Philipp Mondorf

Xinyuan Cheng, Beiduo Chen, Philipp Mondorf et al.

Large reasoning models (LRMs) often generate extensive chain-of-thought (CoT) traces before producing a final answer. As explicit textual artifacts, these traces can be passed to other models to solve the same task, enabling cross-model reasoning transfer. Yet successful transfer alone does not reveal how the provided CoT contributes to another model's answer. We study this question with a controlled provider--receiver framework, where a provider generates a reasoning trace and a receiver solves the same problem from increasingly longer trace prefixes. We compare force-answer, where the receiver answers directly from the prefix, with free-generation, where it may continue reasoning before answering. Across models and benchmarks, full traces often transfer successfully, but prefix trajectories reveal distinct mechanisms. In force-answer mode, AIME transfer is largely driven by explicit answer availability. MMLU-Pro instead reflects a larger role for receiver competence, while ZebraLogic depends on partial structured-answer information rather than complete-answer leakage alone. In free-generation mode, partial CoTs improve performance across benchmarks, indicating that prefixes can guide continued reasoning. Finally, answer agreement among receivers provides a gold-free signal for stopping provider reasoning early. Overall, cross-model CoT transfer is not a single phenomenon: it can reflect answer extraction, reasoning scaffolding, or receiver-dependent competence.

Brian Rabern, Philipp Mondorf, Barbara Plank

Large language models have demonstrated notable performance across various logical reasoning benchmarks. However, it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a unified benchmark designed to isolate three fundamental skills in formal reasoning: (i) $\textit{formal symbolization}\unicode{x2014}$translating premises into first-order logic; (ii) $\textit{countermodel construction}\unicode{x2014}$formulating a finite structure in which all premises are true while the conclusion is false; and (iii) $\textit{validity assessment}\unicode{x2014}$deciding whether a conclusion follows from a given set of premises. Items are drawn from the two-variable fragment of first-order logic (without identity) and are presented in both natural English and a Carroll-style language with nonce words. All examples are verified for correctness and non-triviality using the SMT solver Z3. Across leading models, performance is high on validity but substantially lower on symbolization and countermodel construction, suggesting reliance on surface-level patterns rather than genuine symbolic or rule-based reasoning.

Philipp Mondorf, Samuel J. Bell, Jesse Dodge et al.

As large language models (LLMs) are increasingly deployed to perform tasks with minimal human oversight, it is crucial that these models operate robustly. In particular, a model that can solve a given problem should not fail simply because certain entities$\unicode{x2013}$such as names, numbers, or other contextual details$\unicode{x2013}$have changed while the underlying problem logic remains the same. Prior work suggests that current LLMs still struggle with this form of robustness: they often succeed on some variations of a problem but fail on others. However, existing evaluations often lack a systematic way to identify which logic-preserving variations are most likely to induce failure. Instead, they typically test a random subset of allowable variations, which can overstate robustness. To address this gap, we introduce logic-preserving difficulty scaling (LPDS), a framework that (i) quantifies the difficulty of a problem variation and (ii) systematically searches the space of allowable variations to find those that maximize difficulty and expose failures. We show that as difficulty increases, performance declines and errors in the models' reasoning chains become more pronounced. We further demonstrate that LPDS efficiently finds difficult problem variations for a model, resulting in performance drops up to 5 times larger compared to random sampling. Finally, we show that fine-tuning on more difficult variations leads to more consistent robustness gains than training on easier ones.

Michal Štefánik, Timothee Mickus, Marek Kadlčík et al.

Recent work has shown that different large language models (LLMs) converge to similar and accurate input embedding representations for numbers. These findings conflict with the documented propensity of LLMs to produce erroneous outputs when dealing with numeric information. In this work, we aim to explain this conflict by exploring how language models manipulate numbers and quantify the lower bounds of accuracy of these mechanisms. We find that despite surfacing errors, different language models learn interchangeable representations of numbers that are systematic, highly accurate and universal across their hidden states and the types of input contexts. This allows us to create universal probes for each LLM and to trace information -- including the causes of output errors -- to specific layers. Our results lay a fundamental understanding of how pre-trained LLMs manipulate numbers and outline the potential of more accurate probing techniques in addressed refinements of LLMs' architectures.

