Daily Papers

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule Inducer (NRI), a pretrained model for zero-shot rule induction. Rather than encoding literal identities, NRI represents literals using domain-agnostic statistical properties such as class-conditional rates, entropy, and co-occurrence, which generalize across variable identities and counts without retraining. The model consists of a statistical encoder and a parallel slot-based decoder. Parallel decoding preserves the permutation invariance of logical disjunction; an autoregressive decoder would instead impose an arbitrary clause order. Product T-norm relaxation makes rule execution differentiable, allowing end-to-end training on prediction accuracy alone. We evaluate NRI on rule recovery, robustness to label noise and spurious correlations, and zero-shot transfer to real-world benchmarks, and we believe this work opens up the possibility of foundation models for symbolic reasoning. Code and the reference checkpoint are available at https://github.com/phuayj/neural-rule-inducer.

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.

Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models indeed perform logical reasoning by understanding the underlying logical semantics in the language. To this end, we propose RobustLR, a suite of evaluation datasets that evaluate the robustness of these models to minimal logical edits in rulebases and some standard logical equivalence conditions. In our experiments with RoBERTa and T5, we find that the models trained in prior works do not perform consistently on the different perturbations in RobustLR, thus showing that the models are not robust to the proposed logical perturbations. Further, we find that the models find it especially hard to learn logical negation and disjunction operators. Overall, using our evaluation sets, we demonstrate some shortcomings of the deductive reasoning-based language models, which can eventually help towards designing better models for logical reasoning over natural language. All the datasets and code base have been made publicly available.

Multi-hop query answering over a Knowledge Graph (KG) involves traversing one or more hops from the start node to answer a query. Path-based and logic-based methods are state-of-the-art for multi-hop question answering. The former is used in link prediction tasks. The latter is for answering complex logical queries. The logical multi-hop querying technique embeds the KG and queries in the same embedding space. The existing work incorporates First Order Logic (FOL) operators, such as conjunction (wedge), disjunction (vee), and negation (neg), in queries. Though current models have most of the building blocks to execute the FOL queries, they cannot use the dense information of multi-modal entities in the case of Multi-Modal Knowledge Graphs (MMKGs). We propose RConE, an embedding method to capture the multi-modal information needed to answer a query. The model first shortlists candidate (multi-modal) entities containing the answer. It then finds the solution (sub-entities) within those entities. Several existing works tackle path-based question-answering in MMKGs. However, to our knowledge, we are the first to introduce logical constructs in querying MMKGs and to answer queries that involve sub-entities of multi-modal entities as the answer. Extensive evaluation of four publicly available MMKGs indicates that RConE outperforms the current state-of-the-art.

Reinforcement learning (RL) has been applied to improve large language model (LLM) reasoning, yet the systematic study of how training scales with task difficulty has been hampered by the lack of controlled, scalable environments. We introduce ScaleLogic, a synthetic logical reasoning framework that offers independent control over two axes of difficulty: the depth of the required proof planning (i.e., the horizon) and the expressiveness of the underlying logic. Our proposed framework supports a wide range of logics: from simple implication-only logic ("if-then") towards more expressive first-order reasoning with conjunction ("and"), disjunction ("or"), negation ("not"), and universal quantification ("for all"). Using this framework, we show that the RL training compute T follows a power law with respect to reasoning depth D (T propto D^γ, R^{2} > 0.99), and that the scaling exponent γ increases monotonically with logical expressiveness, from 1.04 to 2.60. On downstream mathematics and general reasoning benchmarks, more expressive training settings yield both larger performance gains (up to +10.66 points) and more compute-efficient transfer compared to less expressive settings, demonstrating that what a model is trained on, not just how much it is trained, shapes downstream transfer. We further show that the power-law relationship holds across multiple RL methods, and curriculum-based training substantially improves scaling efficiency.

