SlowGuess/NeurIPS_2023_OCR huggingface dataset:
where  $\theta$  is the parameters of MLP, and  $T_{K^s\times K^t}$  is the transformation matrix.  $K^{s}$  and  $K^t$  denote the dimensionality of the student proficiency representation in the source and target course respectively. Specifically, the dimensionality of the student representation is determined by the number of knowledge concepts considered.
The transformation matrix  $T_{K^s \times K^t}$  is then used to map student proficiency representation to the target course using matrix multiplication:
$$
\boldsymbol {u} _ {i} ^ {t} = \boldsymbol {u} _ {i} ^ {s} \cdot \boldsymbol {T} _ {K ^ {s} \times K ^ {t}}. \tag {3}
$$
The final output  $\hat{r}_i$  of CC-NCD is formulated as:
$$
\hat {r} _ {i} = L \left(\boldsymbol {Q} _ {p} ^ {t} \circ \left(\boldsymbol {u} _ {i} ^ {t} - \boldsymbol {h} ^ {\text {d i f f}}\right) \times h ^ {\text {d i s c}}; \theta_ {l}\right), \tag {4}
$$
where  $Q_{p}^{t} \in \{0,1\}^{1 \times K^{t}}$  is the concept relevancy of the problem  $p$  in the target course.  $h^{diff} \in (0,1)^{1 \times K^{t}}$ ,  $h^{disc} \in (0,1)$  denotes concept difficulty and problem discrimination learned from the NCD model using data of the target source.  $L(\cdot)$  denotes the Linear Layers in NCD which is shown in full paper Figure 5 and  $\theta_{l}$  is the parameters of  $L(\cdot)$ .
Given the ground truth value  $r$  from  $\mathcal{R}^t$ , all learnable parameters are trained together with the meta network and mapping function by optimizing the cross-entropy loss function as:
$$
\operatorname {l o s s} _ {C C - N C D} = - \sum_ {i} \left(r _ {i} \log \hat {r} _ {i} + \left(1 - r _ {i}\right) \log \left(1 - \hat {r} _ {i}\right)\right). \tag {5}
$$
During the inference stage, given a cold-start student  $s_j$  in the target course, we can get the latent proficiency representation in the target course as:
$$
\boldsymbol {u} _ {j} ^ {t} = \mathbf {A} _ {\mathrm {N C D}} ^ {s} [ j ] \cdot \operatorname {M L P} \left(\mathbf {A} _ {\mathrm {N C D}} ^ {s} [ j ]; \theta\right), \tag {6}
$$
which can be utilized to predict the student's performance in the target course via Equation (4).
D Baseline Model Details
Cognitive diagnosis models:
DINA [4, 22] is a traditional method that is well-suited for binary scoring items, and it can effectively account for student errors due to guessing or slipping.
IRT [5] is an important psychological and educational theory rooted in psychometrics, which employs a linear function to model the features of both students and problems.
MIRT [19] is a multidimensional extension of IRT, modeling multiple knowledge proficiency.
NCD [23] is the first attempt to introduce neural networks for Cognitive Diagnosis, which can model high-order and complex student-problem interaction.
RCD [6] models the interactive and structural relations via a multi-layer student-problem-concept relation map and infers students' proficiency through the representations from this map.
Knowledge tracing models:
DKT [17] is the first approach applying deep learning to knowledge tracing tasks, making use of the recurrent neural network in the process of modeling students' behavior.
DKVMN [26] makes use of a memory network, a static matrix to store all concepts and a dynamic matrix to update students' knowledge states of those concepts.
SAKT [16] employs a self-attention mechanism to capture the connections between exercises and student responses.
AKT [7] utilizes an attention mechanism to analyze the temporal gap between questions and students' prior interactions to better understand their past engagement.
GIKT [25] makes use of a bipartite graph to model the input information, namely problems and concepts, and uses graph convolutional neural network (GCN) to process the data. Then the results were sent to LSTM and get the final prediction.
SGKT [24] uses a session graph and during the process of students' answering, a gated graph neural network was set to handle the problem-concept graph.
PEBG [11] utilizes pre-training model to get the low-dimensional problem embeddings and models the relation between problems and concepts as a bipartite graph.
E Supplementary Experiment Results
We conducted experiments between the selected five courses in Figure 4(a) of the paper. The experimental results are presented in Table 2. We chose  $C++$  Programming as the target course due to its wide range of correlation coefficients with other courses. The source courses are marked within brackets and are ranked from lowest to highest correlation coefficient with  $C++$  Programming: 0.54 for Python Programming (Python), 0.59 for Data Structure and Algorithm Analysis (DS), 0.64 for i (Java), 0.79 for  $C$  Programming (C). To simulate cold-start scenarios, we sampled  $5\%$  of each student's response logs in  $C++$  Programming to form the target course.
From Table 2, we can observe that CCLMF achieves a certain improvement of the two models in all source courses. Notably, the results of the NCD model reveal that the extent of model improvement is related to the correlation coefficient between the source course and the target course. The source course with the highest correlation coefficient (0.79 for C Programming) exhibits the most significant improvement, while the source course with the weakest correlation coefficient (0.54 for Python Programming) demonstrates relatively less improvement.
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