Daily Papers

In-context learning (ICL) is the standard method for low-resource classification, yet its efficacy in specialized domains remains largely unexplored. We address the challenge of classifying semantically complex, multi-party B2B conversations, where traditional ICL encounters significant limitations, especially as context length increases due to the concatenation of multiple few-shot examples. We introduce the Call Playbook dataset, featuring five classification tasks derived from real-world B2B conversations targeting core sales concepts. To bridge the gap between performance and practical utility, we propose novel knowledge extraction methods that distill verbose examples into compact, interpretable representations of structured classification criteria and precise task descriptions. Our approach achieves a 99\% reduction in token usage and improves macro-averaged AUC by up to 7\% over traditional ICL. Notably, it remains robust as context grows, unlike advanced token compression baselines which degrade by over 9 F1 points. Importantly, our framework enables direct refinement of classification logic, addressing critical needs for transparency, efficiency, and user interaction in real-world NLP applications.

Health-related misinformation is very prevalent and potentially harmful. It is difficult to identify, especially when claims distort or misinterpret scientific findings. We investigate the impact of synthetic data generation and lightweight fine-tuning techniques on the ability of large language models (LLMs) to recognize fallacious arguments using the MISSCI dataset and framework. In this work, we propose MisSynth, a pipeline that applies retrieval-augmented generation (RAG) to produce synthetic fallacy samples, which are then used to fine-tune an LLM model. Our results show substantial accuracy gains with fine-tuned models compared to vanilla baselines. For instance, the LLaMA 3.1 8B fine-tuned model achieved an over 35% F1-score absolute improvement on the MISSCI test split over its vanilla baseline. We demonstrate that introducing synthetic fallacy data to augment limited annotated resources can significantly enhance zero-shot LLM classification performance on real-world scientific misinformation tasks, even with limited computational resources. The code and synthetic dataset are available on https://github.com/mxpoliakov/MisSynth.

Despite the remarkable performance of Large Language Models (LLMs) in natural language processing tasks, they still struggle with generating logically sound arguments, resulting in potential risks such as spreading misinformation. To address this issue, we introduce FIPO, a fallacy-informed framework that leverages preference optimization methods to steer LLMs toward logically sound arguments. FIPO includes a classification loss, to capture the fine-grained information on fallacy types. Our results on argumentation datasets show that our method reduces the fallacy errors by up to 17.5%. Furthermore, our human evaluation results indicate that the quality of the generated arguments by our method significantly outperforms the fine-tuned baselines, as well as other preference optimization methods, such as DPO. These findings highlight the importance of ensuring models are aware of logical fallacies for effective argument generation. Our code is available at github.com/lucamouchel/Logical-Fallacies.

Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training is considerably more resource-intensive. This paper proposes a novel mathematical principle by introducing the notion of Boolean variation such that neurons made of Boolean weights and inputs can be trained -- for the first time -- efficiently in Boolean domain using Boolean logic instead of gradient descent and real arithmetic. We explore its convergence, conduct extensively experimental benchmarking, and provide consistent complexity evaluation by considering chip architecture, memory hierarchy, dataflow, and arithmetic precision. Our approach achieves baseline full-precision accuracy in ImageNet classification and surpasses state-of-the-art results in semantic segmentation, with notable performance in image super-resolution, and natural language understanding with transformer-based models. Moreover, it significantly reduces energy consumption during both training and inference.

Retrieval-Augmented Generation (RAG), while serving as a viable complement to large language models (LLMs), often overlooks the crucial aspect of text chunking within its pipeline, which impacts the quality of knowledge-intensive tasks. This paper introduces the concept of Meta-Chunking, which refers to a granularity between sentences and paragraphs, consisting of a collection of sentences within a paragraph that have deep linguistic logical connections. To implement Meta-Chunking, we designed two strategies based on LLMs: Margin Sampling Chunking and Perplexity Chunking. The former employs LLMs to perform binary classification on whether consecutive sentences need to be segmented, making decisions based on the probability difference obtained from margin sampling. The latter precisely identifies text chunk boundaries by analyzing the characteristics of perplexity distribution. Additionally, considering the inherent complexity of different texts, we propose a strategy that combines Meta-Chunking with dynamic merging to achieve a balance between fine-grained and coarse-grained text chunking. Experiments conducted on eleven datasets demonstrate that Meta-Chunking can more efficiently improve the performance of single-hop and multi-hop question answering based on RAG. For instance, on the 2WikiMultihopQA dataset, it outperforms similarity chunking by 1.32 while only consuming 45.8% of the time. Our code is available at https://github.com/IAAR-Shanghai/Meta-Chunking.

