1.5140
1.3450
1.2320
B / 2026100602
3.1300
2.2575
1.7734
1.5014
1.3376
1.2266
B / 2026100603
3.1225
2.2634
1.7902
1.5112
1.3412
1.2268
B / 2026100604
3.1219
2.2698
1.7850
1.5087
1.3407
1.2276
B / 2026100605
3.1250
2.2803
1.7856
1.5053
1.3380
1.2268
U / 2026100601
3.1150
2.2797
1.7758
1.4922
1.3263
1.2168
Table S8: Mean training losses for epochs 1–6 of all fifteen fits. Each epoch contains 1,761,398 queries and 3,441 optimizer updates.
Model / seed
Epoch 7
Epoch 8
Epoch 9
Epoch 10
Epoch 11
Epoch 12
B / 2026100601
1.1491
1.0839
1.0306
0.9834
0.9428
0.9080
B / 2026100602
1.1458
1.0817
1.0281
0.9835
0.9428
0.9077
B / 2026100603
1.1439
1.0777
1.0242
0.9789
0.9379
0.9039
B / 2026100604
1.1455
1.0794
1.0270
0.9810
0.9402
0.9060
B / 2026100605
1.1441
1.0794
1.0258
0.9802
0.9411
0.9062
U / 2026100601
1.1361
1.0728
1.0208
0.9751
0.9355
0.9012
Table S9: Mean training losses for epochs 7–12 of all fifteen fits. The final checkpoint was specified before the experiment. Training loss alone does not show that ranking performance has stopped improving.
Dataset
Family
Width
Heads
Seq. layers
Dropout
Learning rate
RetailRocket
Transformer
64
2
1
0.0
0.001
REES46
Transformer
64
2
1
0.0
0.001
KuaiSAR-small
Transformer
64
2
2
0.1
0.0003
Table S10: Training configurations used in the retrospective Transformer analysis, taken from the saved input summaries. Seq. layers denotes the number of causal sequence-encoder layers. Each model uses two query–stream attention blocks and weight decay 0.0001.
Dataset
Model
Seeds
NDCG@10
KuaiSAR-small
Candidate-dependent, full
5
0.002266
KuaiSAR-small
Candidate-dependent, local
5
0.002188
KuaiSAR-small
User-dependent, local
5
0.001587
REES46
Candidate-dependent, full
5
0.298720
REES46
Candidate-dependent, local
5
0.312651
REES46
User-dependent, local
5
0.247203
Table S11: Nine model means supporting the six retrospective Transformer contrasts. Each entry averages five seed-specific weighted query means. REES46 user-dependent and candidate-dependent local models use replacement checkpoints.
Dataset
Contrast
Historical interval (%)
Revised interval (%)
KuaiSAR-small
Conditioning
[+8.99, +66.07]
[+1.78, +98.26]
KuaiSAR-small
Cross-stream attention
[-19.43, +27.64]
[-22.29, +38.93]
REES46
Conditioning
[+22.63, +29.96]
[+21.48, +31.57]
REES46
Cross-stream attention
[-7.83, -1.29]
[-7.98, -1.12]
RetailRocket
Conditioning
[-6.62, +16.49]
[-6.74, +17.46]
RetailRocket
Cross-stream attention
[-0.50, +20.98]
[-0.52, +23.74]
Table S12: Historical and revised exploratory 95% intervals for all six complete Transformer contrasts. Historical intervals resampled users independently for each seed draw and fixed the ratio denominator; revised intervals use the same sampled users across seeds and recompute both model means.
Dataset
Family
Contrast
Current evidence
KuaiSAR-small
Occurrence
Conditioning
Excluded; paired ranks incomplete
KuaiSAR-small
Occurrence
Cross-stream attention
Excluded; paired ranks incomplete
KuaiSAR-small
Transformer
Conditioning
Reported; paired ranks complete
KuaiSAR-small
Transformer
Cross-stream attention
Reported; paired ranks complete
REES46
Occurrence
Conditioning
Excluded; paired ranks incomplete
REES46
Occurrence
Cross-stream attention
Excluded; paired ranks incomplete
Table S13: Status of all twelve comparisons in the internal analysis plan dated 11 September 2026. All reported Transformer comparisons have five paired seed labels. Comparisons without complete paired query ranks are excluded. Occurrence is the original plan’s name for the excluded model family.
K
Recall
Hit rate
NDCG
MRR
Recall seeds
Hit seeds
1
-3.6655
-3.6603
-3.6603
-3.6603
0/5
0/5
2
-0.5986
-0.7513
-1.4785
-2.0956
1/5
0/5
3
+1.4463
+1.3299
-0.3198
-1.2681
5/5
5/5
5
+1.3752
+1.2705
-0.2859
-1.2214
5/5
5/5
10
+1.8062
+1.7015
+0.0027
-1.0851
5/5
5/5
20
+1.5688
+1.4953
+0.0195
-1.0615
5/5
5/5
Table S14: Exploratory cutoff sensitivity from original historical ranks. Entries are mean paired C/B relative changes (percent). The last columns count seeds favoring C for recall and hit rate. All cutoffs use the original candidate sets, targets and stratum-count weights. NDCG@10 remains the primary outcome; no new primary cutoff is selected.
Stratum
Share (%)
Recall
Hit rate
NDCG
MRR
All-novel
50.9433
-4.5490
-4.6252
-7.1862
-9.6983
All-repeat
47.9298
+3.2887
+3.0563
+0.7636
-0.5539
Mixed
1.1269
+17.9248
+7.5018
+11.5140
+2.8232
Table S15: Exploratory C/B changes by query type at cutoff ten, using original ranks. Shares refer to the complete test partition; each evaluated stratum contains 1,536 queries. Metric changes are means of five paired seed-relative effects (percent). Every seed favors C for recall, hit rate and NDCG in repeat and mixed queries; every seed favors B for those metrics in all-novel queries.
