From Token Probabilities to Semantic Constraints: Towards Declarative Probabilistic Evaluation of Language Models

Kyle Richardson; Cullen Anderson; Pranav Balakrishnan; Takuto Ban; Daksha Ladia; Ankita Gupta; Marisa Hudspeth

cs.CLSep 11, 2026

From Token Probabilities to Semantic Constraints: Towards Declarative Probabilistic Evaluation of Language Models

Authors: Kyle Richardson, Cullen Anderson, Pranav Balakrishnan, Takuto Ban, Daksha Ladia, Ankita Gupta, Marisa Hudspeth

Organizations: Allen Institute for AI · University of Massachusetts Amherst

Abstract

While Large Language Models have improved rapidly, many fundamental questions remain about how to evaluate the knowledge and reasoning abilities they acquire, and how such evaluations relate to the learning signals used in pre-training. In this paper, we propose ModelLog, a declarative probabilistic framework for pre-training evaluation that makes the semantic structure of model behavior explicit and provides new formal tools for relating evaluation to learning. ModelLog specifies evaluation targets as symbolic constraints over token-level predictions and measures how strongly a model's distribution satisfies those constraints. We explore the framework through a new suite of tasks targeting negation, mutual exclusivity, and consistency, finding systematic failures that are difficult to characterize through token likelihood or answer accuracy alone. We further show that these evaluation scores can also be interpreted as losses, whose gradients reflect logical strength, informativeness, and variable-level sensitivity. This links evaluation and learning through a shared semantics, suggesting evaluation methods that diagnose model behavior while also helping to clarify the semantic structure of learning.

Figures & tables

Panel of Figure 1 — Figure 1: An illustration of our evaluation framework ModelLog that maps local next-token predictions from a pre-trained language model ( A ) into propositional variables $\mathcal{M}(\cdot)$ denoting prediction events. Symbolic constraints over these variables ( B ) specify the local semantic relations that should hold among them. Evaluation then becomes probabilistic inference over constraints ( C ): model token probabilities $\mathbb{P}_{\mathcal{M}_{\theta}}(\cdot)$ provide weights over assignments $\mathbb{P}(\mathcal{M}(\cdot))$ , satisfaction or marginal probability measures how strongly the model supports the desired semantic structure, and the gradients of such inferences provide a direct link to learning.

Panel of Figure 2 — Figure 2: Given token predictions ( A ) and a constraint $\mathsf{F}$ over those predictions ( B ), evaluation reduces to weighted model counting ( WMC ) over interpretations $I_{i}$ of $F$ ( C ), weighted by model-induced probabilities from $\mathcal{M}_{\theta}$ ( D ). To make satisfaction scores interpretable, we also compare against an uninformed prior ( E ), which performs weighted model counting under uniform weights, yielding $\textbf{WMC}_{0}(\text{{\color[rgb]{0,0,1}$ \mathsf{F} $}})$ .

Task Subset	Constraint $\mathsf{F}$	$I(\text{{\color[rgb]{0,0,1}$ \mathsf{F} $}})\approx$	Example
Transitivity	$(\mathcal{M}(x_{1},\hbox{\pagecolor{red!50}\color[rgb]{1,1,1}$ y_{1} $})\land\mathcal{M}(x_{2},\hbox{\pagecolor{blue!50}\color[rgb]{1,1,1}$ y_{2} $}))$ $\text{{\color[rgb]{0.66,0.13,0.24}$ \to $}}\mathcal{M}(x_{1},\hbox{\pagecolor{blue!50}\color[rgb]{1,1,1}$ y_{2} $})$	0.193	A Golden Retriever is a dog $\land$ Every dog is a mammal $\to$ A Golden Retriever is a mammal
Forward Implication	$\mathcal{M}(x,\hbox{\pagecolor{red!50}\color[rgb]{1,1,1}$ y_{1} $})\text{{\color[rgb]{0.66,0.13,0.24}$ \to $}}\mathcal{M}(x,\hbox{\pagecolor{blue!50}\color[rgb]{1,1,1}$ y_{2} $})$	0.415	A Golden Retriever is a dog $\to$ A Golden Retriever is a mammal
Negation Consistency	$\mathcal{M}(x,\hbox{\pagecolor{red!50}\color[rgb]{1,1,1}$ y $})\oplus\mathcal{M}(\neg x,\hbox{\pagecolor{red!50}\color[rgb]{1,1,1}$ y $})$	1.0	A Golden Retriever is a dog $\oplus$ A Golden Retriever is not a dog
Entity Mutual Exclusivity	$\mathcal{M}(x,\hbox{\pagecolor{red!50}\color[rgb]{1,1,1}$ y_{1} $})\oplus\mathcal{M}(x,\hbox{\pagecolor{blue!50}\color[rgb]{1,1,1}$ y_{2} $})$	1.0	A Golden Retriever is a mammal $\oplus$ A Golden Retriever is a reptile
Spatial Mutual Exclusivity		1.0	Paris is in Germany $\oplus$ Paris is in France

