Socratic-Solver: AI-Driven Socratic Inquiry

• Socratic-Solvers are AI systems that generate and sequence guided Socratic questions to actively probe and refine reasoning processes.
• They employ a modular architecture integrating strategy anchoring, template retrieval, and prompt construction to tailor questions to diverse contexts.
• Their applications span psychotherapy, education, and scientific ideation, enhancing reflective thinking, curriculum design, and problem-solving.

A Socratic-Solver is a class of artificial intelligence systems, primarily instantiated as LLMs or LLM-based agentic pipelines, that generate, select, and sequence Socratic questions explicitly designed to elicit, challenge, and refine human or agent reasoning in dialogic contexts. Distinct from reactive conversational agents, Socratic-Solvers deliberately initiate structured, theory-driven inquiries that surface latent beliefs, elicit justifications, address misconceptions, or guide a problem-solving trajectory across diverse domains ranging from psychotherapy and education to program synthesis, scientific ideation, and automated curriculum generation (Zhang et al., 2 Feb 2026).

1. Foundational Principles and Motivations

Socratic-Solvers implement the core principle of proactive, structured questioning, rooted in the Socratic method, which aims to facilitate reflection, cognitive restructuring, or self-discovery by the interlocutor. In contrast to systems that default to passive or merely empathetic response generation, Socratic-Solvers transition LLMs into active guides that drive dialogue towards explicit cognitive or pedagogical goals. This shift addresses critical limitations in extant LLM-based systems, such as their propensity for superficial engagement, confirmation bias, and lack of theory-driven probing (Zhang et al., 2 Feb 2026, Lei et al., 26 Sep 2025, Jiang et al., 12 Dec 2025).

Motivationally, three domain archetypes illustrate these goals:

• Therapeutic context: Surface core beliefs and cognitive distortions, guide toward behavioral change (CBT, Socratic Inquiry Framework).
• Educational context: Scaffold reasoning for learners, prompt self-explanation, surface misconceptions (math word problems, STEM interdisciplinary instruction, Socratic playgrounds).
• Reasoning agents: Challenge model-generated solutions, calibrate curriculum difficulty, mitigate solution exposure bias (co-evolutionary curricula, scientific ideation agents).

2. Modular Architecture and Decision Dynamics

Socratic-Solvers generally manifest as modular systems, decomposing dialogic control into distinct decision modules:

Component	Function	Typical Method
Strategy Anchoring	Determines when and what high-level intent to ask	Classifier w/ softmax + threshold
Template Retrieval	Selects granular Socratic method or template	Classifier/embedding retrieval
Prompt Construction	Merges (strategy, template) with system prompt	Prepending/slot-filling
Generation Engine	Produces the finalized question or response	LLM decoding (often LoRA-finetuned)

In the Socratic Inquiry Framework (SIF), decision-making proceeds as follows:

• Strategy Anchoring (SA): Computes a hidden representation $h_i = f_{\theta_1}(\hat C, x_i)$, derives intent probabilities $p(s|h_i) = \mathrm{softmax}(W h_i + b)$, and triggers questioning if $\max_s p(s|h_i)\geq\tau$ for a predefined threshold $\tau\in[0.3,0.5]$.
• Template Retrieval (TR): Given context and intent, predicts a specialized template class $\hat t=\arg\max_t p(t|z'_i)$ from a set (e.g., Definition, Elenchus, Maieutics, Dialectics, Counterfactual, Other).
• Prompt Synthesis: Plans $\hat s,\hat t$ are prepended as natural-language tags or tokens directing the LLM to generate a Socratic question matching both intent and method (Zhang et al., 2 Feb 2026).

3. Learning, Inference, and Curriculum Generation

Socratic-Solvers employ both supervised and preference-based learning paradigms:

• Supervised Learning: Models are fine-tuned on corpora of annotated Socratic dialogues (e.g., Socratic-QA: 17,981 high-quality samples) with explicit labels for strategy and template types.
• Direct Preference Optimization (DPO): Refines models to favor ground-truth or pedagogically valid Socratic questions over negative/invalid ones (irrelevant, repeated, direct solution, premature) using pairwise loss functions. A typical loss is:

$$\mathcal{L}_{\mathrm{DPO}} = -\mathbb{E}_{(p,q_v,q_{iv})} \left[ \log \sigma \left( \beta \left( \ln \frac{\pi_\theta(q_v|p)}{\pi_\mathrm{ref}(q_v|p)} - \ln \frac{\pi_\theta(q_{iv}|p)}{\pi_\mathrm{ref}(q_{iv}|p)} \right) \right) \right]$$

This mechanism ensures validity and avoids common pitfalls such as solution exposure or irrelevance (Kumar et al., 2024).

• Closed-Loop Curriculum Evolution: In multi-agent systems (e.g., Socratic-Zero), a Generator agent distills curriculum design from an oracle Teacher, mimicking its ability to produce questions matched in frontier difficulty to a dynamically evolving Solver. The generator is trained via utility-weighted supervised fine-tuning, maximizing log-likelihood of question synthesis weighted by a Gaussian utility centered at a desired solver success rate (Wang et al., 29 Sep 2025).

4. Taxonomies of Socratic Templates and Methods

Socratic-Solvers operationalize the Socratic method using well-defined, template-based or taxonomy-driven querying schemes. For example (Zhang et al., 2 Feb 2026, Lei et al., 26 Sep 2025):

CBT/therapy context:

• Definition: baseline queries on absolutes
• Elenchus: counter-questioning for cognitive distortion
• Maieutics: alternative exploration under uncertainty
• Dialectics: probe contradictions for cognitive tension
• Counterfactual: reality-testing via “If…then?”
• Other: residuals not matching above

Education/scientific ideation:

• Innovation axis: “How does this go beyond existing methods?”
• Feasibility axis: “What evidence supports that sufficient data exists?”
• Rationality axis: “What theoretical justification underpins this strategy?”

