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A Verifier-Guided Explainable Reasoning Framework with Gold-Anchored QLoRA, Task-Aware Mixture-of-Experts, and Group-Relative RLVR
Thi Kim Trang Vo, Nam Tien Le, Thi Kim Nguyet Vo, Minh Khang Tran, Duy Phuong Tran
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 91%
Last extracted: 9/8/2026, 1:53:23 AM
Summary
The paper proposes a Verifier-Guided Explainable Reasoning Framework for educational question answering that integrates gold-anchored QLoRA fine-tuning, task-aware symbolic routing (Mixture-of-Experts), and Group-Relative Reinforcement Learning with Verifiable Rewards (RLVR). Using Qwen2.5-3B-Instruct as the backbone, the framework routes logic problems to a FOL/Z3 verifier and physics problems to a symbolic solver. The RLVR process optimizes for answer correctness (P1), evidence/unit consistency (P2), and reasoning depth (P3). Results on 438 held-out examples show that RLVR significantly improves reasoning depth (P3) from 50.68% to 72.20%, while final answer accuracy (P1) remains stable around 55.94%, indicating that symbolic verification and self-consistency handle reliability while RLVR enhances explicit reasoning structure.
Entities (10)
Relation Signals (7)
Qwen2.5-3B-Instruct ā isfinetunedwith ā QLoRA
confidence 95% Ā· Qwen2.5-3B-Instruct is first adapted with field-weighted QLoRA supervision anchored to authoritative answers.
RLVR ā optimizesfor ā P@3
confidence 95% Ā· RLVR increases P3 from 50.68% to 72.20%... indicating that RLVR primarily strengthens explicit reasoning structure
Task-Aware Mixture-of-Experts ā routesto ā FOL/Z3 Verifier
confidence 92% Ā· A lightweight router then assigns logic problems to a FOL/Z3 verifier...
RLVR ā optimizesfor ā P1
confidence 90% Ā· hybrid P1 remains approximately stable at 55.94%... RLVR primarily strengthens explicit reasoning structure
Task-Aware Mixture-of-Experts ā routesto ā Symbolic Solver
confidence 90% Ā· ...and physics problems to a formula- and unit aware symbolic solver.
Self-Consistency ā aggregates ā Candidate Responses
confidence 85% Ā· gold-free self-consistency aggregates multiple candidate responses before an optional question-only physics verifier...
Symbolic Verification ā complements ā Neural Policy
confidence 85% Ā· symbolic verification complements the neural policy by improving answer reliability at the system level.
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Abstract
Abstract:Large language models (LLMs) show strong reasoning ability, but their explanations can remain inconsistent, weakly grounded, or difficult to verify. We propose a verifier-guided explainable reasoning framework for transparent educational question answering that combines gold-anchored QLoRA, task-aware symbolic routing, and group-relative RLVR. Qwen2.5-3B-Instruct is first adapted with field-weighted QLoRA supervision anchored to authoritative answers. A lightweight router then assigns logic problems to a FOL/Z3 verifier and physics problems to a formula- and unit aware symbolic solver. Verifier feedback is further used to support candidate evaluation, self-revision, and reward construction during RLVR. Candidate responses are evaluated along three complementary dimensions: P1 for answer correctness, P2 for evidence or unit consistency, and P3 for reasoning depth and explainability. At inference, gold-free self-consistency aggregates multiple candidate responses before an optional question-only physics verifier performs conservative system-level correction. On 438 held-out examples, RLVR increases P3 from 50.68% to 72.20%, while hybrid P1 remains approximately stable at 55.94%. Self-consistency improves model only P1 from 48.86% to 50.23%, with symbolic verification providing the remaining hybrid gain. These results indicate that RLVR primarily strengthens explicit reasoning structure, while symbolic verification complements the neural policy by improving answer reliability at the system level.
