CLEAN: Psychometrically Consistent Incremental Cognitive Diagnosis under Concept-Space Expansion via Architectural Isolation

Tao He; Jinxing Xiang; Fan Jiang

cs.LGOct 1, 2026

CLEAN: Psychometrically Consistent Incremental Cognitive Diagnosis under Concept-Space Expansion via Architectural Isolation

Authors: Tao He, Jinxing Xiang, Fan Jiang

Organizations: Faculty of Education, Shenzhen University Shenzhen, China · School of Education Science, Guangdong Polytechnic Normal University Guangzhou, China

Abstract

Cognitive diagnosis (CD) is a fundamental task in intelligent education that profiles learner proficiency over knowledge concepts. In real-world learning platforms, newly added items continually introduce previously unseen concepts, necessitating dynamic expansion of the underlying concept space. Yet existing incremental CD models assume a fixed concept space, allowing gradients from new items to overwrite historical pathways and induce catastrophic forgetting. More critically, these methods rely solely on soft constraints to preserve historical diagnoses. Such constraints may fail to satisfy the requirement of diagnostic invariance after incremental updates, a requirement known as psychometric consistency in cognitive diagnosis. Therefore, we propose CLEAN (Continual Learning with Expandable and Architecturally Isolated Networks), a novel incremental CD framework supporting concept-space expansion while providing structural guarantees for pointwise invariance of historical diagnoses. Specifically, CLEAN first introduces a strict topological bipartition protocol, freezes historical diagnostic functions and applies deterministic orthogonal column masking to sever gradient interference. Second, to accommodate concept expansion, expandable full-rank branches with micro-variance initialization are deployed to learn novel concepts. Finally, to verify that this architectural design achieves invariance by construction, we formalize Representation Drift (RD) to quantify the perturbation of historical traits. Extensive experiments on three large-scale educational datasets demonstrate that CLEAN achieves zero RD, preserving old-item metrics identically to static anchors through architectural isolation while remaining competitive with or superior to strong continual-learning baselines on new items.

Figures & tables

Figure 1. Incremental update of cognitive diagnosis models. (a) New units expand the

Q

-matrix column-wise, not merely row-wise. (b) Branch I keeps every weight trainable, so gradients from new items reach the historical pathway and old-item diagnoses drift (

\mathrm{RD}>0

); Branch II (CLEAN) freezes that pathway and masks the shared columns, making historical diagnoses invariant pointwise (

\mathrm{RD}=0

Figure 2. Overview of the CLEAN framework at the incremental training stage. An overview of the CLEAN framework, including topological reordering, the generative diagnostic functions, and the aggregation layer.

Figure 3. STB-Induced Block-Structured $Q$ -Matrix. The block-structured Q-matrix induced by STB, separating historical and newly introduced items and knowledge concepts.

