Programmatic Skill Network (PSN)

• PSN is a structured computational framework that models and operationalizes skills using semantic graphs or evolving directed networks, enabling continual learning.
• It employs multi-stage NLP and symbolic agent pipelines to extract skills with high precision and recall from diverse textual and embodied data.
• Core mechanisms such as REFLECT fault localization, maturity gating, and canonical refactoring ensure robust, adaptable skill composition and retention.

A Programmatic Skill Network (PSN) is a structured computational construct that models, extracts, and operationalizes skills, their relations, and their composition either from natural language data or in embodied agent environments. Across its instantiations, PSN manifests as either (a) a semantic graph mapping explicit and implicit skill mentions in text to formal skill ontologies and occupational/curricular pathways (Koundouri et al., 13 Mar 2025), or (b) an evolving directed network of programmatic skills—symbolic, composable programs with explicit logic, parameters, and correctness invariants—supporting continual, open-ended learning (Shi et al., 7 Jan 2026). This article details both conceptual pillars, formal definitions, operational pipelines, and empirical evidence as established in the 2025–2026 literature.

1. Formal Definitions and Network Structure

A programmatic skill network is defined as a directed graph whose nodes correspond to skill programs (or, in the semantic context, normalized skill entities) and whose edges encode invocation, compositional structure, or semantic affinity. In the continual learning setting, a skill $s$ is the tuple

$$s = \bigl(\mathcal{C}_s,\, \mathcal{P}_s,\, \mathcal{E}_s^{\mathrm{pre}},\, \mathcal{E}_s^{\mathrm{post}},\, \mathrm{Children}(s)\bigr),$$

where $\mathcal{C}_s$ denotes control-flow logic (e.g., Python/JavaScript), $\mathcal{P}_s$ its parameters, $\mathcal{E}_s^{\mathrm{pre}}$ and $\mathcal{E}_s^{\mathrm{post}}$ symbolic pre- and post-conditions, and $\mathrm{Children}(s)$ the set of invoked sub-skills (Shi et al., 7 Jan 2026). The global network at time $t$ is

$\mathcal{N}_t = (\mathcal{S}_t,\, \mathcal{L}_t),$

with skills $\mathcal{S}_t$ as nodes, and invocation edges $$\mathcal{L}_t \subseteq \mathcal{S}_t \times \mathcal{S}_t$$.

In the semantic mapping scenario, the PSN is built by associating nodes with skills from standardized frameworks such as ESCO, occupation profiles, and structured course offerings (e.g., SDSN Academy) (Koundouri et al., 13 Mar 2025).

2. Automated Construction: Extraction and Learning Pipelines

Semantic PSNs from text are constructed via multi-stage NLP pipelines:

• Ingestion & Preprocessing: Input documents (HTML, PDF, DOCX, TXT, XML) undergo MIME-type-specific parsing and rigorous cleaning (removal of extraneous markers, retention of legal/quantitative content).
• Segmentation: Text is split into semantically coherent segments of ~120 words to preserve local context.
• Semantic Embedding: Each chunk $x_i$ is represented using the "all-MiniLM-L6-v2" Sentence-BERT model, yielding $v_i \in \mathbb{R}^{384}$, normalized as $\hat{v}_i = v_i / ||v_i||_2$.
• FAISS Similarity-based Skill Extraction: Each chunk embedding is searched against a pre-built normalized FAISS index of ESCO skill embeddings. Cosine similarity $$\mathrm{sim}(\hat{v}_i, \hat{u}_j) = \hat{v}_i \cdot \hat{u}_j$$ is used, with threshold $\tau_{\mathrm{skill}} = 0.35$ for a positive match. Skill frequencies per document are computed as $$f_j = \sum_{i=1}^N 1\{\mathrm{sim}(\hat{v}_i, \hat{u}_j) > \tau_{\mathrm{skill}}\}$$ (Koundouri et al., 13 Mar 2025).

The continual learning-based PSN employs a symbolic agent that acquires new skills (symbolic programs), incrementally composes them, and rewires the network through structured optimization.

• Skill Execution and Feedback: Each skill is executed in an environment, and trace-level feedback $f_s$, outcome $\delta_s$ (success/failure), and call trace $\mathcal{T}_s$ are recorded.
• REFLECT (Trace-Based Optimization): Credit assignment for failures is implemented by symbolic backpropagation over $\mathcal{T}_s$, propagating structured "gradients" to update precisely those parts of the skill library involved in execution (see Section 3).
• Maturity-Aware Gating and Refactoring: Update frequency and structural rewrites are modulated by a skill maturity value $V(s) = \hat{p}_s - u_s$ (empirical success rate minus uncertainty), enabling stable retention of reliable skills while permitting plasticity for novel/immature ones (Shi et al., 7 Jan 2026).