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- Source: https://arxiv.org/abs/2609.05221v1
- Canonical: https://arxiv.org/abs/2609.05221v1
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A Verifier-Guided Explainable Reasoning Framework with Gold-Anchored QLoRA, Task-Aware Mixture-of-Experts, and Group-Relative RLVR Thi Kim Trang Vo1,3, Nam Tien Le2,3, Thi Kim Nguyet Vo4,5, Minh Khang Tran1,3, Duy Phuong Tran1,3 Affiliation: Affiliation: 1University of Information Technology (UIT), Ho Chi Minh City, Vietnam 2Ho Chi Minh City University of Technology (HCMUT), Vietnam 3Vietnam National University, Ho Chi Minh City, Vietnam 4University of Economics Ho Chi Minh City (UEH), Vietnam 5Viet Nam ā The Netherlands Programme (VNP), Vietnam Abstract Large language models (LLMs) show strong reasoning ability, but their explanations can remain inconsistent, weakly grounded, or difficult to verify. We propose a verifier-guided explainable reasoning framework for transparent educational question answering that combines gold-anchored QLoRA, task-aware symbolic routing, and group-relative RLVR. Qwen2.5-3B-Instruct is first adapted with field-weighted QLoRA supervision anchored to authoritative answers. A lightweight router then assigns logic problems to a FOL/Z3 verifier and physics problems to a formula- and unit-aware symbolic solver. Verifier feedback is further used to support candidate evaluation, self-revision, and reward construction during RLVR. Candidate responses are evaluated along three complementary dimensions: P1 for answer correctness, P2 for evidence or unit consistency, and P3 for reasoning depth and explainability. At inference, gold-free self-consistency aggregates multiple candidate responses before an optional question-only physics verifier performs conservative system-level correction. On 438 held-out examples, RLVR increases P3 from 50.68% to 72.20%, while hybrid P1 remains approximately stable at 55.94%. Self-consistency improves model-only P1 from 48.86% to 50.23%, with symbolic verification providing the remaining hybrid gain. These results indicate that RLVR primarily strengthens explicit reasoning structure, while symbolic verification complements the neural policy by improving answer reliability at the system level. Our code implementation is available at: https://github.com/VoThiKimTrang06101997/Explainable-xAI/tree/master/One-Shot-RLVR Index Terms: Explainable AI, Large Language Models (LLM), Educational Question Answering, Reinforcement Learning with Verifiable Rewards (RLVR), QLoRA, Task-Aware Mixture-of-Experts, Neuro-Symbolic Reasoning, First-Order Logic, FOL/Z3 Verifier, Scientific Reasoning. I Introduction Large language models (LLMs) have achieved strong multi-step reasoning performance through chain-of-thought (CoT) prompting and instruction tuning [1, 2]. However, in scientific and educational question answering, a plausible explanation is not necessarily trustworthy. A correct answer may still rely on an invalid inference, an inappropriate physical formula, unsupported evidence, or inconsistent units. Thus, reliable reasoning requires both answer correctness and inspectable intermediate reasoning. Prior work improves reasoning through self-consistency [3], process supervision [4], and scientific-logicality evaluation [5]. Reinforcement learning with verifiable rewards (RLVR) further enables optimization from automatically checkable signals. DeepSeekMath introduced Group Relative Policy Optimization (GRPO) [6], while One-Shot-RLVR demonstrated reasoning improvements with limited supervision [7]. Nevertheless, answer-only rewards cannot distinguish an accidentally correct prediction from a well-supported solution. This challenge is closely aligned with the 2nd International XAI Challenge for Transparent Educational Question-Answering (EXACT 2026), organized with IJCNN 2026 [8]. Its heterogeneous tasks require different verification mechanisms: logic questions require premise-based entailment checking, whereas physics questions additionally require formula, numerical, and unit consistency. To address these requirements, we propose a Verifier-Guided Explainable Reasoning Framework with Gold-Anchored QLoRA, Task-Aware Mixture-of-Experts, and Group-Relative RLVR. Qwen2.5-3B-Instruct [2] is adapted using QLoRA [9], following LoRA [10]. Training targets are anchored to authoritative answers, while field-weighted supervision emphasizes answers, evidence, and units. Unlike conventional neural MoE architectures [11, 12], our lightweight router dispatches tasks to external symbolic experts: FOL/Z3 verification for logic [13] and a formula- and unit-aware solver for physics. We evaluate three complementary dimensions: P1 for final-answer correctness, P2 for evidence or unit