Table 1: A description of the ProbCT diagnostic benchmark in terms of its five task subsets , the structure of the constraints

\mathsf{F}

being tested with their informativeness

I(\text{{\color[rgb]{0,0,1}

\mathsf{F}

}})

and an example set of prefixes.

Model	Transitivity	Forward Implication	Neg. Consistency	Mutual Exclusivity	Spatial Exclusivity
Gemma-3-270M	$\mathbf{81.0}(\pm{\color[rgb]{0.5,0.5,0.5}2.3})$	$79.7(\pm{\color[rgb]{0.5,0.5,0.5}0.5})$	$18.5(\pm{\color[rgb]{0.5,0.5,0.5}1.4})$	$48.7(\pm{\color[rgb]{0.5,0.5,0.5}0.8})$	$18.5(\pm{\color[rgb]{0.5,0.5,0.5}4.8})$
Gemma-3-1B-pt	$69.0(\pm{\color[rgb]{0.5,0.5,0.5}1.5})$	$65.1(\pm{\color[rgb]{0.5,0.5,0.5}1.5})$	$15.9(\pm{\color[rgb]{0.5,0.5,0.5}0.8})$	$57.3(\pm{\color[rgb]{0.5,0.5,0.5}3.9})$	$12.4(\pm{\color[rgb]{0.5,0.5,0.5}4.8})$
Gemma-3-4B-pt	$46.9(\pm{\color[rgb]{0.5,0.5,0.5}1.1})$	$50.8(\pm{\color[rgb]{0.5,0.5,0.5}1.7})$	$18.2(\pm{\color[rgb]{0.5,0.5,0.5}0.9})$	$56.8(\pm{\color[rgb]{0.5,0.5,0.5}5.2})$	$19.9(\pm{\color[rgb]{0.5,0.5,0.5}6.6})$
Gemma-3-12B-pt	$40.4(\pm{\color[rgb]{0.5,0.5,0.5}1.6})$	$45.2(\pm{\color[rgb]{0.5,0.5,0.5}2.0})$	$19.2(\pm{\color[rgb]{0.5,0.5,0.5}0.9})$	$54.7(\pm{\color[rgb]{0.5,0.5,0.5}5.4})$	$23.8(\pm{\color[rgb]{0.5,0.5,0.5}7.7})$
Llama-3.2-1B	$52.7(\pm{\color[rgb]{0.5,0.5,0.5}2.4})$	$68.7(\pm{\color[rgb]{0.5,0.5,0.5}1.8})$	$\mathbf{23.1}(\pm{\color[rgb]{0.5,0.5,0.5}2.1})$	$64.0(\pm{\color[rgb]{0.5,0.5,0.5}3.8})$	$\mathbf{31.5}(\pm{\color[rgb]{0.5,0.5,0.5}7.4})$
Llama-3.2-3B	$45.5(\pm{\color[rgb]{0.5,0.5,0.5}1.3})$	$60.8(\pm{\color[rgb]{0.5,0.5,0.5}2.1})$	$21.6(\pm{\color[rgb]{0.5,0.5,0.5}2.6})$	$61.6(\pm{\color[rgb]{0.5,0.5,0.5}6.0})$	$25.3(\pm{\color[rgb]{0.5,0.5,0.5}6.9})$

Table 2: Main results ( CAcc %) across the different reasoning tasks in ProbCT and model families, averaged over different nucleus values

p\in\{0.8,0.85,0.9,0.95\}

used for calibration.