In this work, we introduce Boolformer, the first Transformer architecture trained to perform end-to-end symbolic regression of Boolean functions. First, we show that it can predict compact formulas for complex functions which were not seen during training, when provided a clean truth table. Then, we demonstrate its ability to find approximate expressions when provided incomplete and noisy observations. We evaluate the Boolformer on a broad set of real-world binary classification datasets, demonstrating its potential as an interpretable alternative to classic machine learning methods. Finally, we apply it to the widespread task of modelling the dynamics of gene regulatory networks. Using a recent benchmark, we show that Boolformer is competitive with state-of-the art genetic algorithms with a speedup of several orders of magnitude. Our code and models are available publicly.

Classification is one of the most widespread tasks in AI applications, serving often as the first step in filtering, sorting, and categorizing data. Since modern AI systems must handle large volumes of input data and early pipeline stages can propagate errors downstream, achieving high efficiency and accuracy is critical. Moreover, classification requirements can change dynamically based on user needs, necessitating models with strong zero-shot capabilities. While generative LLMs have become mainstream for zero-shot classification due to their versatility, they suffer from inconsistent instruction following and computational inefficiency. Cross-encoders, commonly used as rerankers in RAG pipelines, face a different bottleneck: they must process text-label pairs sequentially, significantly reducing efficiency with large label sets. Embedding-based approaches offer good efficiency but struggle with complex scenarios involving logical and semantic constraints. We propose GLiClass, a novel method that adapts the GLiNER architecture for sequence classification tasks. Our approach achieves strong accuracy and efficiency comparable to embedding-based methods, while maintaining the flexibility needed for zero-shot and few-shot learning scenarios. Additionally, we adapted proximal policy optimization (PPO) for multi-label text classification, enabling training classifiers in data-sparse conditions or from human feedback.

Existing methods on understanding the capabilities of LLMs in logical reasoning rely on binary entailment classification or synthetically derived rationales, which are not sufficient for proper investigation of model's capabilities. We present P-FOLIO, a human-annotated dataset consisting of diverse and complex reasoning chains for a set of realistic logical reasoning stories also written by humans. P-FOLIO is collected with an annotation protocol that facilitates humans to annotate well-structured natural language proofs for first-order logic reasoning problems in a step-by-step manner. The number of reasoning steps in P-FOLIO span from 0 to 20. We further use P-FOLIO to evaluate and improve large-language-model (LLM) reasoning capabilities. We evaluate LLM reasoning capabilities at a fine granularity via single-step inference rule classification, with more diverse inference rules of more diverse and higher levels of complexities than previous works. Given that a single model-generated reasoning chain could take a completely different path than the human-annotated one, we sample multiple reasoning chains from a model and use pass@k metrics for evaluating the quality of model-generated reasoning chains. We show that human-written reasoning chains significantly boost the logical reasoning capabilities of LLMs via many-shot prompting and fine-tuning. Furthermore, fine-tuning Llama3-7B on P-FOLIO improves the model performance by 10% or more on three other out-of-domain logical reasoning datasets. We also conduct detailed analysis to show where most powerful LLMs fall short in reasoning. We will release the dataset and code publicly.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Detecting logical fallacies in texts can help users spot argument flaws, but automating this detection is not easy. Manually annotating fallacies in large-scale, real-world text data to create datasets for developing and validating detection models is costly. This paper introduces CoCoLoFa, the largest known logical fallacy dataset, containing 7,706 comments for 648 news articles, with each comment labeled for fallacy presence and type. We recruited 143 crowd workers to write comments embodying specific fallacy types (e.g., slippery slope) in response to news articles. Recognizing the complexity of this writing task, we built an LLM-powered assistant into the workers' interface to aid in drafting and refining their comments. Experts rated the writing quality and labeling validity of CoCoLoFa as high and reliable. BERT-based models fine-tuned using CoCoLoFa achieved the highest fallacy detection (F1=0.86) and classification (F1=0.87) performance on its test set, outperforming the state-of-the-art LLMs. Our work shows that combining crowdsourcing and LLMs enables us to more effectively construct datasets for complex linguistic phenomena that crowd workers find challenging to produce on their own.