Paradigm

Model

Junyi

ASSIST

Math1

ACC old

\uparrow

ACC new

\uparrow

ACC all

\uparrow

\downarrow

ACC old

\uparrow

ACC new

\uparrow

ACC all

\uparrow

\downarrow

ACC old

\uparrow

ACC new

\uparrow

ACC all

\uparrow

\downarrow

Anchor

G-NCDM

\underline{78.40\pm 0.15}

—

78.40\pm 0.15

—

\underline{73.51\pm 0.15}

—

73.51\pm 0.15

—

72.14\pm 0.51

—

72.14\pm 0.51

—

Ours

CLEAN-Full

{\underline{78.40\pm 0.15}}^{*}

{\underline{74.53\pm 0.30}}^{*}

{\underline{77.19\pm 0.11}}^{*}

\bm{0.00\pm 0.00}

{\underline{73.51\pm 0.15}}^{*}

{\underline{72.21\pm 0.19}}^{*}

{\underline{73.11\pm 0.15}}^{*}

\bm{0.00\pm 0.00}

72.14\pm 0.51

72.25\pm 4.69

72.18\pm 1.62

\bm{0.00\pm 0.00}

CLEAN-LoRA

{\underline{78.40\pm 0.15}}^{*}

73.57\pm 0.64

76.89\pm 0.19

\bm{0.00\pm 0.00}

{\underline{73.51\pm 0.15}}^{*}

{72.12\pm 0.24}^{*}

73.08\pm 0.17

\bm{0.00\pm 0.00}

72.14\pm 0.51

{68.50\pm 3.00}

70.85\pm 1.01

\bm{0.00\pm 0.00}

Baselines

Full-Replay Oracle

\bm{78.55\pm 0.25}

\bm{75.47\pm 0.22}

\bm{77.58\pm 0.18}

4.88\pm 1.29

\bm{73.66\pm 0.12}

\bm{72.99\pm 0.33}

\bm{73.45\pm 0.17}

6.92\pm 0.72

\underline{72.20\pm 0.28}

\underline{75.12\pm 0.28}

\underline{73.23\pm 0.17}

6.47\pm 1.60

EWC

71.54\pm 2.03

71.58\pm 0.40

71.56\pm 1.41

8.92\pm 0.20

66.87\pm 0.67

64.09\pm 0.61

66.01\pm 0.62

9.01\pm 0.09

68.59\pm 0.51

73.27\pm 0.86

70.24\pm 0.53

9.70\pm 0.26

Table 1. Performance comparison on the Junyi, a0910, and Math1 datasets under the Random-Split setting. ↑ (↓) means the higher (lower) score the better performance.

Figure 4. Training dynamics of $\mathrm{ACC}_{\mathrm{new}}$ and $\mathrm{ACC}_{\mathrm{old}}$ on Math1 under Random-Split. Training curves of old-item and new-item accuracy on Math1 under the Random-Split setting.

Figure 5. UMAP visualization of historical representation drift for four methods on the Math1 dataset. The left and right sides show the ends of the foundation and incremental training phases, respectively. UMAP visualization comparing the historical representations before and after incremental learning for four methods on the Math1 dataset.

Architecture	ACC ${}_{\mathrm{old}}\uparrow$	ACC ${}_{\mathrm{new}}\uparrow$	F1 ${}_{\mathrm{old}}\uparrow$	F1 ${}_{\mathrm{new}}\uparrow$	RMSE ${}_{\mathrm{old}}\downarrow$	RMSE ${}_{\mathrm{new}}\downarrow$	RD $\downarrow$
Anchor	69.42	–	78.69	–	45.64	–	–
CLEAN w/o OCM and SBF	44.46	69.16	38.06	76.94	54.73	45.15	0.00
CLEAN w/o OCM	60.22	68.50	67.63	78.14	48.78	45.07	0.00
CLEAN w/o SBF	55.99	68.91	60.29	78.09	49.53	45.26	0.00
CLEAN-Full	69.42	67.52	78.69	77.91	45.64	45.32	0.00

Table 2. Ablation study results.

