Interpretable Bayesian Language Model

• The HIBLM framework integrates explicit Bayesian reasoning with modular uncertainty quantification, enabling human-accessible, mathematically robust outputs.
• It decomposes inference into clear stages with posterior estimations and calibrated confidence, ensuring each step’s uncertainty is communicated via natural language.
• HIBLMs have demonstrated strong performance in applications like disease diagnosis and concept learning, highlighting their potential for scalable, interpretable AI.

A human-interpretable Bayesian LLM (HIBLM) fuses explicit probabilistic reasoning, modular uncertainty quantification, and language-based or natural-language-expressible latent structures, producing outputs that are both mathematically principled and accessible to human users. In recent literature, frameworks such as DiagnoLLM, verbalized probabilistic graphical modeling (vPGM), natural-language-driven Bayesian concept learners, and bounded pragmatic speakers each operationalize HIBLM in distinct domains while converging on the principles of factorized inference, modular structure reflection, and post-hoc or intrinsic explainability (Xu et al., 8 Nov 2025, Ellis, 2023, Nguyen, 2023, Huang et al., 8 Jun 2024).

1. Model Architectures and Bayesian Foundations

Recent human-interpretable Bayesian LLMs are characterized by explicit mappings between modular probabilistic structures and LLM workflows. For example, DiagnoLLM implements a three-stage pipeline: (1) Bayesian deconvolution of omics data via Gaussian Process priors (GP-unmix), (2) eQTL-guided neural classification, and (3) post-hoc narrative generation via an LLM, each step returning posteriors or attributions with explicit uncertainty estimates (Xu et al., 8 Nov 2025).

The vPGM paradigm likewise structures inference as a sequence of latent-variable computations: LLMs are prompted to verbalize the conditional probability distributions (CPDs) of a PGM, enumerate latent variable dependencies, and simulate message passing through chain-of-thought prompts, thereby mimicking a graphical model’s update equations but expressing outputs in natural language with explicit calibrated confidence (Huang et al., 8 Jun 2024).

The key property is the exposure and propagation of uncertainty from each probabilistic computation stage to the narrative or human-facing report, ensuring that both predictions and their confidence intervals are communicable.

2. Formal Bayesian Inference and Modular Decomposition

HIBLMs operationalize probabilistic inference through a combination of explicit formulas, approximate message passing, and language-based representations of latent structures or hypotheses. The principal parameterization distributes as follows:

• Latent Variable Modeling: For DiagnoLLM, the latent tensor $Z_{gj}$ (gene $g$, cell type $j$) is given a prior $Z_{gj} \sim \mathcal{N}(\mu_j, \Sigma_j)$, where $(\mu_j, \Sigma_j)$ are derived from reference single-cell data. Bayesian inference is performed using MCMC, and priors are dynamically refined via posterior empirical moments (Xu et al., 8 Nov 2025).
• Posterior Representation: Each step outputs $\mathbb{E}[Z_{gj}|X]$ (mean) and $\mathrm{Var}[Z_{gj}|X]$ (variance), which are propagated through the classification and language-generation pipelines.
• Bayesian Proposal-Reweighting: In NL-Bayes, hypotheses $h$ (in natural language) are sampled, reweighted via $P_{\rm prior}(h) \times P_{\rm likelihood}(D|h)$, and normalized to represent the learner’s posterior (Ellis, 2023).
• Message Passing in Language: vPGM formalizes this as $$\mathbb{E}_{P(Z|X)}[P(Y|Z)] = \sum_{Z} P(Y|Z)P(Z|X)$$, with $P(Z|X)$ and $P(Y|Z)$ calculated by sequential LLM reasoning steps (Huang et al., 8 Jun 2024).

This modularization makes it possible to inspect priors, likelihoods, and posterior predictions separately and track how uncertainty and evidence are transformed through each component.

3. Interpretability Mechanisms and Reporting

The central interpretability features in HIBLMs are as follows:

• Feature Attribution: DiagnoLLM integrates Integrated Gradients to attribute classification decisions to specific molecular or clinical features, which are then included in LLM-generated reports (Xu et al., 8 Nov 2025).
• Posterior Uncertainty Propagation: Variances on deconvolved features and classifier softmax probabilities are explicitly surfaced to downstream reporting modules, allowing statements such as “We are 95% confident that microglial IL1B is elevated.”
• Prompted Narrative Synthesis: LLMs are not end-to-end predictors, but serve as post-hoc reasoners: they ingest structured outputs (label, confidence, top feature attributions, key priors) and generate tailored rationales, contrasting technical clinician reports with accessible patient summaries (Xu et al., 8 Nov 2025).

vPGM and related models similarly express the reasoning path as a chain-of-thought over latent variables, with each CPD verbalized, allowing human scrutiny of where uncertainty or evidence originates (Huang et al., 8 Jun 2024).

