Continual Structured Knowledge Reasoning (CSKR)

• CSKR is a continual learning paradigm that enables AI models to integrate and transfer structured knowledge such as databases and knowledge graphs while preserving prior capabilities.
• It employs a dual-stage process by decoupling schema filtering (task-agnostic) and query construction (task-specific) to efficiently adapt to new tasks.
• By leveraging complementary memory mechanisms and structure-guided pseudo-data synthesis, CSKR improves metrics like average accuracy while minimizing catastrophic forgetting.

Continual Structured Knowledge Reasoning (CSKR) is the paradigm of enabling AI systems—particularly neural-symbolic and LLMs—to perform structured reasoning across sequential, heterogeneous, and evolving knowledge tasks without catastrophic forgetting. CSKR focuses on the continual integration, transfer, and adaptation of structured knowledge (such as databases, knowledge graphs, and code representations), addressing the challenges of knowledge heterogeneity, retention, and efficient cross-task generalization.

1. Formal Definition and Problem Formulation

CSKR considers a setting where a model is exposed to a sequential stream of structured reasoning tasks. Each task involves mapping a natural language query into a structured query (e.g., SQL, SPARQL) over a specified schema, knowledge graph, or other structured knowledge source. The critical constraint is that the model must continually adapt to new tasks while retaining previously acquired reasoning capabilities, all within a bounded or fixed parameter budget.

Formally, at the $k$-th task, given

• input: dataset $$\mathcal{D}^k = \{(\mathcal{Q}_i, \mathcal{S}_i, \mathcal{Y}_i)\}$$, where $\mathcal{Q}_i$ is a query, $\mathcal{S}_i$ the schema/structure, and $\mathcal{Y}_i$ the gold structured query,
• and a model parameterized by (frozen) $\theta$ and task-adaptive modules $P$,

the objective is to learn,

$$\min_{P} \sum_{k} \mathcal{L}(\mathcal{D}^k ; \theta, P) + \sum_{k'} \lambda \mathcal{L}_{\text{memory}}(\mathcal{M}^{k'}; \theta, P)$$

where $\mathcal{M}^{k'}$ denotes a task memory (see Section 3).

2. Knowledge Decoupling: Task-specific and Task-agnostic Stages

K-DeCore (Chen et al., 21 Sep 2025) exemplifies knowledge decoupling by dividing the reasoning process into two compositional stages:

• Schema Filtering (Task-agnostic): A lightweight module (e.g., parameter-efficient Peft) identifies and extracts the minimal relevant schema from the possibly large or heterogeneous schema $\mathcal{S}$, given input $\mathcal{Q}$. This is formalized as

$$\mathcal{S}^* = f(\mathcal{Q}, \mathcal{S}; \theta, P_a)$$

This mapping is consistent across tasks, promoting transferability.

• Query Building (Task-specific): Another module, receiving $\mathcal{Q}, \mathcal{S}^*,$ and $\mathcal{S}$, generates the actual structured query. This stage is responsible for task-specific reasoning patterns and representations.

This separation enables the system to capture and transfer the invariant schema identification knowledge while flexibly adapting to task- or domain-specific idiosyncrasies in the query construction.

3. Dual-Perspective Memory Consolidation

Catastrophic forgetting is alleviated by maintaining memories along complementary perspectives:

• Schema-Guided Memory $\mathcal{M}_a^k$: Constructed via clustering schema-filtered samples. The most representative (i.e., closest to cluster center in embedding space) samples are kept for rehearsal in the schema filtering module.
• Query-Structure Memory $\mathcal{M}_b^k$: Encompasses a diverse set of structured queries, including both real and synthesized (see Section 4) queries. This ensures coverage of various logical forms.

By separately preserving the schemas and the final query patterns, K-DeCore ensures that both critical phases of reasoning—understanding what information is needed and knowing how to express it in a structured form—are continually reinforced as new tasks are encountered.

4. Structure-Guided Pseudo-Data Synthesis

To improve generalization in evolving task settings or limited data regimes, K-DeCore implements structure-guided pseudo-data synthesis:

• For each current task, the system samples $T$ distinct query structures from observed queries and slightly mutates them with the LLM, yielding novel structured forms $Y^\text{pseudo}$.
• Novel queries are instantiated by randomly assigning compatible schema elements from memory. Only executable, syntactically valid queries are retained.
• A dedicated module $P_c$ generates corresponding natural language questions, ensuring the pseudo-data remains semantically anchored.

The loss for this phase is:

$$\mathcal{L}(\mathcal{D}^k; \theta, P_c) = -\sum_i \sum_j \log P(q_j | Y, q_{<j}; \theta, P_c)$$

This approach both enriches the training distribution and prevents overfitting to the structural patterns of previously seen tasks.

5. Parameter Efficiency and Backbone Model Compatibility

A distinguishing feature of K-DeCore is its fixed-parameter design: only a small number of additional parameters (PEFT modules such as LoRA adapters) are added to pretrained LLMs, regardless of the number of tasks. This is crucial for scalable, resource-efficient continual learning and enables compatibility with both encoder–decoder (e.g., T5-Large) and decoder-only (e.g., Llama-3-8B-Instruct, QWEN2.5-7B-Instruct) architectures.

This framework avoids the parameter growth or task explosion issues seen in naïve finetuning or naive replay-based continual learning, maintaining inference and update costs that do not scale with the task sequence length.

6. Experimental Evidence and Performance Metrics

On a curated stream of four benchmark datasets—Spider (SQL), ComplexWebQuestions (KG/SPARQL), GrailQA (multi-hop KGQA), and MTOP (task-oriented semantic parsing)—K-DeCore demonstrates improvement over previous continual learning methods and standard finetuning along the following axes:

• Average Accuracy (AA): Average final performance across all tasks.
• Backward Transfer (BWT): Model’s ability to preserve or degrade earlier task performance after new task learning. Higher (less negative) is better.
• Forward Transfer (FWT): Effect of knowledge learned from past tasks on new task performance (positive FWT indicates successful transfer).

Experimental tables confirm that K-DeCore reaches higher AA, exhibits less negative BWT (less forgetting), and improved FWT relative to baselines using the same fixed-size model.

7. Implications for Future CSKR Systems

K-DeCore operationalizes a best-practice set for CSKR:

• Explicit structural decoupling aligns with the heterogeneity of real-world structured data and allows for cross-domain generalization.
• Complementary memory mechanisms balance transfer and retention, a critical property as knowledge structures and reasoning formats evolve.
• Structure-aware pseudo-sample synthesis overcomes data paucity and increases coverage without catastrophic memory expansion or retraining.
• Task independence and parameter efficiency are achieved without sacrificing performance or compatibility with modern, large-scale LLM backbones.

This constellation of mechanisms demonstrates a scalable route to continual, adaptive, and data-efficient structured knowledge reasoning required for modern AI applications.