Panel of Figure 3 — Figure 3: Probabilistic Consistency score histograms $\rho(\cdot,\theta_{C})$ for our largest models in each model family, using nucleus value $p=0.95$ . Points highlighted in red are inconsistent, while points highlighted in blue are consistent. The solid vertical black line corresponds to the average probabilistic consistency (see also § F ).

Model	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{2}){-}\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{1})$	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{2}{>}\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{1})$	CAcc
Gemma-3-270M	$0.17$	$64.7$	$75.4$
Gemma-3-1B-pt	$-0.02$	$49.5$	$57.8$
Gemma-3-4B-pt	$-0.19$	$34.7$	$44.1$
Gemma-3-12B-pt	$-0.24$	$30.1$	$38.3$

Table 3: Inverse-scaling ( McKenzie et al., 2023 ) behavior for the forward implication:

\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1}\text{{\color[rgb]{0.66,0.13,0.24}

\to

}}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2}

for Gemma-3 .

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2}){-}\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})

is the mean difference between conclusion and premise probabilities.

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2}{>}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})

is the percentage of points where

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2})>\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})

. See § C for similar patterns across our full set of models.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Constraint	Raw	Filtered	Gemma-3	Llama-3	Qwen3
Forward Implication	2,000	1,049	514	369	369
Transitivity	2,000	1,091	486	307	307
Mutual Exclusivity	2,000	1,468	975	781	781
Negation Consistency	2,000	956	956	856	856
Spatial Exclusivity	2,000	915	897	739	739

Appendix

Table 4: Dataset sizes at each filtering stage. Raw : initial generated examples. Filtered : after LLM-as-judge filtering. Gemma-3 , Llama-3 , Qwen3 : remaining examples after removing multi-token prediction events per model family.

Dataset	Human Accept	LLM Accept	Ann1 Precision	Ann2 Precision
Forward Implication	0.78	0.44	0.91	0.95
Mutual Exclusivity	0.84	0.76	0.95	0.97
Negation	0.62	0.46	0.96	0.96
Spatial Mutex	0.46	0.50	0.88	0.92
Transitivity	0.86	0.56	1.00	1.00

Appendix

Table 5: Human validation of the KB to LLM filtering pipeline on

n=50

sampled examples per dataset. Human Accept is the fraction accepted by both annotators. LLM Accept is the fraction accepted by GPT-5o-mini . Ann1 Precision and Ann2 Precision give the fraction of LLM-accepted items each annotator independently judged correct i.e., the LLM filter’s precision as measured by each annotator.

Model	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{1})$	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{2})$	$\Delta$	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{2}{>}\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{1})$	CAcc
Gemma-3-270M	$0.53(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.70(\pm{\color[rgb]{0.5,0.5,0.5}0.02})$	$0.17(\pm{\color[rgb]{0.5,0.5,0.5}0.01})$	$64.7(\pm{\color[rgb]{0.5,0.5,0.5}0.2})$	$75.4(\pm{\color[rgb]{0.5,0.5,0.5}1.2})$
Gemma-3-1B-pt	$0.60(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.58(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.02(\pm{\color[rgb]{0.5,0.5,0.5}0.00})$	$49.5(\pm{\color[rgb]{0.5,0.5,0.5}0.6})$	$57.8(\pm{\color[rgb]{0.5,0.5,0.5}3.3})$
Gemma-3-4B-pt	$0.69(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.50(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.19(\pm{\color[rgb]{0.5,0.5,0.5}0.00})$	$34.7(\pm{\color[rgb]{0.5,0.5,0.5}0.4})$	$44.1(\pm{\color[rgb]{0.5,0.5,0.5}3.4})$
Gemma-3-12B-pt	$0.70(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.45(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.24(\pm{\color[rgb]{0.5,0.5,0.5}0.01})$	$30.1(\pm{\color[rgb]{0.5,0.5,0.5}0.5})$	$38.3(\pm{\color[rgb]{0.5,0.5,0.5}4.3})$
Llama-3.2-1B	$0.73(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.66(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.06(\pm{\color[rgb]{0.5,0.5,0.5}0.01})$	$45.2(\pm{\color[rgb]{0.5,0.5,0.5}0.8})$	$64.3(\pm{\color[rgb]{0.5,0.5,0.5}2.8})$
Llama-3.2-3B	$0.67(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.57(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.10(\pm{\color[rgb]{0.5,0.5,0.5}0.00})$	$41.5(\pm{\color[rgb]{0.5,0.5,0.5}0.7})$	$54.5(\pm{\color[rgb]{0.5,0.5,0.5}3.7})$

Appendix

Table 6: Inverse scaling analysis for the forward implication

\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1}\text{{\color[rgb]{0.66,0.13,0.24}

\to

}}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2}

across all model families.