consistency, and P3 for reasoning depth and explainability. Verifier feedback supports candidate evaluation, self-revision, and group-relative RLVR, while inference combines gold-free self-consistency with optional conservative physics verification. On 438 held-out examples, RLVR increases P3 from 50.68%50.68\% to 72.20%72.20\%, while hybrid P1 remains approximately stable at 55.94%55.94\%, indicating that RLVR primarily strengthens explicit reasoning structure while symbolic verification contributes complementary system-level reliability. Our contributions are mainly: ā¢ Gold-anchored QLoRA: a field-weighted adaptation strategy that preserves authoritative answers and structured evidence before RLVR. ā¢ Task-aware neuro-symbolic verification: lightweight routing to FOL/Z3 logic verification and formula- and unit-aware physics verification. ā¢ Verifier-guided P1/P2/P3 RLVR: a framework that separates answer correctness, evidence/unit consistency, and reasoning depth while distinguishing neural-policy performance from hybrid-system gains. I Method I-A Framework Overview We formulate transparent educational QA as a generationāverificationāoptimization problem in which both the final answer and its reasoning are evaluated. As shown in Fig. 1, the framework consists of seven stages: (1) gold-anchored canonicalization, (2) field-weighted QLoRA SFT and calibration, (3) task-aware Mixture-of-Experts (MoE) routing, (4) symbolic verification, (5) self-revision and candidate ranking, (6) P1/P2/P3 group-relative RLVR, and (7) gold-free self-consistency with optional physics verification. Our MoE is a task-level routing mechanism, not a Transformer-internal sparse MoE architecture [11, 12]. The LLM backbone is unchanged; the router only selects an external Logic or Physics verification expert. Figure 1: Overview of the proposed verifier-guided framework. Gold-anchored targets support QLoRA SFT and calibration. A task-aware MoE router selects the Logic/FOL/Z3 or Physics/SOL verification path. Verifier signals support revision and group-relative RLVR. At inference, one greedy and four sampled responses are grouped by answer equivalence before optional question-only physics verification. I-B Gold-Anchored QLoRA Fine-Tuning For each example xi=(qi,aiā,mi)x_i=(q_i,a_i^*,m_i), where qiq_i is the question, aiāa_i^* is the authoritative answer, and mim_i contains task metadata, teacher-generated supervision may be repaired while the source answer remains locked: yiT [1.65cm][l]y_i^T =Repairā”(xi,aiā), =Repair(x_i,a_i^*), (1) aialigned [1.65cm][l]a_i^aligned =aiā. =a_i^*. The aligned target contains the answer, unit, premises, explanation, and a compact reasoning trace, preventing noisy teacher outputs from replacing authoritative labels. We adapt Qwen2.5-3B-Instruct [2] using 4-bit NF4 QLoRA [9], following LoRA [10], with r=32r=32, Ī±=64Ī±=64, and dropout 0.050.05. Completion-only SFT uses āSFT=ātwtāmtāātmaxā”(1,ātwtāmt),L_SFT= _tw_tm_t _t \! (1, _tw_tm_t ), (2) where mtm_t masks prompt tokens and wtw_t assigns larger weights to answer, unit, and premise fields. A subsequent answer-focused calibration stage further strengthens these fields before RLVR. I-C Task-Aware Mixture-of-Experts Routing and Symbolic Verification Unlike neural MoE models that route tokens through trainable expert layers, our task-aware MoE operates only at the verification level. Given an input representation hā”(x)h(x), the router estimates pā”(eā£x)=softmaxā”(Wrāhā(x)+br),p(e x)=softmax\! (W_rh(x)+b_r ), (3) and selects eā=argā”maxeā”pā”(eā£x),eāLogic,Physics.e^*= _ep(e x), eā\Logic,Physics\. (4) Thus, routing does not modify the Qwen Transformer or activate Transformer-level experts; it only dispatches each problem to an external task-specific verifier. 1) Logic Expert. For logic tasks, natural-language premises are converted into first-order-logic (FOL) representations and checked using Z3 [13]. A candidate claim c is entailed when Pā§cāUNSATā”(Pā§Ā¬c).P c (P c). (5) Contradiction is checked analogously through UNSATā”(Pā§c)UNSAT(P c). For multiple-choice questions, candidate options are compared according to their symbolic support. 