Philipp Mondorf, Barbara Plank

Large language models (LLMs) have recently shown impressive performance on tasks involving reasoning, leading to a lively debate on whether these models possess reasoning capabilities similar to humans. However, despite these successes, the depth of LLMs' reasoning abilities remains uncertain. This uncertainty partly stems from the predominant focus on task performance, measured through shallow accuracy metrics, rather than a thorough investigation of the models' reasoning behavior. This paper seeks to address this gap by providing a comprehensive review of studies that go beyond task accuracy, offering deeper insights into the models' reasoning processes. Furthermore, we survey prevalent methodologies to evaluate the reasoning behavior of LLMs, emphasizing current trends and efforts towards more nuanced reasoning analyses. Our review suggests that LLMs tend to rely on surface-level patterns and correlations in their training data, rather than on sophisticated reasoning abilities. Additionally, we identify the need for further research that delineates the key differences between human and LLM-based reasoning. Through this survey, we aim to shed light on the complex reasoning processes within LLMs.

Nils Grünefeld, Bertram Højer, Philipp Mondorf et al.

Language model (LM) "reasoning", commonly described as Chain-of-Thought or test-time scaling, often improves benchmark performance, but the dynamics underlying this process remain poorly understood. We study these dynamics through the lens of uncertainty quantification by treating the "reasoning" traces, the intermediate token sequences generated by LMs, as evolving model states. We summarize each trace by an uncertainty trace profile: a small set of features describing the shape of the uncertainty signal over its trace, such as its slope and linearity. We find that across five LMs evaluated on GSM8K and ProntoQA, these profiles predict whether a trace yields a correct final answer with AUROC up to 0.807, improving markedly on recent related work. We reach AUROC 0.801 using only the first few hundred tokens of full traces, suggesting that errors can be detected early in the generation. A detailed comparison of correct and incorrect traces further reveals qualitatively distinct uncertainty profiles, with correct traces showing a steeper and less linear decline in uncertainty. Together, the results suggest that our method, grounded in decision-making under uncertainty, provides a principled lens for studying the generative process underlying LM "reasoning".

Philipp Mondorf, Barbara Plank

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like $\textit{supposition following}$ or $\textit{chain construction}$. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

Leonardo Bertolazzi, Philipp Mondorf, Barbara Plank et al.

The ability of large language models (LLMs) to validate their output and identify potential errors is crucial for ensuring robustness and reliability. However, current research indicates that LLMs struggle with self-correction, encountering significant challenges in detecting errors. While studies have explored methods to enhance self-correction in LLMs, relatively little attention has been given to understanding the models' internal mechanisms underlying error detection. In this paper, we present a mechanistic analysis of error detection in LLMs, focusing on simple arithmetic problems. Through circuit analysis, we identify the computational subgraphs responsible for detecting arithmetic errors across four smaller-sized LLMs. Our findings reveal that all models heavily rely on $\textit{consistency heads}$--attention heads that assess surface-level alignment of numerical values in arithmetic solutions. Moreover, we observe that the models' internal arithmetic computation primarily occurs in higher layers, whereas validation takes place in middle layers, before the final arithmetic results are fully encoded. This structural dissociation between arithmetic computation and validation seems to explain why smaller-sized LLMs struggle to detect even simple arithmetic errors.

Qiqi Chen, Xinpeng Wang, Philipp Mondorf et al.

Tree of Thoughts (ToT) is a reasoning strategy for Large Language Models (LLMs) that employs a generator to suggest reasoning steps and a discriminator to decide which steps to implement. ToT demonstrates strong performance on reasoning tasks, often surpassing simple methods such as Input-Output (IO) prompting and Chain-of-Thought (CoT) reasoning. However, ToT does not consistently outperform such simpler methods across all models, leaving large knowledge gaps on the conditions under which ToT is most beneficial. In this paper, we analyze the roles of the generator and discriminator separately to better understand the conditions when ToT is beneficial. We find that the generator plays a more critical role than the discriminator in driving the success of ToT. Scaling the generator leads to notable improvements in ToT performance, even when using a smaller model as the discriminator, whereas scaling the discriminator with a fixed generator yields only marginal gains. Our results show that models across different scales exhibit comparable discrimination capabilities, yet differ significantly in their generative performance for ToT.

Jasmin Orth, Philipp Mondorf, Barbara Plank

Conditional acceptability refers to how plausible a conditional statement is perceived to be. It plays an important role in communication and reasoning, as it influences how individuals interpret implications, assess arguments, and make decisions based on hypothetical scenarios. When humans evaluate how acceptable a conditional "If A, then B" is, their judgments are influenced by two main factors: the $\textit{conditional probability}$ of $B$ given $A$, and the $\textit{semantic relevance}$ of the antecedent $A$ given the consequent $B$ (i.e., whether $A$ meaningfully supports $B$). While prior work has examined how large language models (LLMs) draw inferences about conditional statements, it remains unclear how these models judge the $\textit{acceptability}$ of such statements. To address this gap, we present a comprehensive study of LLMs' conditional acceptability judgments across different model families, sizes, and prompting strategies. Using linear mixed-effects models and ANOVA tests, we find that models are sensitive to both conditional probability and semantic relevance-though to varying degrees depending on architecture and prompting style. A comparison with human data reveals that while LLMs incorporate probabilistic and semantic cues, they do so less consistently than humans. Notably, larger models do not necessarily align more closely with human judgments.

