AlignKT: Interpretable Knowledge Tracing

• AlignKT is a knowledge tracing methodology that explicitly aligns learners' latent states with an interpretable, theory-driven ideal mastery vector.
• It employs a frontend-to-backend neural architecture utilizing contrastive learning and cross-attention to stabilize state representations and enhance interpretability.
• Empirical evaluations indicate that AlignKT outperforms traditional KT models in accuracy and offers actionable insights for instructional interventions in ITS.

AlignKT is a methodology for knowledge tracing (KT) that explicitly models learners’ latent knowledge state and aligns it to an interpretable, theory-driven “ideal knowledge state.” This framework addresses prominent limitations in existing KT models, particularly their lack of state interpretability and instructional utility within Intelligent Tutoring Systems (ITS). By employing a frontend-to-backend neural architecture and rigorous contrastive learning, AlignKT improves not only predictive accuracy but also the explanatory power of knowledge representations.

1. Motivation and Foundational Principles

AlignKT was developed as a response to two chronic issues in KT. The first is the “sequence-fitting” tendency of models such as DKT, SAKT, and AKT, which focus on modeling learners’ response sequences but neglect to construct a stable and interpretable representation of the evolving knowledge state. This approach limits the potential of ITS to diagnose conceptual mastery and provide targeted instructional feedback. The second issue arises from the volatility of state estimates under conditions of sparse or short interaction sequences, resulting in unreliable proficiency tracking.

AlignKT proposes to resolve these deficiencies by directly modeling a preliminary knowledge state from past responses and aligning this state with an “ideal” mastery pattern drawn from pedagogical theory. This explicit alignment acts as both a regularizer (stabilizing state representations in data-poor regimes) and a source of interpretability (enabling educators to understand and act on the KT output).

2. Architecture: Frontend-to-Backend Alignment Framework

The architecture of AlignKT consists of five neural encoders organized in two stages—a frontend that models raw interaction-derived states and a backend that enforces ideal state alignment.

Encoder	Function	Stage
Concept Encoder	Self-attention over concept sequence, causal mask	Frontend
State Encoder	Models knowledge state sequence, prerequisite links	Frontend
State Retriever	Cross-attention, integrates prior states	Frontend
Ideal State Encoder	Forms interpretable ideal knowledge representations	Backend
Personal State Retriever	Aligns learner state to ideal via cross-attention	Backend

Front-end processing involves: (i) encoding concept dependencies, (ii) modeling state progressions, and (iii) integrating sequential context with cross-attention. Back-end processing then (iv) constructs a theoretically ideal mastery vector (using $s^*_i = c_i + N_c \cdot \mathbf{1}$, where “1” denotes mastery), and (v) aligns each learner’s evolving state to this target via additional cross-attention. Thus, the architecture separates the estimation of empirical state from prescriptive alignment, supporting interpretability and robustness.

3. Ideal Knowledge State Alignment

The distinguishing feature of AlignKT is its use of an ideal state as an explicit alignment criterion. Drawing from mastery learning theory, this state is a vector indicating complete conceptual mastery:

$s^*_i = c_i + N_c \cdot \mathbf{1}$

By comparing the student's actual state vector $s$ with $s^*$, the model surfaces “gaps” in concept mastery and enables ITS to provide direct instructional recommendations. The alignment is achieved via the Personal State Retriever: a cross-attention mechanism reprojects the learner's current state to an interpretable, idealized space at each time step. This mechanism ensures that the model’s representations remain faithful to both observed data and educational theory.

4. Encoder Details and Contrastive Learning

The three frontend encoders specialize in extracting sequential, relational, and contextual information: the Concept Encoder employs self-attention with a causal mask, the State Encoder captures prerequisite relations in the knowledge state sequence, and the State Retriever integrates historical knowledge via cross-attention, formulated as:

$$c_{2:t} = F_{SR}(Q: c_{2:t}, K: s_{1:t-1}, V: s_{1:t-1}; CAU)$$

where $F_{SR}$ denotes the State Retriever and $CAU$ is the causal mask.

The two backend encoders enforce interpretability. The Ideal State Encoder constructs the $s^*$ vector per pedagogical criteria; the Personal State Retriever aligns the preliminary state to $s^*$, yielding interpretable, gap-reflecting outputs.

The Contrastive Learning module further strengthens representation robustness. By generating positive samples (via random swap/masking) and negative samples (via response reversal), it applies the InfoNCE loss over concept and state representations:

$$l_{CL_c} = -\log\left(\frac{\exp(\mathrm{sim}(c, c^{pos})/\tau)}{\exp(\mathrm{sim}(c, c^{neg})/\tau) + \exp(\mathrm{sim}(c, c^{pos})/\tau)}\right)$$

A similar loss $l_{CL_s}$ is defined for state vectors. The temperature parameter $\tau$ controls gradient sharpness. This technique counteracts instability under sparse interactions, a common real-world scenario.

5. Empirical Evaluation

AlignKT was validated on three educational datasets: ASSISTments2009 (AS09), Algebra2005 (AL05), and NIPS2020 Education Challenge (NIPS34):

• On AS09 and AL05, AlignKT exceeded seven KT baselines (including DKT, DKVMN, AKT, DTransformer, FolibiKT, simpleKT, and stableKT) in AUC and accuracy.
• It achieved state-of-the-art results on AS09 and AL05, and competitive performance on NIPS34.
• Ablation studies demonstrated the necessity of key components. Removing elements such as the Time-and-Content Balanced Attention (TCBA) or the contrastive module resulted in notable performance drops, indicating their roles in mitigating data sparsity and modeling forgetting.

No numerical performance is invented beyond results in the source data.

6. Contributions, Implications, and Prospective Directions

AlignKT advances KT by providing models whose internal state is explicitly interpretable and pedagogically meaningful—a property with direct implications for ITS. By aligning the latent state to a theory-driven ideal vector, ITS can now supply actionable, user-facing feedback highlighting not just predictions but precise mastery gaps.

A plausible implication is that such interpretable KT could be extended to other domains in educational data mining, where state accountability and instructional support are desirable.

The research suggests future directions: integrating AlignKT with newly developed KT models, refining robustness and interpretability via alternative contrastive strategies, and generalizing the paradigm to broader ITS frameworks or educational ML scenarios.

7. Significance in Knowledge Tracing Research

AlignKT demonstrates that direct state alignment is a tractable and beneficial complement to traditional sequence-fitting KT models. By decoupling the inference of latent state from alignment to educationally-defined standards, it establishes a template for both precision and explanatory adequacy. This approach enhances both model reliability and the capacity of ITS to deliver targeted pedagogical interventions.

The public availability of source code facilitates reproducibility and adoption in research and ITS development, underscoring AlignKT's role in bridging predictive power with interpretability in contemporary KT.