2) Physics Expert. For physics tasks, the verifier extracts variables and units, retrieves a supported relation set ā°E, solves the relation, and normalizes the result: zSOL [1.55cm][l]z_SOL =Solveā”(ā°,V,U), =Solve(E,V,U), (6) aSOL [1.55cm][l]a_SOL =NormalizeUnitā”(zSOL). =NormalizeUnit(z_SOL). The physics expert checks formula applicability, numerical consistency, and units, while the LLM remains the primary reasoning model. I-D Verifier-Guided Self-Revision Verifier feedback identifies unsupported premises, incorrect formulas, unit inconsistencies, or answerāexplanation conflicts. A candidate may therefore be revised as y~k=Reviseā”(yk,Fverifierā(yk)), y_k=Revise\! (y_k,F_verifier(y_k) ), (7) where FverifierF_verifier denotes task-specific feedback. Candidates are also compared using verifier-derived quality signals, encouraging responses whose answers and reasoning are jointly better supported. I-E P1/P2/P3 Group-Relative RLVR Starting from the calibrated SFT checkpoint, we apply reinforcement learning with verifiable rewards (RLVR) following One-Shot-RLVR [7] and the group-relative optimization principle of GRPO [6]. For each training question, K=3K=3 responses are sampled. The reward used in the final experiment is Ri,k= R_i,k= 0.50āRexact+0.20āRdense 0.50R_exact+0.20R_dense (8) +0.15āRP2+0.10āRP3+0.05āRfmt. +0.15R_P2+0.10R_P3+0.05R_fmt. Here, RexactR_exact measures exact final-answer correctness, RdenseR_dense provides task-aware partial answer credit, RP2R_P2 measures premise consistency for logic or unit consistency for physics, and RP3R_P3 rewards explicit reasoning depth: RP3=minā”(1,NCoT4).R_P3= (1, N_CoT4 ). (9) For each response group, the relative advantage is Ai,k=Ri,kāĪ¼iĻi+Ļµ,A_i,k= R_i,k- _i _i+Īµ, (10) with Ī¼i=1Kāāk=1KRi,k. _i= 1K _k=1^KR_i,k. (11) Groups with negligible reward variance are skipped because they provide no useful relative preference signal. A frozen copy of the calibrated SFT checkpoint serves as the reference policy. In the active implementation, reference regularization uses the difference between sequence-average log probabilities: āref=(āĀÆĪøāāĀÆref)2.L_ref= ( _Īø- _ref )^2. (12) Following the group-relative RL formulation [6] and verifiable-reward training setting [7], the policy uses the clipped surrogate implemented in our training code. Let āĀÆĪø _Īø and āĀÆold _old denote the sequence-average log probabilities under the current and rollout policies: Ļi,kā(Īø)=expā”(āĀÆĪø,i,kāāĀÆold,i,k). _i,k(Īø)= \! ( _Īø,i,k- _old,i,k ). (13) The group-relative policy loss is āpolicy=ā1Kāk=1Kmin( _policy=- 1K _k=1^K ( Ļi,kāAi,k, _i,kA_i,k, (14) OPENclipā”(Ļi,k,1āĪµ,1+Īµ)āAi,k), ( _i,k,1- ,1+ )A_i,k ), where Īµ=0.2 =0.2 in the final run. Combining this clipped objective with reference regularization gives the RLVR loss āRLVR=āpolicy+Ī²āāref.L_RLVR=L_policy+ _ref. (15) Thus, Ai,kA_i,k favors candidates whose verifiable reward exceeds the group mean, clipping limits overly large policy updates, and ārefL_ref constrains drift from the calibrated SFT policy. I-F Gold-Free Self-Consistency and Final Output At held-out inference, five responses are generated, =y(g),y(1),y(2),y(3),y(4),Y= \y^(g),y^(1),y^(2),y^(3),y^(4) \, (16) where y(g)y^(g) is generated greedily and the remaining four responses are sampled. They are grouped by task-aware answer equivalence: =ClusterEquivalentā”().C=ClusterEquivalent(Y). (17) The largest cluster is selected. If clusters have equal size, preference is given to the cluster containing the greedy response; remaining ties are resolved by a gold-free structural quality score [3]. No validation gold label is used during this selection. For physics, a conservative question-only verifier may override the selected answer only when cverifierā„0.98,c_verifierā„ 0.98, (18) otherwise it abstains. The final output contains the answer and, where applicable, unit, supporting premises, symbolic/FOL information, reasoning trace, and verification confidence. I Experiments I-A Experimental Setup We evaluate the proposed framework on the EXACT logic and physics data [8]. After preprocessing, 2,162 examples are divided using a group-safe 80:20 split into 1,724 training and 438 held-out validation samples. Shared logic premise blocks, duplicate normalized physics questions, and identical model inputs are kept within the same partition to reduce leakage. Retrieval is disabled (RETRIEVAL_TOP_K=0), and validation labels are accessed only after generation. Table I summarizes the resulting data split. Table I: Experimental data composition. Task Total Train Val. Logic Multiple Choice 360 287 73 Logic Yes/No 415 331 84 Logic Uncertain 33 26 7 Physics 1,354 1,080 274 Total 2,162 1,724 438 The backbone is Qwen2.5-3B-Instruct [2] with 4-bit NF4 QLoRA [9]. Maximum sequence, prompt, and generation lengths are 1,280, 1,024, and 224 tokens. Stage A performs three SFT epochs at 5Ć10ā55Ć 10^-5, Stage B performs one calibration epoch at 2Ć10ā52Ć 10^-5, and Stage C performs 240 RLVR rollout steps at 2Ć10ā62Ć 10^-6. Evaluation uses five-generation gold-free self-consistency: one greedy response and four sampled responses (T=0.35T=0.35, top-p=0.90p=0.90). The question-only physics verifier intervenes only for supported rules with confidence ā„0.98ā„ 0.98. Experiments run on one NVIDIA L4 24 GB GPU in a PyTorch/Hugging Face environment using Transformers, PEFT, Accelerate, bitsandbytes, and