The bounded pragmatic speaker paradigm adds a further interpretable dimension by framing every model output as the result of a prior (base speaker) and a “listener”/utility (e.g., RL reward or explicit pragmatic score), both of which can be queried and visualized (Nguyen, 2023). This modularity enables direct inspection of beliefs and rationale behind each utterance.

4. Applications and Empirical Performance

Human-interpretable Bayesian LLMs have demonstrated utility in disease diagnosis, human-like concept learning, compositional reasoning tasks, and open-ended coaching scenarios.

• Disease Diagnosis: DiagnoLLM achieves 88% accuracy and F1≈0.86 in Alzheimer’s Disease detection on the ROSMAP cohort, with single-cell deconvolution outperforming prior art by 37–54% Pearson $r$ for marker genes (Xu et al., 8 Nov 2025).
• Few-Shot Concept Learning: NL-Bayes attains $R^2\approx0.89$ with human numerical concept learning judgements, closely matching subject-level accuracy and outperforming end-to-end LMs. On logical concept learning, it achieves $R^2\approx0.81$ and 90% accuracy, approaching human baseline (Ellis, 2023).
• Compositional QA and Coaching: vPGM yields 82.01% accuracy and ECE=3.58% (95% relative reduction vs standard CoT) on ScienceQA, with human-evaluated interpretability and clarity superior to prior chain-of-thought models (Huang et al., 8 Jun 2024).

Empirical results consistently show that uncertainty propagation, modular prior/likelihood reporting, and narrative explanation (clinician/patient, expert/layperson) are feasible and produce actionable and accurate guidance in both structured and freeform domains.

5. Comparative Approaches and Limitations

Comparative evaluations reveal strengths and challenges of HIBLMs versus both end-to-end neural models and classical program induction methods:

Model	Interpretability Level	Calibration	Domain Flexibility
DiagnoLLM	High (modular, narrative)	Calibrated (posterior variance, softmax)	Biomedical, omics-diagnosis
vPGM	High (latent structure, stepwise justification)	Near-perfect (ECE < 4%)	Reasoning, QA, medical coaching
NL-Bayes	Explicit (NL hypotheses, feature-level weights)	$R^2$ ≈ 0.9	Human concept learning
Monolithic LM	Opaque	Poor	Task-specific
Classical BPL	Explicit (logic/prog)	Moderate	Small domains

Major limitations remain. RLHF-based bounded pragmatic speakers capture only single reward directions, lack full counterfactual or intention coverage, and are bottlenecked by scalar feedback (Nguyen, 2023). NL-Bayes accuracy declines when proposal distributions are not well-conditioned on input (Ellis, 2023). DiagnoLLM’s LLM-generated narratives, while interpretable, may have inconsistency between attribution and story coherence in edge cases (Xu et al., 8 Nov 2025).

6. Extensions, Generalization, and Future Directions

Emerging directions in HIBLM research include:

• Structured Listener Models: Expanding single-dimension reward or utility to multi-dimensional listener distributions (e.g., faithfulness, completeness, style), enabling richer factorizations and interpretability in speaker–listener settings (Nguyen, 2023).
• Explicit World Modeling: Replacing reward proxies with model-based utility grounded in probabilistic simulation of downstream effects (Nguyen, 2023).
• Marginalization via Prompt Aggregation: Systematically sampling multiple chain-of-thoughts or latent variable paths and averaging predictions, as in vPGM, to achieve true Bayesian confidence calibration (Huang et al., 8 Jun 2024).
• Domain Adaptation: Iterative refinement of priors to handle domain or cohort shift, as in MCMC prior re-estimation in DiagnoLLM (Xu et al., 8 Nov 2025).
• Rich Feedback Channels: Leveraging structured examples or counterfactual training pairs to speed up amortized inference and enhance model transparency.

A plausible implication is that combining modular probabilistic formalisms with LLM-based language interfaces creates a scalable pathway for deploying interpretable Bayesian reasoning in diverse domains, spanning biomedicine, scientific QA, and human-comparable concept induction. The critical research frontier is ensuring that explanations, uncertainty communication, and modular exposure keep pace with escalating model and task complexity.