Figure 6. UMAP visualization of prediction-space drift for different ablation variants on the a0910 dataset. Each pair shows learner embeddings in the old-item prediction space at $t{=}0$ (left) and after incremental training at $t{=}1$ (right; $\times 5$ for display). Points are colored by score rate on old items. UMAP visualization comparing prediction representations before and after incremental learning for different CLEAN ablation variants on the a0910 dataset.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Model	$\mathrm{ACC}_{\mathrm{old}}\uparrow$	$\mathrm{ACC}_{\mathrm{new}}\uparrow$	$\mathrm{F1}_{\mathrm{old}}\uparrow$	$\mathrm{F1}_{\mathrm{new}}\uparrow$	$\mathrm{RMSE}_{\mathrm{old}}\downarrow$	$\mathrm{RMSE}_{\mathrm{new}}\downarrow$	$\mathrm{RD}\downarrow$
G-NCDM (Anchor)	$\bm{70.24\pm 0.54}$	–	$\underline{79.65\pm 0.69}$	–	$\bm{45.22\pm 0.29}$	–	–
EWC	$68.73\pm 0.77$	$65.48\pm 0.58$	$76.90\pm 0.61$	$73.06\pm 0.62$	$49.69\pm 0.54$	$51.52\pm 0.32$	$8.47\pm 0.12$
DER++	$67.33\pm 0.28$	$65.29\pm 0.57$	$75.90\pm 0.18$	$72.97\pm 0.58$	$50.09\pm 0.26$	$51.08\pm 0.33$	$11.60\pm 0.06$
C-LoRA	$68.81\pm 0.66$	$67.22\pm 0.70$	$77.80\pm 0.64$	$75.60\pm 0.57$	$46.24\pm 0.45$	$47.41\pm 0.41$	$14.38\pm 0.24$
X-DER	$\underline{69.95\pm 0.57}$	$66.87\pm 0.54$	$\bm{79.70\pm 0.68}$	$77.15\pm 0.55$	$\underline{45.33\pm 0.31}$	$46.39\pm 0.15$	$\underline{3.34\pm 0.62}$
Full-Replay Oracle (reference)	$69.52\pm 0.77$	$67.82\pm 0.61$	$78.93\pm 0.89$	$77.63\pm 0.55$	$45.64\pm 0.31$	$45.99\pm 0.23$	$3.44\pm 1.04$

Appendix

Table 3. User-Split results for score prediction.

Model	$\mathrm{ACC}_{\mathrm{old}}\uparrow$	$\mathrm{ACC}_{\mathrm{new}}\uparrow$	$\mathrm{F1}_{\mathrm{old}}\uparrow$	$\mathrm{F1}_{\mathrm{new}}\uparrow$	$\mathrm{RMSE}_{\mathrm{old}}\downarrow$	$\mathrm{RMSE}_{\mathrm{new}}\downarrow$	$\mathrm{RD}\downarrow$
G-NCDM (Anchor)	78.40 $\pm$ 0.15	–	85.53 $\pm$ 0.14	–	38.72 $\pm$ 0.05	–	–
EWC	71.54 $\pm$ 2.03	71.58 $\pm$ 0.40	79.18 $\pm$ 2.05	78.27 $\pm$ 0.52	44.83 $\pm$ 1.34	43.98 $\pm$ 0.21	8.92 $\pm$ 0.20
DER++	76.53 $\pm$ 0.28	74.27 $\pm$ 0.26	83.66 $\pm$ 0.24	80.44 $\pm$ 0.25	40.00 $\pm$ 0.25	41.61 $\pm$ 0.13	3.09 $\pm$ 1.14
C-LoRA	71.26 $\pm$ 2.01	73.12 $\pm$ 0.36	79.41 $\pm$ 1.74	79.32 $\pm$ 0.34	44.10 $\pm$ 1.31	42.93 $\pm$ 0.21	19.69 $\pm$ 0.27
X-DER	77.59 $\pm$ 0.42	73.19 $\pm$ 0.69	85.28 $\pm$ 0.21	79.73 $\pm$ 0.50	39.60 $\pm$ 0.32	42.54 $\pm$ 0.24	6.36 $\pm$ 1.06
Full-Replay Oracle (reference)	78.55 $\pm$ 0.25	75.47 $\pm$ 0.22	85.74 $\pm$ 0.17	81.49 $\pm$ 0.26	38.71 $\pm$ 0.12	40.86 $\pm$ 0.09	4.88 $\pm$ 1.29

Appendix

Table 4. Detailed metric results on the Junyi-Random dataset.