repository-side FOL/Z3 and SOL modules. I-B Quantitative Results We report three complementary reasoning dimensions. P1 is final answer correctness after the complete inference pipeline. P2 is a task-aware supporting-consistency score: for logic it is the partial F1 between predicted and reference premise indices, whereas for physics it checks normalized unit consistency (with partial multi-unit credit for multi-valued answers). P3 is the generated reasoning-depth proxy defined in Eq. (9). Table I compares calibrated SFT and the final RLVR policy on the same 438 held-out examples. Table I: Held-out validation results (%). Macro P1 is the unweighted mean over the four evaluated task families. Model P1 Macro P1 Logic P1 Physics P1 P2 P3 Format Strict Calibrated SFT 56.62 76.82 83.54 40.51 77.70 50.68 98.17 41.44 RLVR 55.94 76.14 82.32 40.15 75.33 72.20 94.52 40.14 Ī -0.68 -0.69 -1.22 -0.36 -2.37 +21.52 -3.65 -1.30 The three metrics reveal different effects of RLVR. P1 changes only from 56.62% to 55.94% (ā0.68-0.68 points), so the completed RLVR run does not produce an additional held-out answer-accuracy gain. P2 decreases from 77.70% to 75.33% (ā2.37-2.37 points), indicating that richer generated reasoning does not automatically preserve premise selection or physical-unit consistency. In contrast, P3 rises from 50.68% to 72.20%, a gain of 21.52 points, making reasoning depth the dominant observed post-training change. This pattern is technically consistent with the group-relative reward. Exact P1 has the largest individual coefficient, but candidates inside a rollout group frequently share the same answer reward. When this occurs, P1 contributes little relative ranking signal, whereas differences in P2, P3, dense answer credit, and formatting can still produce non-zero advantages. Since P3 is explicitly rewarded, the policy can therefore learn to emit more complete reasoning traces even when final-answer accuracy has already saturated within a group. The format decrease from 98.17% to 94.52% further shows that longer structured outputs create more opportunities for malformed fields or schema violations. P2 should also be interpreted jointly with the task mixture rather than as a single homogeneous quantity. Physics contributes 274 of the 438 validation examples and retains high unit consistency (91.79% for SFT and 89.23% for RLVR), which lifts the micro-averaged P2. Logic P2 instead measures premise selection and is substantially lower. Consequently, the overall P2 decrease reflects both a modest physics-unit decline and weaker premise consistency in some logic categories, rather than one uniform failure mode. Finally, P3 is a reasoning-depth proxy, not a proof of logical validity. A longer trace can make intermediate assumptions easier to inspect while still containing an unsupported premise or numerical mistake. Reporting P1, P2, P3, and Strict together therefore separates final correctness, supporting consistency, reasoning explicitness, and end-to-end structural validity. The small Macro-P1 change (76.82% to 76.14%) likewise indicates that the P1 shift is not caused by collapse of a single task family. 1) Task-Level P1/P2/P3 Analysis. Table I decomposes all three metrics by task family. The P2 values are computed with the same task-aware definition used in the overall score and are therefore directly consistent with Table I. P1 P2 P3 Task SFT RLVR SFT RLVR SFT RLVR Logic MC 91.78 91.78 57.26 53.70 40.75 72.95 Logic Yes/No 75.00 72.62 52.20 51.87 42.86 75.00 Logic Uncertain 100.00 100.00 45.31 38.16 53.57 71.43 Physics 40.51 40.15 91.79 89.23 55.66 71.17 Table I: Task-level P1/P2/P3 performance (%). Policy Inference Overall Logic Physics SFT Greedy 50.46 83.54 30.66 SFT + Five-generation self-consistency 51.14 83.54 31.75 SFT + Physics verifier 56.62 83.54 40.51 RLVR Greedy 48.86 82.32 28.83 RLVR + Five-generation self-consistency 50.23 82.32 31.02 RLVR + Physics verifier 55.94 82.32 40.15 Table IV: Inference-component ablation on P1 (%). Type N SFT RLVR Plain numeric 195 49.74 49.74 Scientific numeric 48 6.25 6.25 Binary 4 75.00 75.00 Categorical text 8 37.50 37.50 Numeric assignment 3 66.67 66.67 Multiple values 6 50.00 33.33 Table V: Physics P1 by answer representation (%). For P1, Logic Multiple Choice remains exactly 91.78%, Logic Uncertain remains 100% on its seven-example subset, Logic Yes/No decreases by 2.38 points, and Physics changes only from 40.51% to 40.15%. Hence, the small global P1 decrease is distributed across limited task-level changes rather than a broad loss of answer capability. For P2, Logic Multiple Choice changes from 57.26% to 53.70%, Logic Yes/No from 52.20% to 51.87%, Logic Uncertain from 45.31% to 38.16%, and Physics from 91.79% to 89.23%. The largest