Due to the size and complexity of modern large language models (LLMs), it has proven challenging to uncover the underlying mechanisms that models use to solve reasoning problems. For instance, is their reasoning for a specific problem localized to certain parts of the network? Do they break down the reasoning problem into modular components that are then executed as sequential steps as we go deeper in the model? To better understand the reasoning capability of LLMs, we study a minimal propositional logic problem that requires combining multiple facts to arrive at a solution. By studying this problem on Mistral and Gemma models, up to 27B parameters, we illuminate the core components the models use to solve such logic problems. From a mechanistic interpretability point of view, we use causal mediation analysis to uncover the pathways and components of the LLMs' reasoning processes. Then, we offer fine-grained insights into the functions of attention heads in different layers. We not only find a sparse circuit that computes the answer, but we decompose it into sub-circuits that have four distinct and modular uses. Finally, we reveal that three distinct models - Mistral-7B, Gemma2-9B and Gemma-2-27B - contain analogous but not identical mechanisms.

Large language models (LLMs) have emerged as a dominant AI paradigm due to their exceptional text understanding and generation capabilities. However, their tendency to generate inconsistent or erroneous outputs challenges their reliability, especially in high-stakes domains requiring accuracy and trustworthiness. Existing research primarily focuses on detecting and mitigating model misbehavior in general-purpose scenarios, often overlooking the potential of integrating domain-specific knowledge. In this work, we advance misbehavior detection by incorporating domain knowledge. The core idea is to design a general specification language that enables domain experts to customize domain-specific predicates in a lightweight and intuitive manner, supporting later runtime verification of LLM outputs. To achieve this, we design a novel specification language, ESL, and introduce a runtime verification framework, RvLLM, to validate LLM output against domain-specific constraints defined in ESL. We evaluate RvLLM on three representative tasks: violation detection against Singapore Rapid Transit Systems Act, numerical comparison, and inequality solving. Experimental results demonstrate that RvLLM effectively detects erroneous outputs across various LLMs in a lightweight and flexible manner. The results reveal that despite their impressive capabilities, LLMs remain prone to low-level errors due to limited interpretability and a lack of formal guarantees during inference, and our framework offers a potential long-term solution by leveraging expert domain knowledge to rigorously and efficiently verify LLM outputs.

Neural Information Processing Systems http://nips.cc/

Artificial Intelligence (AI) is a powerful new language of science as evidenced by recent Nobel Prizes in chemistry and physics that recognized contributions to AI applied to those areas. Yet, this new language lacks semantics, which makes AI's scientific discoveries unsatisfactory at best. With the purpose of uncovering new facts but also improving our understanding of the world, AI-based science requires formalization through a framework capable of translating insight into comprehensible scientific knowledge. In this paper, we argue that logic offers an adequate framework. In particular, we use logic in a neurosymbolic framework to offer a much needed semantics for deep learning, the neural network-based technology of current AI. Deep learning and neurosymbolic AI lack a general set of conditions to ensure that desirable properties are satisfied. Instead, there is a plethora of encoding and knowledge extraction approaches designed for particular cases. To rectify this, we introduced a framework for semantic encoding, making explicit the mapping between neural networks and logic, and characterizing the common ingredients of the various existing approaches. In this paper, we describe succinctly and exemplify how logical semantics and neural networks are linked through this framework, we review some of the most prominent approaches and techniques developed for neural encoding and knowledge extraction, provide a formal definition of our framework, and discuss some of the difficulties of identifying a semantic encoding in practice in light of analogous problems in the philosophy of mind.

Transformer-based language models (LMs) can perform a wide range of tasks, and mechanistic interpretability (MI) aims to reverse engineer the components responsible for task completion to understand their behavior. Previous MI research has focused on linguistic tasks such as Indirect Object Identification (IOI). In this paper, we investigate the ability of GPT-2 small to handle binary truth values by analyzing its behavior with syllogistic prompts, e.g., "Statement A is true. Statement B matches statement A. Statement B is", which requires more complex logical reasoning compared to IOI. Through our analysis of several syllogism tasks of varying difficulty, we identify multiple circuits that mechanistically explain GPT-2's logical-reasoning capabilities and uncover binary mechanisms that facilitate task completion, including the ability to produce a negated token not present in the input prompt through negative heads. Our evaluation using a faithfulness metric shows that a circuit comprising five attention heads achieves over 90% of the original model's performance. By relating our findings to IOI analysis, we provide new insights into the roles of specific attention heads and MLPs in LMs. These insights contribute to a broader understanding of model reasoning and support future research in mechanistic interpretability.