Paired outcome
Share (%)
Δ Recall
Δ NDCG
Δ MRR
B only
2.9002
-0.028362
-0.010923
-0.005929
C only
3.6613
+0.034963
+0.014213
+0.008377
Both hit
42.0206
+0.001131
-0.003284
-0.006029
Neither hit
51.4179
+0.000000
+0.000000
+0.000000
Within queries hit by both models:
C first hit earlier
5.1862
+0.000252
+0.008747
+0.011180
Table S16: Exploratory paired-query decomposition at cutoff ten from original saved ranks. Shares and absolute metric contributions average over five seeds using original query weights. The first four rows partition all query–seed observations. The final three rows partition the both-hit row; their shares are also expressed relative to all query weight.
Score source
Mean paired C/B
One-sided 95% upper
Original GPU evaluation
+0.002698
+0.490404
New CPU diagnostic
+0.008627
+0.526662
Table S17: Original primary result and separate CPU score diagnostic for NDCG@10. Effects and bounds are percentages and retain the same five-seed calculation. All tested exact-tie policies give identical cutoff-ten metrics on the CPU vectors. The CPU result does not replace the historical estimate or reconstruct historical GPU tie behavior.
K
Recall
Hit rate
NDCG
MRR
NDCG seeds
1
-12.3233
-12.3293
-12.3293
-12.3293
0/5
2
-4.0882
-3.9869
-6.2650
-7.1758
0/5
3
-2.8691
-2.6988
-5.1816
-6.2535
1/5
5
-5.2148
-5.1563
-6.1217
-6.7087
1/5
10
-0.2634
-0.2022
-3.1374
-5.0403
0/5
20
-1.8052
-1.7661
-3.5464
-5.1044
0/5
Table S18: Exploratory changed-task diagnostic on new CPU scores. Only targets absent from the recorded history are retained, all recorded-history competitors are excluded, and 3,072 original queries with at least one novel target are evaluated. Original weights are renormalized over this subset. Entries are mean paired C/B relative changes (percent). The last column counts seeds favoring C for NDCG. This is neither a cold-start experiment nor a replacement for the original evaluation.
Sessionized interaction histories contain behavioral patterns that can improve sequential recommendation. However, existing models process all sessions through the same parameterized blocks, regardless of their behavioral differences. Mixture of Experts (MoE) enables conditional computation, but it leaves open what should guide expert allocation. We propose RouteRec, a sequential recommender that uses observed session behavior as the routing criterion. RouteRec summarizes four types of behavioral evidence from sessionized histories: interaction tempo, item-group focus, repetition and carryover, and popularity tendency. It uses these cues to route computation at macro, mid, and micro scopes. Cue-derived scores first select expert groups; within each selected group, the current backbone state then refines expert selection. Across six public datasets and 18 dataset-metric combinations, RouteRec ranks first in 12 and second in three, yielding the best overall average rank of 1.61 compared with 4.11 for the next-best baseline. Additional analyses suggest that the behavioral cues guide expert allocation beyond added capacity and produce routing patterns aligned with observed behavior. Our code is available at https://github.com/jy1559/RouteRec
Junyeong Song, Jaemin Yoo
Korea Advanced Institute of Science and Technology Daejeon, Republic of Korea · Seoul National University Seoul, Republic of Korea
Long-history recommenders often compress each user's history into a compact, candidate-independent memory that is cached and reused to score large candidate pools. We show that real user histories exhibit multi-scale semantic structure, with short-lived intent, medium-term interests, and long-term preferences coexisting in one sequence, and that monolithic cached memories preserve these scales unevenly: linear probes recover recent and mid-range content far worse than long-range content. We call this failure mode temporal aliasing. We propose MARS, a multi-resolution user memory that writes the full history into recurrent state tracks anchored to different half-lives, and a sparse routing reader that materializes compact seed memories by selecting the relevant temporal resolutions for each seed, preserving fixed-size candidate scoring. MARS outperforms strong baselines on three public datasets, with gains that grow with history length. Component-matched ablations with paired tests show that temporal diversity and selective routing each contribute beyond what hard-window memories or added capacity provide. The advantage of MARS over its interface-matched baseline also widens after within-user behavioral shifts, at about 1.02× that baseline's warm-cache serving latency for 1,000 candidates per user.
Recommender systems increasingly face a choice among heterogeneous agents -- collaborative filters, sequential models, content-based retrievers, and LLM-based rerankers -- yet no single agent is uniformly best. We study this choice as task-aware agent ranking under cost constraints using RouteRec, a framework that compares request-level hard selection with item-level learned aggregation over four traditional recommender agents and one LLM reranker agent. On MovieLens-1M, the full quality oracle has substantial headroom (HR@10 = 0.584), confirming that useful cross-agent signal exists. Under a leakage-free 5-fold out-of-fold protocol, however, hard selection remains below BM25 (0.223 vs. 0.254), and selective LLM escalation does not improve it. The same protocol yields a different outcome for learned aggregation: its cheap-only variant matches BM25 in HR and has a higher NDCG point estimate (0.123 vs. 0.114), while gated all-agent aggregation reaches HR@10 = 0.295 with 70.2% LLM calls. The resulting lesson is not that routing is solved, but that request-level selection of one complete agent list is too coarse for this sparse fixed-candidate setting; item-level aggregation is the more promising action space.
Kaiji Zhou, Vladimir Kalmykov, Yue Feng
University of Birmingham Birmingham, United Kingdom