percentage-point logic decrease occurs on the seven-example Uncertain subset and should not be over-interpreted. The physics P2 value is much higher because it measures unit consistency, whereas logic P2 is a partial premise-selection F1. This confirms that P2 is best used as a task-aware diagnostic rather than as a substitute for P1. For P3, every populated task family improves: Logic Multiple Choice increases by 32.19 points, Logic Yes/No by 32.14, Logic Uncertain by 17.86, and Physics by 15.51. This consistency across heterogeneous tasks strengthens the interpretation that RLVR primarily reshapes reasoning explicitness. The physics result is especially informative: P3 rises substantially while P1 stays near 40%, showing that producing a deeper trace is not sufficient to solve numerical execution or formula-selection errors. I-C Ablation Study We isolate the contribution of greedy decoding, five-generation gold-free self-consistency, and deterministic physics verification. Table IV reports P1 because this ablation is designed specifically to measure final answer correction at inference; complete component-wise P2/P3 traces are not logged for every intermediate decoding mode and are therefore not inferred. Five-generation self-consistency increases overall P1 by 0.68 points for SFT and 1.37 points for RLVR. Symbolic verification provides a substantially larger physics gain: relative to self-consistency, physics P1 improves by 8.76 points for SFT and 9.12 points for RLVR. The verifier intervenes on only 43 of 274 physics queries (15.69%), correcting 26 SFT and 27 RLVR errors while introducing two regressions for each policy. This sparse intervention pattern supports the intended design: the symbolic module acts as a selective checker for supported high-confidence relations rather than as a second model that replaces the LLM on every physics query. The ablation also clarifies where the observed system-level gain originates. For both policies, moving from greedy decoding to five-generation self-consistency yields only a small increase, whereas the physics verifier produces the dominant final correction. This separation is important because it prevents the verifier gain from being misattributed to RLVR itself: the policy changes the distribution and structure of generated reasoning, while the deterministic checker repairs a smaller subset of supported numerical cases after generation. The similar verifier gains for SFT and RLVR further suggest that the symbolic module is exploiting task structure that remains useful across both neural checkpoints rather than compensating for one particular policy. 1) Physics Error Analysis. Table V further decomposes physics answer correctness by representation. Plain numeric answers reach 49.74% P1, whereas scientific-notation answers reach only 6.25%. At the same time, physics P2 (unit consistency) remains 89.23% after RLVR. The gap between high unit consistency and much lower answer correctness indicates that the dominant physics failures are not primarily unit recognition; they are more consistent with formula selection, numerical execution, exponent normalization, and answer representation errors. The RLVR training trajectory provides a complementary explanation. Of 240 rollout groups, 57 (23.75%) have zero reward variance and are skipped, leaving 183 informative groups and 30 optimizer updates. The right panel of Fig. 3 summarizes 20-step rolling means observed during RLVR training. The first versus last 20-step means are approximately 0.86ā 0.90 for reward, 0.93ā 0.95 for P1, 0.67ā 0.75 for P2, and 0.53ā 0.74 for P3. Thus, the value near 0.94 refers to sampled P1 during RLVR training rather than the held-out P1 values in Tables IāIV. Under Eq. (10), zero-variance groups provide no relative ranking signal, so optimization is concentrated on groups where candidate rewards differ; the strongest sustained change is consequently observed in P3. I-D Comparison with Prior Reasoning Frameworks Table VI provides a contextual comparison with representative reasoning and verification approaches. Because datasets, models, inference budgets, and evaluation metrics differ, the reported numbers are not directly comparable. Table VI: Contextual comparison with representative reasoning and verification approaches. Results are not directly comparable across benchmarks. Method Benchmark / Model Supervision Reasoning / Verification Reported Result Letās Verify Step by Step [4] MATH subset / large LLM Process supervision Process Reward Model 78.2% accuracy DeepSeekMath [6] MATH / DeepSeekMath-7B SFT + GRPO Outcome-verifiable group-relative optimization 51.7%; 60.9% with 64-sample self-consistency One-Shot-RLVR [7] MATH500 / Qwen2.5-Math-1.5B One-example RLVR Group-relative verifiable