Ensuring logical consistency in predictions is a crucial yet overlooked aspect in multi-attribute classification. We explore the potential reasons for this oversight and introduce two pressing challenges to the field: 1) How can we ensure that a model, when trained with data checked for logical consistency, yields predictions that are logically consistent? 2) How can we achieve the same with data that hasn't undergone logical consistency checks? Minimizing manual effort is also essential for enhancing automation. To address these challenges, we introduce two datasets, FH41K and CelebA-logic, and propose LogicNet, an adversarial training framework that learns the logical relationships between attributes. Accuracy of LogicNet surpasses that of the next-best approach by 23.05%, 9.96%, and 1.71% on FH37K, FH41K, and CelebA-logic, respectively. In real-world case analysis, our approach can achieve a reduction of more than 50% in the average number of failed cases compared to other methods.

Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to resolve this fundamental tension. In this work, we argue that task context operates as a non-isometric dynamical operator that enforces a necessary "topological distortion." By applying Gram-Schmidt decomposition to residual-stream activations , we reveal a dual-modulation mechanism driving this process: a class-agnostic topological preservation that anchors global structure to prevent semantic collapse, and a specific algebraic divergence that directionally tears apart cross-class concepts to forge logical boundaries. We validate this geometric evolution across a gradient of tasks, from simple mapping to complex primality testing. Crucially, targeted specific vector ablation establishes a strict causal binding between this topology and model function: algebraically erasing the divergence component collapses parity classification accuracy from 100% to chance levels (38.57%). Furthermore, we uncover a three-phase layer-wise geometric dynamic and demonstrate that under social pressure prompts, models fail to generate sufficient divergence. This results in a "manifold entanglement" that geometrically explains sycophancy and hallucination. Ultimately, our findings revise the linear-isometric presumption, demonstrating that the emergence of discrete logic in LLMs is purchased at an irreducible cost of topological deformation.

Current LLM safety research predominantly focuses on mitigating Goal Hijacking, preventing attackers from redirecting a model's high-level objective (e.g., from "summarizing emails" to "phishing users"). In this paper, we argue that this perspective is incomplete and highlight a critical vulnerability in Reasoning Alignment. We propose a new adversarial paradigm: Reasoning Hijacking and instantiate it with Criteria Attack, which subverts model judgments by injecting spurious decision criteria without altering the high-level task goal. Unlike Goal Hijacking, which attempts to override the system prompt, Reasoning Hijacking accepts the high-level goal but manipulates the model's decision-making logic by injecting spurious reasoning shortcut. Though extensive experiments on three different tasks (toxic comment, negative review, and spam detection), we demonstrate that even newest models are prone to prioritize injected heuristic shortcuts over rigorous semantic analysis. The results are consistent over different backbones. Crucially, because the model's "intent" remains aligned with the user's instructions, these attacks can bypass defenses designed to detect goal deviation (e.g., SecAlign, StruQ), exposing a fundamental blind spot in the current safety landscape. Data and code are available at https://github.com/Yuan-Hou/criteria_attack

Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them. This scenario necessitates the use of composite class labels. In this paper, we propose a novel framework called Hyper-Evidential Neural Network (HENN) that explicitly models predictive uncertainty due to composite class labels in training data in the context of the belief theory called Subjective Logic (SL). By placing a grouped Dirichlet distribution on the class probabilities, we treat predictions of a neural network as parameters of hyper-subjective opinions and learn the network that collects both single and composite evidence leading to these hyper-opinions by a deterministic DNN from data. We introduce a new uncertainty type called vagueness originally designed for hyper-opinions in SL to quantify composite classification uncertainty for DNNs. Our results demonstrate that HENN outperforms its state-of-the-art counterparts based on four image datasets. The code and datasets are available at: https://github.com/Hugo101/HyperEvidentialNN.

Since large language models have approached human-level performance on many tasks, it has become increasingly harder for researchers to find tasks that are still challenging to the models. Failure cases usually come from the long-tail distribution - data that an oracle language model could assign a probability on the lower end of its distribution. Current methodology such as prompt engineering or crowdsourcing are insufficient for creating long-tail examples because humans are constrained by cognitive bias. We propose a Logic-Induced-Knowledge-Search (LINK) framework for systematically generating long-tail knowledge statements. Grounded by a symbolic rule, we search for long-tail values for each variable of the rule by first prompting a LLM, then verifying the correctness of the values with a critic, and lastly pushing for the long-tail distribution with a reranker. With this framework we construct a dataset, Logic-Induced-Long-Tail (LINT), consisting of 200 symbolic rules and 50K knowledge statements spanning across four domains. Human annotations find that 84% of the statements in LINT are factually correct. In contrast, ChatGPT and GPT4 struggle with directly generating long-tail statements under the guidance of logic rules, each only getting 56% and 78% of their statements correct. Moreover, their "long-tail" generations in fact fall into the higher likelihood range, and thus are not really long-tail. Our findings suggest that LINK is effective for generating data in the long-tail distribution while enforcing quality. LINT can be useful for systematically evaluating LLMs' capabilities in the long-tail distribution. We challenge the models with a simple entailment classification task using samples from LINT. We find that ChatGPT and GPT4's capability in identifying incorrect knowledge drop by ~3% in the long-tail distribution compared to head distribution.

