MARS: A Momentum-Aware Adaptive Rating System for Personalized Assessment

Vikrant Sahu; Khethavath Sunil Naik; Gagan Raj Gupta

cs.CYOct 15, 2026

MARS: A Momentum-Aware Adaptive Rating System for Personalized Assessment

Authors: Vikrant Sahu, Khethavath Sunil Naik, Gagan Raj Gupta

Organizations: Department of Computer Science and Engineering, Indian Institute of Technology Bhilai, Chhattisgarh, India

Abstract

Adaptive assessment systems personalize learning by estimating learner proficiency and recommending suitable questions. However, many existing approaches rely on fixed difficulty labels, static rating updates, or black-box prediction models that provide limited control over rating stability, interpretability, and time-constrained routing. This paper proposes MARS, a Momentum-Aware Adaptive Rating System for interpretable adaptive assessment. MARS represents the question bank as a directed weighted knowledge graph and updates learner proficiency using dynamic rating sensitivity, response quality, and momentum-aware learner velocity. We also formulate a time-budgeted mark-maximization objective in which the policy selects questions within a fixed test duration under negative marking. Experiments on ASSISTments 2009 and MARS-SimExam evaluate MARS for prediction, rating stability, and adaptive routing. Results show that MARS provides smoother rating updates than Fixed Elo and achieves the highest score under time-budgeted negative-marking routing, improving the total score by 8.09 over the strongest baseline and reducing overtime violations from 50% to 5.6%. These results suggest that MARS is suitable for real-time, interpretable, and deployment-friendly adaptive assessment.

Figures & tables

Fig. 1: Overview of the MARS online rating and routing pipeline.

Dataset	Learners	Items	Interactions	Topics
ASSISTments 2009	4,217	26,688	346,860	123
MARS-SimExam	300	1,091	277,500	54

TABLE I: Dataset Summary

Model	AUC	Accuracy	LogLoss	Brier
Majority	0.5000	0.6883	0.6207	0.2147
FixedElo	0.7737	0.7430	0.6425	0.1873
BKT	0.7529	0.7390	0.5215	0.1758
DKT	0.8648	0.8027	0.4017	0.1332
GKT	0.8658	0.8124	0.3967	0.1298
MARS	0.7532	0.7260	0.6858	0.1987

TABLE II: Online correctness prediction results on ASSISTments.

Model	AUC	Accuracy	LogLoss	Brier
Majority	0.5000	0.3130	0.8529	0.3272
FixedElo	0.8244	0.8413	0.4665	0.1301
BKT	0.7043	0.6024	0.8637	0.2941
DKT	0.7398	0.6410	0.6129	0.2132
GKT	0.6909	0.4475	0.7436	0.2739
MARS	0.8265	0.8407	0.4906	0.1329

TABLE III: Online correctness prediction results on the synthetic dataset.

Policy	Score	Score/min	Marks	Overtime	Time (s)
BKT	75.68	1.36	93.53	48.9%	3282.91
DKT	81.19	1.48	98.69	50.0%	3282.84
GKT	66.01	1.19	86.56	46.7 %	3280.63
MARS	89.28	1.70	98.27	5.6%	3132.54

TABLE IV: Time-budgeted adaptive routing.

Model	Complexity	Memory	Online	Suitable Use
Fixed Elo	$O(1)$	Low	$O(1)$	Web rating engine
BKT	$O(S)$	Low	$O(1)$	Skill mastery tracking
DKT	$O(Th^{2})$	High	$O(h^{2})$	GPU/server prediction
GKT	$O(\|E\|h)$	High	$O(\|E\|h)$	Graph KT server
MARS	$O(d^{k_{h}})$	Low	$O(1)$	Adaptive learning platform

TABLE V: Adaptability Comparison

Symbol	Value	Meaning	Practical effect
$w_{\text{score}}$	7.83	Expected score weight	Prioritizes questions with high expected score under negative marking.
$w_{\text{score/time}}$	0.55	Score-per-time weight	Rewards questions that provide more expected score per second.
$w_{\text{diff}}$	1.98	Difficulty-fit weight	Encourages questions near the learner’s adaptive target difficulty.
$w_{\text{topic}}$	0.80	Weak-topic bonus	Increases priority for topics where the learner shows weakness.
$w_{\text{div}}$	1.14	Diversity weight	Discourages repeatedly selecting questions from the same topic region.
$w_{\text{time}}$	0.31	Time penalty weight	Penalizes questions with high predicted response time.

TABLE VI: Main MARS hyperparameters used in the time-budgeted routing experiment.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Model Variant	AUC	Acc.	LogLoss	Brier	MAU	SDU
MARS-Final	0.7532	0.7260	0.6858	0.1987	4.9461	7.6794
w/o Momentum	0.7504	0.7232	0.6892	0.1999	4.7384	7.7633
w/ Fixed K	0.7698	0.7377	0.6654	0.1916	9.3175	13.6527
w/o QualityFactor	0.7529	0.7247	0.6875	0.1993	4.9353	7.6716
w/o RapidCap	0.7566	0.7314	0.6728	0.1949	5.1348	7.8485
w/ StreakMultiplier	0.7244	0.7325	1.0238	0.2016	5.3362	8.8159

Appendix

TABLE VII: Ablation study of MARS components (

N=104,858

for all variants).

MAU

and

SDU

denote Mean Absolute Update and Update Standard Deviation, respectively.

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