One of the fundamental problems in Artificial Intelligence is to perform complex multi-hop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary first-order logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported. An additional limitation of present methods is also that they cannot naturally model uncertainty. Here, we present BetaE, a probabilistic embedding framework for answering arbitrary FOL queries over KGs. BetaE is the first method that can handle a complete set of first-order logical operations: conjunction (wedge), disjunction (vee), and negation (neg). A key insight of BetaE is to use probabilistic distributions with bounded support, specifically the Beta distribution, and embed queries/entities as distributions, which as a consequence allows us to also faithfully model uncertainty. Logical operations are performed in the embedding space by neural operators over the probabilistic embeddings. We demonstrate the performance of BetaE on answering arbitrary FOL queries on three large, incomplete KGs. While being more general, BetaE also increases relative performance by up to 25.4% over the current state-of-the-art KG reasoning methods that can only handle conjunctive queries without negation.

This study investigates the in-context learning capabilities of various decoder-only transformer-based language models with different model sizes and training data, including GPT2, SmolLM2, OpenELM, TinyLlama, Stable LM, and Gemma 2. We identify a critical parameter threshold (~1.6 billion), beyond which reasoning performance improves significantly in tasks such as commonsense reasoning in multiple-choice question answering and deductive reasoning. Specifically, models above this threshold achieve better success rates in chain-of-thought (CoT) prompting for deductive reasoning tasks, especially those requiring longer reasoning chains, such as proof by contradiction and disjunction elimination. To address limitations in sub-threshold models, we demonstrate that fine-tuning with task-specific exemplars substantially enhances reasoning performance, enabling accurate CoT generation even without additional exemplars in the prompt for tasks with shorter reasoning chains. Finally, our analysis of attention maps reveals that models capable of generating correct CoTs exhibit higher token-level attention scores on subsequent correct tokens and the correct parts of speech, providing interpretability insights into reasoning processes. These findings collectively advance understanding of reasoning capabilities in decoder-only transformer-based models. The code is available at: https://github.com/AnnonymousForPapers/CoT_Reasoning_Test.

Complex query answering (CQA) is an essential task for multi-hop and logical reasoning on knowledge graphs (KGs). Currently, most approaches are limited to queries among binary relational facts and pay less attention to n-ary facts (n>=2) containing more than two entities, which are more prevalent in the real world. Moreover, previous CQA methods can only make predictions for a few given types of queries and cannot be flexibly extended to more complex logical queries, which significantly limits their applications. To overcome these challenges, in this work, we propose a novel N-ary Query Embedding (NQE) model for CQA over hyper-relational knowledge graphs (HKGs), which include massive n-ary facts. The NQE utilizes a dual-heterogeneous Transformer encoder and fuzzy logic theory to satisfy all n-ary FOL queries, including existential quantifiers, conjunction, disjunction, and negation. We also propose a parallel processing algorithm that can train or predict arbitrary n-ary FOL queries in a single batch, regardless of the kind of each query, with good flexibility and extensibility. In addition, we generate a new CQA dataset WD50K-NFOL, including diverse n-ary FOL queries over WD50K. Experimental results on WD50K-NFOL and other standard CQA datasets show that NQE is the state-of-the-art CQA method over HKGs with good generalization capability. Our code and dataset are publicly available.

Neural link predictors are immensely useful for identifying missing edges in large scale Knowledge Graphs. However, it is still not clear how to use these models for answering more complex queries that arise in a number of domains, such as queries using logical conjunctions (land), disjunctions (lor) and existential quantifiers (exists), while accounting for missing edges. In this work, we propose a framework for efficiently answering complex queries on incomplete Knowledge Graphs. We translate each query into an end-to-end differentiable objective, where the truth value of each atom is computed by a pre-trained neural link predictor. We then analyse two solutions to the optimisation problem, including gradient-based and combinatorial search. In our experiments, the proposed approach produces more accurate results than state-of-the-art methods -- black-box neural models trained on millions of generated queries -- without the need of training on a large and diverse set of complex queries. Using orders of magnitude less training data, we obtain relative improvements ranging from 8% up to 40% in Hits@3 across different knowledge graphs containing factual information. Finally, we demonstrate that it is possible to explain the outcome of our model in terms of the intermediate solutions identified for each of the complex query atoms. All our source code and datasets are available online, at https://github.com/uclnlp/cqd.