\Delta

is shorthand for

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2}){-}\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})

, the mean difference between conclusion and premise probabilities.

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2}{>}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})

is the percentage of points where

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2})>\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})

. Calibration is done using nucleus entropy averaged over nucelus values

p\in\{0.80,0.85,0.90,0.95\}

Model	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{1})$	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{2})$	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{3})$	$\Delta$	$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{3}{>}\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{1}\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{2})$	CAcc
Gemma-3-270M	$0.48(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.64(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.64(\pm{\color[rgb]{0.5,0.5,0.5}0.02})$	$0.34(\pm{\color[rgb]{0.5,0.5,0.5}0.02})$	$82.7(\pm{\color[rgb]{0.5,0.5,0.5}1.8})$	$77.6(\pm{\color[rgb]{0.5,0.5,0.5}1.8})$
Gemma-3-1B-pt	$0.55(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.61(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.52(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.20(\pm{\color[rgb]{0.5,0.5,0.5}0.02})$	$68.5(\pm{\color[rgb]{0.5,0.5,0.5}0.7})$	$64.6(\pm{\color[rgb]{0.5,0.5,0.5}0.4})$
Gemma-3-4B-pt	$0.65(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.71(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.45(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.01(\pm{\color[rgb]{0.5,0.5,0.5}0.01})$	$48.5(\pm{\color[rgb]{0.5,0.5,0.5}0.2})$	$42.6(\pm{\color[rgb]{0.5,0.5,0.5}0.3})$
Gemma-3-12B-pt	$0.64(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.72(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.40(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.05(\pm{\color[rgb]{0.5,0.5,0.5}0.02})$	$42.3(\pm{\color[rgb]{0.5,0.5,0.5}0.5})$	$36.0(\pm{\color[rgb]{0.5,0.5,0.5}0.5})$
Llama-3.2-1B	$0.65(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.84(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.58(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.02(\pm{\color[rgb]{0.5,0.5,0.5}0.01})$	$54.0(\pm{\color[rgb]{0.5,0.5,0.5}0.6})$	$51.3(\pm{\color[rgb]{0.5,0.5,0.5}2.6})$
Llama-3.2-3B	$0.60(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$0.82(\pm{\color[rgb]{0.5,0.5,0.5}0.03})$	$0.47(\pm{\color[rgb]{0.5,0.5,0.5}0.04})$	$-0.02(\pm{\color[rgb]{0.5,0.5,0.5}0.02})$	$47.2(\pm{\color[rgb]{0.5,0.5,0.5}0.4})$	$43.5(\pm{\color[rgb]{0.5,0.5,0.5}1.7})$

Appendix

Table 7: Inverse scaling analysis for transitivity

(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1}\text{{\color[rgb]{0.66,0.13,0.24}

\land

}}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2})\text{{\color[rgb]{0.66,0.13,0.24}

\to

}}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{3}

, across all model families.

\Delta

is shorthand for

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{3}){-}\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2})

, the mean gap between the conclusion probability and the product of premise probabilities.

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{3}{>}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1}\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2})

is the percentage of points where

\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{3})>\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1})\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2})

. Calibration is done using nucleus entropy averaged over nucleus values

p\in\{0.80,0.85,0.90,0.95\}

			$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{1})$		$\mathbb{P}_{\theta_{C}}(\text{{\color[rgb]{0,0,1}$ \mathsf{P} $}}_{2})$		$\rho$
Prefix	$a$	$b$	270M	12B	270M	12B	270M	12B
Ctenocephalides Felis is a type of …	flea	insect	$0.07$	$0.83$	$0.78$	$0.03$	$0.94$	$-2.21$
Satsuma is a type of …	mandarin	fruit	$0.03$	$0.62$	$0.76$	$0.12$	$0.97$	$-1.17$
Hesperocyparis Goveniana is a type of …	cypress	tree	$0.07$	$0.84$	$0.89$	$0.45$	$0.97$	$-0.85$
Arbalest is a type of …	crossbow	weapon	$0.13$	$0.89$	$0.51$	$0.55$	$0.76$	$-0.59$
Pannier is a type of …	bag	container	$0.20$	$0.83$	$0.58$	$0.32$	$0.67$	$-1.26$