General dialogic taxonomies (Paul, Elder; PICOT frames):

• Clarification
• Assumption probing
• Evidence/reasoning
• Viewpoints
• Implications/consequences
• Meta-questioning

Templates are dynamically slot-filled with contextually extracted concepts or client/student language for adaptive precision.

5. Empirical Performance and Evaluation

Socratic-Solvers have been empirically evaluated on automatic metrics (BERTScore, BLEURT, ROUGE-L, METEOR, chrF, Distinct-n) and domain-specific criteria:

• Proactive Questioning Ability (PQA): Fraction of turns initiating with a Socratic question; integration of SIF lifts PQA from ~0.51 to ~0.97 in multi-turn therapeutic dialogue (Zhang et al., 2 Feb 2026).
• Dialogic Quality: Strategy comprehensiveness, professionalism, authenticity, ethical safety (human evaluation).
• Academic/Solving Gains: For code debugging and mathematical reasoning, DPO-finetuned Socratic-Solvers consistently outperform both supervised and chain-of-thought baselines (Rouge-L F1 = 18.3 vs. SFT 17.2, BERTScore F1 42.0 vs. 41.1; (Kumar et al., 2024)).
• Group and scalable instruction: MedTutor-R1 in clinical multi-agent simulation achieves +20% average pedagogical score improvement, robustness under group handling, and performance matching or exceeding GPT-4o in teaching quality (He et al., 5 Dec 2025).

Ablation studies confirm that removal of structured knowledge graphs or adversarial Socratic refinement causes substantial degradation in novelty, motivation, or experiment scores for ideation tasks (Lei et al., 26 Sep 2025).

6. Representative Algorithms and Implementation Patterns

Canonical Socratic-Solver pipelines are characterized by:

• Modular classifier endpoints for strategy and template prediction (pre-LLM inference)
• Prompt templates enumerating explicit strategy/method upfront (always prepend: “Therapeutic strategy: {ŝ}. Socratic method: {ţ}.”)
• LoRA/tunable LLMs fine-tuned on Socratic corpora
• Confidence thresholding for proactive intervention control (skip if $p(\hat s)<\tau$)
• Support for easy integration with off-the-shelf LLMs via REST APIs (POST /anchor, /retrieve, /generate; (Zhang et al., 2 Feb 2026))
• Dynamic multi-agent negotiation and role separation for co-agent Socratic dialogue (reflection-in-reflection models; (Holub et al., 21 Jan 2026))
• Weighted curriculum generation and selection (value-weighted SFT; (Wang et al., 29 Sep 2025))

Pseudocode for a minimal turn in SIF:

function SocraticTurn(C, x_i): Ć = truncate_context(C, budget) h = fθ1(Ć, x_i) p_s = softmax(W*h + b) if max(p_s)<τ: return reactive_response(C,x_i) ŝ = argmax(p_s) z = fθ2(Ć, x_i) p_t = softmax(z) ţ = argmax(p_t) prompt = build_prompt(ŝ, ţ, Ć, x_i) y = LLM_LoRA.generate(prompt) return y

(Zhang et al., 2 Feb 2026)

7. Domain Extensions, Limitations, and Future Directions

• Socratic-Solvers have been extended beyond psychotherapy and code debugging to geometry image synthesis (Socratic-Geo), collaborative medical instruction (MedTutor-R1), and interdisciplinary STEM education (ERL4SIIP). Domain adaptation typically requires new prompt templates, reward structures, and verification mechanisms (Jiao et al., 3 Feb 2026, He et al., 5 Dec 2025, Jiang et al., 12 Dec 2025).
• Limitations include reliance on annotated Socratic corpora for each domain, quality/dependence on teacher models for initial calibration, and theoretical gaps in convergence for co-evolutionary systems. Domain generalization, automated post-hoc validation, and more sophisticated multi-agent orchestration remain open problems (Wang et al., 29 Sep 2025).
• Future research is directed at cross-domain knowledge graph construction, debate-based Socratic multi-agent systems, context calibration for different learner profiles, and scalable, privacy-preserving deployment (Zhang et al., 2 Feb 2026, Lei et al., 26 Sep 2025, Jiang et al., 12 Dec 2025).

• (Zhang et al., 2 Feb 2026) The Art of Socratic Inquiry: A Framework for Proactive Template-Guided Therapeutic Conversation Generation
• (Kumar et al., 2024) Improving Socratic Question Generation using Data Augmentation and Preference Optimization
• (Lei et al., 26 Sep 2025) MotivGraph-SoIQ: Integrating Motivational Knowledge Graphs and Socratic Dialogue for Enhanced LLM Ideation
• (Jiang et al., 12 Dec 2025) Evolutionary Reinforcement Learning based AI tutor for Socratic Interdisciplinary Instruction
• (Wang et al., 29 Sep 2025) Socratic-Zero : Bootstrapping Reasoning via Data-Free Agent Co-evolution
• (Holub et al., 21 Jan 2026) Reflecting in the Reflection: Integrating a Socratic Questioning Framework into Automated AI-Based Question Generation
• (He et al., 5 Dec 2025) MedTutor-R1: Socratic Personalized Medical Teaching with Multi-Agent Simulation