ppotash/latent-coherence

Latent Coherence

Do LLM probability judgments obey the law of total probability? This dataset tests whether a model's direct answer P(X) agrees with its own decomposition Σ P(z)·P(X|z), where the latent z must be inferred from records in the context. A causal family runs the same check on P(y | do(x)) against the back-door adjustment. Every query has an exact ground-truth probability, so coherence and accuracy can be measured separately.

• Paper: arxiv.org/abs/2610.31833
• Code, evaluation harness and results: github.com/ppotash/latent-coherence

Loading

from datasets import load_dataset

items = load_dataset("ppotash/latent-coherence", "items", split="synthetic")      # or split="hover"
prompts = load_dataset("ppotash/latent-coherence", "prompts", split="hover")

config	split	rows
items	synthetic	1,500
items	hover	1,698
prompts	synthetic	66,600
prompts	hover	103,842

Item families

family	records in context	latent z
source	reports on a claim from 1–3 sources, each with a track record	whether a source is careful or careless
diagnostic	a fault-diagnosis inspection log	which of three causes is present
causal	a count table over a confounder, a treatment and an outcome	back-door adjustment for P(y | do(x))
hover	a fictionalized multi-hop claim from HoVer, split into sub-claims reported by sources of varying reliability	truth of the bridge sub-claim; a source's kind

source, diagnostic and hover come at two spec_levels: full states every probability, and qualitative gives only verbal descriptions ("usually", "most sources are careful"). causal is full only.

Ground truth: exact enumeration (source, hover), naive Bayes (diagnostic), and empirical frequencies of the table, which is the whole population (causal). Items are filtered so that targets and latent probabilities lie in [0.1, 0.9] and the latent shifts the target by at least 0.10–0.15.

items fields

• id, family, spec_level, context
• prompt_prefix: the exact text before each question (instructions + context)
• queries: list of {qid, qtype, event, truth, given, questions}. questions lists the exact question texts as {framing, paraphrase, text}: three wordings (paraphrase 0–2) and, for conditional queries, two framings (learn: "Suppose you additionally learn, from a completely reliable check…", assume: "Assume hypothetically…"). Causal queries use fixed wordings (framing = "custom").
• identities: list of {name, kind, lhs, terms} that coherent answers satisfy:
  • total_probability: P(lhs) = Σ P(w)·P(c) over terms = [[w, c], ...]
  • normalization: Σ P(q) = 1 over terms = [[q], ...]
• similar_names: HoVer items whose invented names look alike (exclude them if you prefer)
• hover_uid, num_hops, original_claim: provenance of HoVer items (null otherwise)
• meta_json: generating parameters and other family-specific metadata, as JSON
• in_study, repeated_wordings: whether the item was selected for the published study, and whether it was asked in all three wordings there. In that study, all models but one answered only the first 5 selected items of each full-spec synthetic group (in item order), since models solve those essentially exactly.

prompts fields

One row per prompt: row_id, item_id, family, spec_level, qid, qtype, framing, paraphrase, system (system prompt), prompt (user message), truth, plus core, which marks the prompts used in the published study (the queries the main identities need, in the learn framing), and similar_names, in_study, repeated_wordings as above. Every query should be its own single-turn call, so no answer is visible to another query.

Scoring coherence

import math

def logit(p, eps=0.01):
    p = min(max(p, eps), 1 - eps)
    return math.log(p / (1 - p))

def residuals(item, answers):
    """answers: {qid: model probability} for one item (first wording)."""
    out = {}
    for idn in item["identities"]:
        if idn["kind"] != "total_probability":
            continue
        decomp = sum(answers[w] * answers[c] for w, c in idn["terms"])
        out[idn["name"]] = logit(answers[idn["lhs"]]) - logit(decomp)
    return out

The repository's lceval.py analyze adds the rest: separating persistent incoherence from rewording noise using the three wordings, bootstrap CIs, accuracy against truth, and paired model comparisons.

Construction and caveats

Synthetic items are generated by code. For HoVer, Gemini 3.8 Flash decomposed each claim into logically independent sub-claims and replaced every named entity with an invented name, a second Gemini pass audited the decomposition, and Claude cross-checked each accepted claim (849 of 908 passed). Truth values are then sampled from stated parameters, so HoVer items also have exact ground truth. A decomposition error would affect the ground truth of that item's target, but not coherence, which compares a model with itself.

License and attribution

CC BY-SA 4.0. The HoVer-derived items adapt claims from HoVer (Jiang et al., 2020), released under CC BY-SA 4.0.

Citation

@misc{potash2026latentcoherence,
  title         = {Latent Coherence: Do Frontier Language Models' Probability Judgments Obey the Law of Total Probability?},
  author        = {Potash, Peter},
  year          = {2026},
  eprint        = {2610.31833},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2610.31833}
}

@inproceedings{jiang2020hover,
  title     = {{HoVer}: A Dataset for Many-Hop Fact Extraction and Claim Verification},
  author    = {Jiang, Yichen and Bordia, Shikha and Zhong, Zheng and Dognin, Charles and Singh, Maneesh and Bansal, Mohit},
  booktitle = {Findings of the Association for Computational Linguistics: EMNLP 2020},
  year      = {2020}
}