Philipp Mondorf, Mingyang Wang, Sebastian Gerstner et al.

The Circuit Localization track of the Mechanistic Interpretability Benchmark (MIB) evaluates methods for localizing circuits within large language models (LLMs), i.e., subnetworks responsible for specific task behaviors. In this work, we investigate whether ensembling two or more circuit localization methods can improve performance. We explore two variants: parallel and sequential ensembling. In parallel ensembling, we combine attribution scores assigned to each edge by different methods-e.g., by averaging or taking the minimum or maximum value. In the sequential ensemble, we use edge attribution scores obtained via EAP-IG as a warm start for a more expensive but more precise circuit identification method, namely edge pruning. We observe that both approaches yield notable gains on the benchmark metrics, leading to a more precise circuit identification approach. Finally, we find that taking a parallel ensemble over various methods, including the sequential ensemble, achieves the best results. We evaluate our approach in the BlackboxNLP 2025 MIB Shared Task, comparing ensemble scores to official baselines across multiple model-task combinations.

Yupei Du, Philipp Mondorf, Silvia Casola et al.

Large language models readily memorize arbitrary training instances, such as label noise, yet they perform strikingly well on reasoning tasks. In this work, we investigate how language models memorize label noise, and why such memorization in many cases does not heavily affect generalizable reasoning capabilities. Using two controllable synthetic reasoning datasets with noisy labels, four-digit addition (FDA) and two-hop relational reasoning (THR), we discover a reliance of memorization on generalizable reasoning mechanisms: models continue to compute intermediate reasoning outputs even when retrieving memorized noisy labels, and intervening reasoning adversely affects memorization. We further show that memorization operates through distributed encoding, i.e., aggregating various inputs and intermediate results, rather than building a look-up mechanism from inputs to noisy labels. Moreover, our FDA case study reveals memorization occurs via outlier heuristics, where existing neuron activation patterns are slightly shifted to fit noisy labels. Together, our findings suggest that memorization of label noise in language models builds on, rather than overrides, the underlying reasoning mechanisms, shedding lights on the intriguing phenomenon of benign memorization.

Philipp Mondorf, Shijia Zhou, Monica Riedler et al.

Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their knowledge to novel compositional scenarios, revealing notable limitations in systematic generalization. There has been an ongoing debate about whether neural networks possess the capacity for systematic generalization, with recent studies suggesting that meta-learning approaches designed for compositionality can significantly enhance this ability. However, these insights have largely been confined to linguistic problems, leaving their applicability to other tasks an open question. In this study, we extend meta-learning for compositionality to the domain of abstract spatial reasoning. To this end, we introduce $\textit{Compositional-ARC}-$a dataset designed to evaluate the capacity of models to systematically generalize from known geometric transformations (e.g., translation, rotation) of abstract two-dimensional objects to novel combinations of these transformations (e.g., translation+rotation). Our results show that a small transformer-based encoder-decoder model, trained via meta-learning for compositionality, can systematically generalize to previously unseen transformation compositions. Notably, despite having only 5.7M parameters, this model significantly outperforms state-of-the-art LLMs$-$including o3-mini, GPT-4o, and Gemini 2.0 Flash, which fail to exhibit similar systematic behavior$-$and performs on par with the winning model of the ARC prize 2024, an 8B-parameter LLM trained via test-time training. Our findings highlight the effectiveness of meta-learning in promoting systematicity beyond linguistic tasks, suggesting a promising direction toward more robust and generalizable models.

Anna Bavaresco, Raffaella Bernardi, Leonardo Bertolazzi et al.

There is an increasing trend towards evaluating NLP models with LLMs instead of human judgments, raising questions about the validity of these evaluations, as well as their reproducibility in the case of proprietary models. We provide JUDGE-BENCH, an extensible collection of 20 NLP datasets with human annotations covering a broad range of evaluated properties and types of data, and comprehensively evaluate 11 current LLMs, covering both open-weight and proprietary models, for their ability to replicate the annotations. Our evaluations show substantial variance across models and datasets. Models are reliable evaluators on some tasks, but overall display substantial variability depending on the property being evaluated, the expertise level of the human judges, and whether the language is human or model-generated. We conclude that LLMs should be carefully validated against human judgments before being used as evaluators.

Philipp Mondorf, Barbara Plank

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce $\textit{TruthQuest}$, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on $\textit{TruthQuest}$ show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.