State-of-the-art approaches for integrating symbolic knowledge with deep learning architectures have demonstrated promising results in static domains. However, methods to handle temporal logic specifications remain underexplored. The only existing approach relies on an explicit representation of a finite-state automaton corresponding to the temporal specification. Instead, we aim at proposing a neurosymbolic framework designed to incorporate temporal logic specifications, expressed in Linear Temporal Logic over finite traces (LTLf), directly into deep learning architectures for sequence-based tasks. We extend the Iterative Local Refinement (ILR) neurosymbolic algorithm, leveraging the recent introduction of fuzzy LTLf interpretations. We name this proposed method Temporal Iterative Local Refinement (T-ILR). We assess T-ILR on an existing benchmark for temporal neurosymbolic architectures, consisting of the classification of image sequences in the presence of temporal knowledge. The results demonstrate improved accuracy and computational efficiency compared to the state-of-the-art method.

This paper introduces a new family of cognitive modal logics designed to formalize conjectural reasoning: a modal system in which cognitive contexts extend known facts with hypothetical assumptions to explore their consequences. Unlike traditional doxastic and epistemic systems, conjectural logics rely on a principle, called Axiom C ($φ\rightarrow \Boxφ$), that ensures that all established facts are preserved across hypothetical layers. While Axiom C was dismissed in the past due to its association with modal collapse, we show that the collapse only arises under classical and bivalent assumptions, and specifically in the presence of Axiom T. Hence we avoid Axiom T and adopt a paracomplete semantic framework, grounded in Weak Kleene logic or Description Logic, where undefined propositions coexist with modal assertions. This prevents the modal collapse and guarantees a layering to distinguish between factual and conjectural statements. Under this framework we define new modal systems, e.g., KC and KDC, and show that they are complete, decidable, and robust under partial knowledge. Finally, we introduce a dynamic operation, $\mathsf{settle}(φ)$, which formalizes the transition from conjecture to accepted fact, capturing the event of the update of a world's cognitive state through the resolution of uncertainty.

Generative Large Language Models (LLMs)inevitably produce untruthful responses. Accurately predicting the truthfulness of these outputs is critical, especially in high-stakes settings. To accelerate research in this domain and make truthfulness prediction methods more accessible, we introduce TruthTorchLM an open-source, comprehensive Python library featuring over 30 truthfulness prediction methods, which we refer to as Truth Methods. Unlike existing toolkits such as Guardrails, which focus solely on document-grounded verification, or LM-Polygraph, which is limited to uncertainty-based methods, TruthTorchLM offers a broad and extensible collection of techniques. These methods span diverse tradeoffs in computational cost, access level (e.g., black-box vs white-box), grounding document requirements, and supervision type (self-supervised or supervised). TruthTorchLM is seamlessly compatible with both HuggingFace and LiteLLM, enabling support for locally hosted and API-based models. It also provides a unified interface for generation, evaluation, calibration, and long-form truthfulness prediction, along with a flexible framework for extending the library with new methods. We conduct an evaluation of representative truth methods on three datasets, TriviaQA, GSM8K, and FactScore-Bio. The code is available at https://github.com/Ybakman/TruthTorchLM

Large Language Models (LLMs) such as ChatGPT demonstrated the potential to replicate human language abilities through technology, ranging from text generation to engaging in conversations. However, it remains controversial to what extent these systems truly understand language. We examine this issue by narrowing the question down to the semantics of LLMs at the word and sentence level. By examining the inner workings of LLMs and their generated representation of language and by drawing on classical semantic theories by Frege and Russell, we get a more nuanced picture of the potential semantic capabilities of LLMs.