Appendix

Table 8: Examples of inverse scaling for forward implication, comparing Gemma-3-270M and Gemma-3-12B using nucleus entropy with nucleus value

p=0.95

. Each row defines

\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{1}=\mathcal{M}(\text{Prefix},a)

and

\text{{\color[rgb]{0,0,1}

\mathsf{P}

}}_{2}=\mathcal{M}(\text{Prefix},b)

, where

a

and

b

are the premise and conclusion completions respectively.

Model	Transitivity	Forward Implication	Neg. Consistency	Mutual Exclusivity	Spatial Exclusivity
Gemma-3-270M	$40.8(\pm{\color[rgb]{0.5,0.5,0.5}6.9})$	$39.5(\pm{\color[rgb]{0.5,0.5,0.5}5.8})$	$7.5(\pm{\color[rgb]{0.5,0.5,0.5}0.4})$	$64.1(\pm{\color[rgb]{0.5,0.5,0.5}0.2})$	$32.6(\pm{\color[rgb]{0.5,0.5,0.5}5.3})$
Gemma-3-1B-pt	$39.0(\pm{\color[rgb]{0.5,0.5,0.5}7.2})$	$40.0(\pm{\color[rgb]{0.5,0.5,0.5}6.7})$	$10.8(\pm{\color[rgb]{0.5,0.5,0.5}0.9})$	$71.1(\pm{\color[rgb]{0.5,0.5,0.5}2.6})$	$28.8(\pm{\color[rgb]{0.5,0.5,0.5}5.0})$
Gemma-3-4B-pt	$47.5(\pm{\color[rgb]{0.5,0.5,0.5}5.6})$	$42.9(\pm{\color[rgb]{0.5,0.5,0.5}6.5})$	$17.0(\pm{\color[rgb]{0.5,0.5,0.5}1.4})$	$73.9(\pm{\color[rgb]{0.5,0.5,0.5}4.0})$	$41.4(\pm{\color[rgb]{0.5,0.5,0.5}6.9})$
Gemma-3-12B-pt	$45.1(\pm{\color[rgb]{0.5,0.5,0.5}7.9})$	$40.7(\pm{\color[rgb]{0.5,0.5,0.5}6.7})$	$13.9(\pm{\color[rgb]{0.5,0.5,0.5}0.9})$	$74.9(\pm{\color[rgb]{0.5,0.5,0.5}4.0})$	$48.7(\pm{\color[rgb]{0.5,0.5,0.5}7.9})$
Llama-3.2-1B	$64.5(\pm{\color[rgb]{0.5,0.5,0.5}4.3})$	$\mathbf{60.8(\pm{\color[rgb]{0.5,0.5,0.5}5.3})}$	$15.9(\pm{\color[rgb]{0.5,0.5,0.5}1.3})$	$79.7(\pm{\color[rgb]{0.5,0.5,0.5}3.6})$	$\mathbf{52.9(\pm{\color[rgb]{0.5,0.5,0.5}6.4})}$
Llama-3.2-3B	$53.4(\pm{\color[rgb]{0.5,0.5,0.5}7.9})$	$45.9(\pm{\color[rgb]{0.5,0.5,0.5}8.0})$	$13.6(\pm{\color[rgb]{0.5,0.5,0.5}1.8})$	$79.0(\pm{\color[rgb]{0.5,0.5,0.5}4.0})$	$49.3(\pm{\color[rgb]{0.5,0.5,0.5}6.6})$

Appendix

Table 9: Enforcing Factuality: CAcc (%) over conjunction of true statements using nucleus entropy calibration averaged over