3. Core Mechanisms: Credit Assignment, Optimization, and Refactoring

The optimization and maintenance of PSN are governed by three principal mechanisms (Shi et al., 7 Jan 2026):

• REFLECT Fault Localization: Structured feedback from execution traces is propagated down the call graph. Updates are proposed for control-flow logic, parameters, or pre/post-conditions in those subskills contributing to failure, by distributing pseudo-gradient maps and applying algorithmic patching only along executed subpaths.
• Progressive Optimization with Maturity Gating: Update scheduling for each skill $s$ is governed by

$$P(\text{update}\ s) = (1-\epsilon)\; \sigma(\gamma (0.6 - V(s))) + \epsilon,$$

with $\sigma$ the logistic sigmoid, $\gamma=5.0$, $\epsilon=0.1$. Thus, highly mature skills are rarely updated, while immature or unreliable ones are frequently revised.

• Canonical Structural Refactoring and Rollback Validation: Upon successful skill executions, the PSN applies canonical rewrites—parametric or behavioral coverage, sibling specialization abstraction, common subskill extraction, duplication removal—which modify the graph's structure. These rewrites are validated by replaying the last $m=3$ tasks; any refactoring resulting in a drop $\Delta \mathrm{SR} < -0.20$ in success rate is reverted.

4. PSN Graph: Nodes, Edges, and Scoring Functions

The PSN's graph topology supports rigorous linking among skills, occupations, and curricular pathways (Koundouri et al., 13 Mar 2025):

• Node Types: Skills (from ESCO), occupations (ESCO profiles), courses (SDSN/AE4RIA offering).
• Edge Construction:
  • Skill–Skill: $$A_{\mathrm{ss}}(i,j) = \mathrm{cos}(\hat{u}_i, \hat{u}_j)$$ if above threshold.
  • Skill–Occupation: $A_{\mathrm{so}}(i,j) = 1$ if $s_i$ is a required skill for occupation $o_j$, weighted by document-occupation similarity or normalized frequency.
  • Skill–Course: $$A_{\mathrm{sc}}(i,k) = \mathrm{sim}(\hat{u}_i, \hat{c}_k)$$ for course embeddings above $\tau_{\mathrm{course}}$.

Scoring functions include:

• Occupation Overlap: $$\rho_j = |\mathrm{ExtractedSkills} \cap \mathrm{RequiredSkills}(j)|\,/\,|\mathrm{RequiredSkills}(j)|$$
• Textual Similarity: $$\sigma_j = \mathrm{cos}(V_{\mathrm{doc}}, V_{\mathrm{occ}}(j))$$
• Composite Score: $C_j = \alpha \rho_j + (1-\alpha)\sigma_j$, with $\alpha$ empirically tuned (e.g., $\alpha=0.5$) (Koundouri et al., 13 Mar 2025).

Normalization of skill presence per document is given as $p_i(d) = f_i(d) / \sum_{\ell=1}^M f_\ell(d)$.

5. Evaluation Methodology and Empirical Findings

In semantic PSN extraction, a suite of evaluation protocols addresses both explicit and implicit skill references (Koundouri et al., 13 Mar 2025):

• Synthetic Document Generation: 200 ESCO skills are sampled, mixed into 80 synthetic documents (equal split explicit/implicit).
• Metrics: Precision, recall, and F1 according to strict (name-based) and relaxed (context-cue) matches.
• Performance:
  • Explicit skill extraction: Precision 0.9917, Recall 0.9625, F1 0.9763.
  • Implicit skill extraction: Precision 0.9208, Recall 0.9750, F1 0.9467.
  • SDG extraction (explicit): F1 0.7400; (implicit): F1 0.4250.

For programmatic PSNs in open-ended environments (Shi et al., 7 Jan 2026):

• MineDojo (Minecraft): PSN agents acquire complex tool-use milestones more rapidly than Voyager, ReAct, Reflexion, and AutoGPT. PSN achieves $51 \pm 9$ iterations for diamond tool mastery.
• Crafter: PSN demonstrates consistently increasing cumulative reward and maintains skill retention throughout curriculum advancement, outperforming both skill-proliferation and planning-only baselines.

Ablation studies confirm:

• The necessity of the optimizer for deep compositionality,
• The maturity gating mechanism for preventing oscillatory forgetting,
• Online refactoring's superiority over post-hoc compression.

6. Applications, Visualization, and Future Directions

Semantic PSNs underpin interactive platforms for policy analysis, curriculum design, and workforce transition support (Koundouri et al., 13 Mar 2025). A Python Flask/Dash/Plotly stack provides real-time graph visualization, skill frequency tables, occupation-course linking, search/filter by SDG, and dynamic node-edge interaction, anchored in ESCO and SDG ontologies.

Symbolic PSNs, as agentic frameworks, facilitate continual robotic/autonomous agent learning with robust skill reuse, stability/plasticity trade-offs, and transparent programmatic introspection (Shi et al., 7 Jan 2026). Limitations currently include batch-size-one updating and lack of formal convergence guarantees in program space.

Planned future developments include scaling parallel execution, formalizing symbolic trust-region methods, and integrating differentiable skill proxies to bridge the discrete–continuous optimization gap.

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Key References:

• "Semantic Synergy: Unlocking Policy Insights and Learning Pathways Through Advanced Skill Mapping" (Koundouri et al., 13 Mar 2025)
• "Evolving Programmatic Skill Networks" (Shi et al., 7 Jan 2026)