Trilemma Of Truth Eval

trilemma-of-truth-eval

The Trilemma of Truth in Large Language Models — Savcisens et al. (2025) (arXiv:2506.23921, 2025)

What this evaluates

Evaluates large language models' ability to distinguish factually true statements from factually false and unverifiable ('neither') statements. It probes both prompt-based output probabilities and internal hidden activations to measure veracity classification accuracy and uncertainty quantification.

Datasets

• Trilemma of Truth Datasets — total 22275; splits: test (-1); HF carlomarxx/trilemma-of-truth; repo https://github.com/carlomarxdk/trilemma-of-truth

Metrics

• MCC (primary) — range: [-1, 1]
  • Matthew’s Correlation Coefficient for multiclass classification: MCC = (cs - Σ(pktk)) / sqrt((s^2 - Σpk^2) * (s^2 - Σtk^2)), where c is correct predictions, s is total samples, pk and tk are predicted and true class counts.
• W-MCC — range: [-1, 1]
  • Weighted-MCC adjusts MCC by the acceptance rate to penalize excessive abstentions: W-MCC = MCC * (1 - (#abstained / #total_predictions)).

Input / output format

Input: Instruction prompt concatenated with a statement (e.g., 'The city of X is located in Y.') for zero-shot evaluation; or token-level hidden activations from the LLM for probing methods.

Output: For zero-shot: token probabilities mapped to veracity labels {true, false, neither, abstain}. For probes: predicted veracity label {true, false, neither}.

Scoring recipe

import math
def compute_mcc(preds, gold):
    c = sum(p == g for p, g in zip(preds, gold))
    s = len(gold)
    pk = [sum(p == k for p in preds) for k in ['true','false','neither']]
    tk = [sum(g == k for g in gold) for k in ['true','false','neither']]
    num = c*s - sum(p*t for p,t in zip(pk,tk))
    den = math.sqrt((s**2 - sum(p**2 for p in pk)) * (s**2 - sum(t**2 for t in tk)))
    return num/den if den > 0 else 0.0

def compute_w_mcc(preds, gold, abstained_count):
    mcc = compute_mcc(preds, gold)
    total = len(preds)
    return mcc * (1 - abstained_count / total)

Common pitfalls

• Treating 'neither' statements as false; they are synthetically generated unverifiable claims and must be classified as a separate class.
• Reporting standard MCC when probes abstain; the protocol requires Weighted-MCC (W-MCC) to penalize high abstention rates.
• Assuming linear probes capture veracity symmetrically; the paper notes asymmetry between truth/false signals and that nonlinear probes are necessary for RLHF-distilled models.

Evidence (verbatim from paper)

We use Matthew’s Correlation Coefficient (MCC) to summarize the statistical accuracy of probes. The multiclass MCC value is calculated using Eq.[14]. where c is the number of correct predictions, s is the total number of samples, K is the total number of classes, t_k is the number of k-class samples in the data set, and p_k is the number of times k-class was predicted. MCC = 1 indicates that a classifier predicted every instance correctly. MCC = 0 implies that the predictions are random. MCC = -1 indicates that the predictions are inversely correlated with the ground-truth labels. Zero-shot prompting, one-vs-all sAwMIL, and multiclass sAwMIL can abstain from making predictions. If a probe abstains too often, it suggests poor performance. For these cases, we use Weighted-MCC (W-MCC), where the acceptance rate serves as the weight (see Eq.[15]).

Citation

@misc{savcisens2025trilemma,
  title={The Trilemma of Truth in Large Language Models},
  author={Savcisens et al. (2025)},
  year={2025},
  note={arXiv:2506.23921}
}

• arXiv: 2506.23921