p\in\{0.8,0.85,0.9,0.95\}

Model	Transitivity	Forward Implication	Neg. Consistency	Mutual Exclusivity	Spatial Exclusivity
Gemma-3-270M	$\mathbf{81.0}(\pm{\color[rgb]{0.5,0.5,0.5}2.3})$	$79.7(\pm{\color[rgb]{0.5,0.5,0.5}0.5})$	$18.5(\pm{\color[rgb]{0.5,0.5,0.5}1.4})$	$48.7(\pm{\color[rgb]{0.5,0.5,0.5}0.8})$	$18.5(\pm{\color[rgb]{0.5,0.5,0.5}4.8})$
Gemma-3-1B-pt	$69.0(\pm{\color[rgb]{0.5,0.5,0.5}1.5})$	$65.1(\pm{\color[rgb]{0.5,0.5,0.5}1.5})$	$15.9(\pm{\color[rgb]{0.5,0.5,0.5}0.8})$	$57.3(\pm{\color[rgb]{0.5,0.5,0.5}3.9})$	$12.4(\pm{\color[rgb]{0.5,0.5,0.5}4.8})$
Gemma-3-4B-pt	$46.9(\pm{\color[rgb]{0.5,0.5,0.5}1.1})$	$50.8(\pm{\color[rgb]{0.5,0.5,0.5}1.7})$	$18.2(\pm{\color[rgb]{0.5,0.5,0.5}0.9})$	$56.8(\pm{\color[rgb]{0.5,0.5,0.5}5.2})$	$19.9(\pm{\color[rgb]{0.5,0.5,0.5}6.6})$
Gemma-3-12B-pt	$40.4(\pm{\color[rgb]{0.5,0.5,0.5}1.6})$	$45.2(\pm{\color[rgb]{0.5,0.5,0.5}2.0})$	$19.2(\pm{\color[rgb]{0.5,0.5,0.5}0.9})$	$54.7(\pm{\color[rgb]{0.5,0.5,0.5}5.4})$	$23.8(\pm{\color[rgb]{0.5,0.5,0.5}7.7})$
Llama-3.2-1B	$52.7(\pm{\color[rgb]{0.5,0.5,0.5}2.4})$	$68.7(\pm{\color[rgb]{0.5,0.5,0.5}1.8})$	$\mathbf{23.1}(\pm{\color[rgb]{0.5,0.5,0.5}2.1})$	$64.0(\pm{\color[rgb]{0.5,0.5,0.5}3.8})$	$\mathbf{31.5}(\pm{\color[rgb]{0.5,0.5,0.5}7.4})$
Llama-3.2-3B	$45.5(\pm{\color[rgb]{0.5,0.5,0.5}1.3})$	$60.8(\pm{\color[rgb]{0.5,0.5,0.5}2.1})$	$21.6(\pm{\color[rgb]{0.5,0.5,0.5}2.6})$	$61.6(\pm{\color[rgb]{0.5,0.5,0.5}6.0})$	$25.3(\pm{\color[rgb]{0.5,0.5,0.5}6.9})$

Appendix

Table 10: CAcc (%) using nucleus entropy calibration averaged over nucleus values

p\in\{0.8,0.85,0.9,0.95\}

. Reproduced from Table 2 for ease of comparison with the alternative calibrations in Tables 11 and 12

Model	Transitivity	Forward Implication	Neg. Consistency	Mutual Exclusivity	Spatial Exclusivity
Gemma-3-270M	$79.2$	$81.5$	$\mathbf{20.9}$	$47.5$	$31.4$
Gemma-3-1B-pt	$65.2$	$68.9$	$18.3$	$65.5$	$26.5$
Gemma-3-4B-pt	$48.1$	$56.8$	$17.9$	$68.8$	$37.0$
Gemma-3-12B-pt	$40.5$	$52.1$	$18.3$	$72.0$	$44.4$
Llama-3.2-1B	$58.3$	$75.6$	$17.6$	$72.6$	$\mathbf{50.9}$
Llama-3.2-3B	$50.8$	$66.1$	$16.1$	$74.9$	$45.5$

Appendix

Table 11: CAcc (%) using entropy calibration.