reward 36.0% ā 73.6% Scientific Logicality [5] PhysLogic / multiple LLMs Logicality-guided Process-aware scientific reasoning evaluation Improved logicality and physics performance Ours EXACT / Qwen2.5-3B-Instruct Gold-anchored QLoRA + RLVR FOL/Z3 + Physics/SOL + five-generation gold-free self-consistency 55.94% P1; 75.33% P2; 72.20% P3 Prior work emphasizes either intermediate process supervision or verifiable mathematical outcomes. Our framework instead combines heterogeneous logic and physics reasoning with task-specific symbolic verification and reports all three core diagnostics together. P1 captures whether the final answer is correct, P2 measures whether its supporting premises or physical units remain consistent, and P3 measures whether the generated response exposes explicit intermediate reasoning. The comparison is therefore methodological rather than a direct leaderboard. I-E Discussion The verified results expose a clear three-way P1āP2āP3 trade-off. Relative to calibrated SFT, RLVR changes P1 by ā0.68-0.68 points and P2 by ā2.37-2.37 points but improves P3 by +21.52+21.52 points. The result does not support the claim that RLVR improves every metric; instead, it supports a more specific conclusion: under the present reward weighting and optimization budget, RLVR mainly strengthens reasoning explicitness while preserving answer accuracy within approximately one percentage point of the calibrated baseline. P2 provides an additional diagnostic that prevents the P3 result from being overstated. The modest P2 decline shows that a deeper response can introduce an incorrect or unnecessary premise, or lose unit consistency, even when the trace becomes more complete. Conversely, P1 can remain correct despite a weaker supporting trace. Reporting all three metrics therefore makes the source of a gain or degradation visible and better matches the objective of transparent educational QA than relying on one aggregate accuracy number. Five-generation self-consistency and symbolic verification address different parts of this trade-off. Self-consistency reduces single-generation variance, whereas the deterministic physics verifier selectively corrects cases that can be solved by supported high-confidence relations. The verifierās large physics P1 gain despite sparse activation indicates that some residual errors are execution failures rather than failures to produce reasoning text. Together, these observations motivate treating the neural policy, reasoning objective, and symbolic checker as complementary components rather than attributing all system-level improvement to RLVR alone. I-F Visualization Results The five diagnostics summarize the same measurements reported in the tables. Figure 2 shows task-level P1, P2, and P3 from Table I; Fig. 3 separates inference-stage P1 correction from RLVR training-time dynamics. Figure 2: Task-level diagnostics from Table I. Left: P1 correctness. Middle: P2 consistency. Right: P3 reasoning depth. Figure 2 makes the P1āP2āP3 trade-off directly checkable against Table I. P1 is nearly unchanged: Logic MC remains 91.8%, Logic Yes/No changes 75.0ā 72.6%, Logic Uncertain remains 100.0%, and Physics changes 40.5ā 40.1%. P2 decreases from 57.3ā 53.7%, 52.2ā 51.9%, 45.3ā 38.2%, and 91.8ā 89.2%, respectively. In contrast, P3 rises in every task: 40.8ā 72.9%, 42.9ā 75.0%, 53.6ā 71.4%, and 55.7ā 71.2%. The visual pattern therefore supports the same conclusion as Table I: RLVR changes reasoning depth more strongly than final-answer correctness. Figure 3: Inference and training dynamics. Left: P1 progression from Table IV. Right: 20-step rolling reward/P1/P2/P3 during RLVR training. Figure 3 (left) reproduces Table IV: SFT progresses 50.5ā 51.1ā 56.6%, while RLVR progresses 48.9ā 50.2ā 55.9% from greedy decoding to self-consistency and then hybrid verification. Hence, self-consistency gives the modest model-only gain and the verifier supplies the larger final correction. The right panel is not a held-out accuracy plot; it summarizes 20-step rolling statistics observed during RLVR training. Its first/last 20-step means are reward 0.86/0.90, P1 0.93/0.95, P2 0.67/0.75, and P3 0.53/0.74. The value near 0.94 therefore refers to sampled training-time P1, not the held-out values reported in Tables I or IV. Together, the five plots separate RLVRās reasoning-depth shift, self-consistencyās variance reduction, and the physics verifierās selective correctness gain. I-G Inference Results The final inference pipeline combines five-generation gold-free self-consistency with optional symbolic verification. One greedy and four sampled responses are grouped by answer equivalence, after which the selected physics response may be conservatively checked by the question-only verifier. Fig. 