Model	$\mathrm{ACC}_{\mathrm{old}}\uparrow$	$\mathrm{ACC}_{\mathrm{new}}\uparrow$	$\mathrm{F1}_{\mathrm{old}}\uparrow$	$\mathrm{F1}_{\mathrm{new}}\uparrow$	$\mathrm{RMSE}_{\mathrm{old}}\downarrow$	$\mathrm{RMSE}_{\mathrm{new}}\downarrow$	$\mathrm{RD}\downarrow$
G-NCDM (Anchor)	73.51 $\pm$ 0.15	–	81.35 $\pm$ 0.26	–	42.68 $\pm$ 0.12	–	–
EWC	66.87 $\pm$ 0.67	64.09 $\pm$ 0.61	74.79 $\pm$ 0.91	71.84 $\pm$ 0.72	52.50 $\pm$ 0.38	53.88 $\pm$ 0.41	9.01 $\pm$ 0.09
DER++	69.50 $\pm$ 0.44	67.66 $\pm$ 0.51	77.74 $\pm$ 0.53	76.34 $\pm$ 0.40	45.08 $\pm$ 0.42	46.25 $\pm$ 0.26	3.64 $\pm$ 0.94
C-LoRA	67.64 $\pm$ 0.28	64.28 $\pm$ 0.46	75.79 $\pm$ 0.35	72.01 $\pm$ 0.48	52.13 $\pm$ 0.18	53.94 $\pm$ 0.35	13.11 $\pm$ 0.09
X-DER	72.86 $\pm$ 0.24	69.83 $\pm$ 0.44	81.18 $\pm$ 0.28	78.26 $\pm$ 0.24	43.02 $\pm$ 0.21	44.79 $\pm$ 0.26	7.32 $\pm$ 1.57
Full-Replay Oracle (reference)	73.66 $\pm$ 0.12	72.99 $\pm$ 0.33	81.58 $\pm$ 0.21	80.20 $\pm$ 0.45	42.77 $\pm$ 0.10	43.08 $\pm$ 0.12	6.92 $\pm$ 0.72

Appendix

Table 5. Detailed metric results on the ASSISTments-Random dataset.

Model	$\mathrm{ACC}_{\mathrm{old}}\uparrow$	$\mathrm{ACC}_{\mathrm{new}}\uparrow$	$\mathrm{F1}_{\mathrm{old}}\uparrow$	$\mathrm{F1}_{\mathrm{new}}\uparrow$	$\mathrm{RMSE}_{\mathrm{old}}\downarrow$	$\mathrm{RMSE}_{\mathrm{new}}\downarrow$	$\mathrm{RD}\downarrow$
G-NCDM (Anchor)	72.14 $\pm$ 0.51	–	71.72 $\pm$ 1.65	–	42.43 $\pm$ 0.42	–	–
EWC	68.59 $\pm$ 0.51	73.27 $\pm$ 0.86	66.01 $\pm$ 1.63	61.64 $\pm$ 1.55	50.30 $\pm$ 0.45	43.11 $\pm$ 0.68	9.70 $\pm$ 0.26
DER++	71.72 $\pm$ 0.52	75.52 $\pm$ 0.22	72.87 $\pm$ 1.36	67.02 $\pm$ 1.14	42.56 $\pm$ 0.36	39.00 $\pm$ 0.10	1.32 $\pm$ 1.11
C-LoRA	68.88 $\pm$ 0.51	71.98 $\pm$ 0.68	66.45 $\pm$ 1.61	59.86 $\pm$ 1.08	50.28 $\pm$ 0.46	46.05 $\pm$ 0.58	10.82 $\pm$ 0.27
X-DER	72.54 $\pm$ 0.21	75.12 $\pm$ 0.35	73.45 $\pm$ 1.47	66.10 $\pm$ 1.02	42.15 $\pm$ 0.34	39.07 $\pm$ 0.19	7.24 $\pm$ 2.00
Full-Replay Oracle (reference)	72.20 $\pm$ 0.28	75.12 $\pm$ 0.28	71.94 $\pm$ 0.85	66.63 $\pm$ 0.98	42.18 $\pm$ 0.31	39.66 $\pm$ 0.28	6.47 $\pm$ 1.60

Appendix

Table 6. Detailed metric results on the Math1-Random dataset.

Figure 7. Sensitivity analysis of the coefficient $\alpha$ under the Random-Split setting. Sensitivity analysis of the coefficient alpha under the Random-Split setting.

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