Model	Transitivity	Forward Implication	Neg. Consistency	Mutual Exclusivity	Spatial Exclusivity
Gemma-3-270M	$77.8(\pm{\color[rgb]{0.5,0.5,0.5}1.5})$	$83.7(\pm{\color[rgb]{0.5,0.5,0.5}2.2})$	$17.0(\pm{\color[rgb]{0.5,0.5,0.5}3.3})$	$42.2(\pm{\color[rgb]{0.5,0.5,0.5}5.7})$	$55.3(\pm{\color[rgb]{0.5,0.5,0.5}13.1})$
Gemma-3-1B-pt	$68.0(\pm{\color[rgb]{0.5,0.5,0.5}3.6})$	$74.2(\pm{\color[rgb]{0.5,0.5,0.5}5.8})$	$\mathbf{17.4(\pm{\color[rgb]{0.5,0.5,0.5}2.4})}$	$63.4(\pm{\color[rgb]{0.5,0.5,0.5}1.4})$	$42.9(\pm{\color[rgb]{0.5,0.5,0.5}15.0})$
Gemma-3-4B-pt	$53.2(\pm{\color[rgb]{0.5,0.5,0.5}7.4})$	$63.7(\pm{\color[rgb]{0.5,0.5,0.5}7.7})$	$15.4(\pm{\color[rgb]{0.5,0.5,0.5}3.5})$	$72.2(\pm{\color[rgb]{0.5,0.5,0.5}4.7})$	$52.9(\pm{\color[rgb]{0.5,0.5,0.5}16.5})$
Gemma-3-12B-pt	$45.4(\pm{\color[rgb]{0.5,0.5,0.5}7.7})$	$56.5(\pm{\color[rgb]{0.5,0.5,0.5}8.2})$	$17.2(\pm{\color[rgb]{0.5,0.5,0.5}2.3})$	$71.8(\pm{\color[rgb]{0.5,0.5,0.5}6.2})$	$59.4(\pm{\color[rgb]{0.5,0.5,0.5}17.1})$
Llama-3.2-1B	$68.6(\pm{\color[rgb]{0.5,0.5,0.5}8.5})$	$82.0(\pm{\color[rgb]{0.5,0.5,0.5}5.6})$	$11.6(\pm{\color[rgb]{0.5,0.5,0.5}4.9})$	$70.1(\pm{\color[rgb]{0.5,0.5,0.5}1.5})$	$\mathbf{68.6(\pm{\color[rgb]{0.5,0.5,0.5}12.9})}$
Llama-3.2-3B	$56.0(\pm{\color[rgb]{0.5,0.5,0.5}7.8})$	$73.6(\pm{\color[rgb]{0.5,0.5,0.5}6.7})$	$12.3(\pm{\color[rgb]{0.5,0.5,0.5}3.9})$	$76.4(\pm{\color[rgb]{0.5,0.5,0.5}4.3})$	$59.5(\pm{\color[rgb]{0.5,0.5,0.5}14.7})$

Appendix

Table 12: CAcc (%) using nucleus calibration averaged over nucleus values

p\in\{0.8,0.85,0.9,0.95\}

Constraint-Guided Reasoning in Language Models

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Evaluation Awareness in Language Models: Representation, Verbalization, and Control
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Evaluation Awareness in Language Models: Representation, Verbalization, and Control

Farzaneh Heidari, Amin Memarian, Guillaume Rabusseau

Mila – Quebec AI Institute · DIRO, Université de Montréal · CIFAR AI Chair

Evaluation Awareness in Language Models LLM Interpretability

Open paper AskPDF arXiv

Both capability and safety benchmarks rest upon the assumption that the behavior of language models undergoing a test is informative about their behavior in deployment. This assumption can fail, should models infer that they are being evaluated and condition their response on such context. This hypothesis, termed ``evaluation awareness'', has been observed in frontier and open-weight language models alike. We provide a systematic study of this phenomenon, by probing for it across six language models (from four families and three sizes) and three metrics. More precisely, we examine whether (i) being under evaluation is linearly represented within the models' activations space, (ii) it is verbalized in their output tokens (as scored by an LLM-as-judge), and (iii) steering causally affects their behavior. For the open-checkpoint Olmo models, we further test these measures at every training stage. In doing so, we report that evaluation awareness is linearly decodable from the residual streams of every model (best AUROC

\geq 0.7

). By contrast, these representations align only in part with verbalization: their correlations and mutual information are nonzero in some settings, yet vary substantially across models, layers, and readout choices. Nevertheless, steering along probe-derived directions can shift the verbalization scores. Finally, a comparison across the Olmo checkpoints reveals that evaluation awareness is already present within base models, becomes amplified throughout the stages of supervised fine-tuning, and remains stable thereafter---unlike the effects of steering, that grow more pronounced at every successive training stage. These results show the need for evaluations to account for the disjunction between what models represent internally, what they verbalize, and their steering.

Abstract

Constraint-Guided Reasoning in Language Models

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