4 presents six representative correct cases covering three logic and three physics output formats. Each case exposes the question, premises or physical information, model answer, reasoning response, gold answer, and verification notes. The cases are selected only after generation for qualitative visualization; gold labels are not available to clustering or the question-only verifier. Figure 4: Representative correct inference cases across six logic and physics task formats. The qualitative cases complement the quantitative P1/P2/P3 analysis. Logic examples make premise use directly inspectable, whereas physics examples expose the chosen relation, numerical substitution, units, and verifier status. They also illustrate why the metrics should not be collapsed: P1 can be correct while premise selection is incomplete, P2 can remain high despite a numerical answer error, and P3 can increase simply because more reasoning steps are made explicit. The intended system therefore uses the LLM for general reasoning and reserves symbolic intervention for supported, verifiable cases. IV Conclusion and Future Work We presented a verifier-guided framework combining gold-anchored QLoRA, task-aware symbolic routing, self-revision, and group-relative RLVR for transparent educational QA. It separately evaluates P1 final-answer correctness, P2 evidence/unit consistency, and P3 reasoning depth. On 438 held-out examples, RLVR raises P3 from 50.68% to 72.20%, while hybrid P1 remains close to calibrated SFT (55.94% vs. 56.62%) and P2 is 75.33%. Five-generation gold-free self-consistency gives a modest model-only gain, whereas the conservative physics verifier yields the largest physics-P1 gain. Thus, RLVR mainly reshapes explicit reasoning, while symbolic verification selectively corrects high-confidence numerical failures. The current RLVR objective improves reasoning depth more strongly than answer accuracy, and longer outputs can introduce premise, unit, or formatting inconsistencies. Physics also remains limited by formula selection, numerical execution, and scientific-notation normalization. Future work will study (i) improved P1/P2/P3 reward balancing, (i) stronger numerical and symbolic normalization, (i) broader logic/physics verifier coverage, (iv) complete reward-component and routing ablations, and (v) larger scientific reasoning benchmarks. We also plan to calibrate verifier confidence, use symbolic feedback earlier in candidate revision, and test robustness under paraphrased premises, altered numerical scales, and unit conversions, aiming to preserve the P3 gain while improving correctness, consistency, and transfer. Beyond these extensions, a stronger evaluation protocol should quantify the stability of the observed gains across random seeds and alternative validation splits. In particular, the seven-example Logic Uncertain subset is too small to support strong conclusions by itself, while physics dominates the held-out distribution and therefore has a disproportionate effect on overall P1. Future experiments will report confidence intervals, per-task calibration, and repeated runs so that changes in P1, P2, and P3 can be distinguished from sampling variation. We will also evaluate the verifier as an explicit selective-prediction component by measuring coverage, correction rate, regression rate, and confidence calibration rather than accuracy alone. A second direction concerns efficiency and transfer. The current pipeline uses multiple generations for gold-free self-consistency and invokes symbolic verification only on supported high-confidence cases. We plan to study whether candidate count can be reduced adaptively when answer clusters agree early, and whether verifier routing can be learned with lower inference overhead. Finally, the same separation between answer correctness, supporting consistency, and reasoning depth can be tested on broader STEM domains and multilingual educational QA. Such experiments would clarify whether the present neuralāsymbolic design transfers beyond the EXACT setting while preserving the interpretability advantages of structured outputs and selective verification. Finally, we will study reward-weight sensitivity, reference regularization, verifier-confidence calibration, repeated-run uncertainty, and the latency/memory overhead of multi-candidate generation and symbolic checking so that reasoning gains can be assessed jointly with correctness and deployment cost. References [1] J. Wei, X. Wang, D. Schuurmans, M. Bosma, B. Ichter, F. Xia, E. Chi, Q. V. Le, and D. Zhou (2022) Chain-of-thought prompting elicits reasoning in large language models. In Advances in Neural Information Processing Systems, Vol. 35. Cited by: Ā§I. 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