Differentiable Logic Gate Networks (DLGNs) are a very fast and energy-efficient alternative to conventional feed-forward networks. With learnable combinations of logical gates, DLGNs enable fast inference by hardware-friendly execution. Since the concept of DLGNs has only recently gained attention, these networks are still in their developmental infancy, including the design and scalability of their output layer. To date, this architecture has primarily been tested on datasets with up to ten classes. This work examines the behavior of DLGNs on large multi-class datasets. We investigate its general expressiveness, its scalability, and evaluate alternative output strategies. Using both synthetic and real-world datasets, we provide key insights into the importance of temperature tuning and its impact on output layer performance. We evaluate conditions under which the Group-Sum layer performs well and how it can be applied to large-scale classification of up to 2000 classes.

In this paper, we present our submission to the MM-ArgFallacy2025 shared task, which aims to advance research in multimodal argument mining, focusing on logical fallacies in political debates. Our approach uses pretrained Transformer-based models and proposes several ways to leverage context. In the fallacy classification subtask, our models achieved macro F1-scores of 0.4444 (text), 0.3559 (audio), and 0.4403 (multimodal). Our multimodal model showed performance comparable to the text-only model, suggesting potential for improvements.

While pre-trained language models (PLMs) are the go-to solution to tackle many natural language processing problems, they are still very limited in their ability to capture and to use common-sense knowledge. In fact, even if information is available in the form of approximate (soft) logical rules, it is not clear how to transfer it to a PLM in order to improve its performance for deductive reasoning tasks. Here, we aim to bridge this gap by teaching PLMs how to reason with soft Horn rules. We introduce a classification task where, given facts and soft rules, the PLM should return a prediction with a probability for a given hypothesis. We release the first dataset for this task, and we propose a revised loss function that enables the PLM to learn how to predict precise probabilities for the task. Our evaluation results show that the resulting fine-tuned models achieve very high performance, even on logical rules that were unseen at training. Moreover, we demonstrate that logical notions expressed by the rules are transferred to the fine-tuned model, yielding state-of-the-art results on external datasets.

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.

In-context learning (ICL) is often motivated by the intuition that demonstrations help because they provide correct input-output examples. However, we reveal a counterintuitive phenomenon: correctness does not guarantee exemplar utility, and some correct demonstrations can even reduce ICL accuracy. To study this correctness-utility gap, we introduce task-preserving perturbations, where only the exemplar input is changed, while the example remains a correct instance of the same task. Concretely, each perturbed exemplar is assigned the target induced by the task mapping. This framework covers both label-updating perturbations, where task-relevant semantics change and targets are recomputed, and stricter target-preserving perturbations, where the original target remains valid. We formalize the resulting failure mode as contextual evidence shift: task-preserving perturbations can change the effective mixture of evidence used by the model for contextual inference, thereby separating exemplar correctness from exemplar utility. Across sentiment classification, logical reasoning, and math word problems, we find that task-preserving perturbed demonstrations can substantially degrade ICL performance, especially for smaller models, harder tasks, and higher perturbation ratios. Our results show that robust ICL requires evaluating not only whether demonstrations are correct, but also how they influence contextual inference. Code is available at https://github.com/Chenghao-Qiu/Task-Preserving-ICL.

Verifying a question's validity before answering is crucial in real-world applications, where users may provide imperfect instructions. In this scenario, an ideal model should address the discrepancies in the query and convey them to the users rather than generating the best possible answer. Addressing this requirement, we introduce a new compositional visual question-answering dataset, VISREAS, that consists of answerable and unanswerable visual queries formulated by traversing and perturbing commonalities and differences among objects, attributes, and relations. VISREAS contains 2.07M semantically diverse queries generated automatically using Visual Genome scene graphs. The unique feature of this task, validating question answerability with respect to an image before answering, and the poor performance of state-of-the-art models inspired the design of a new modular baseline, LOGIC2VISION that reasons by producing and executing pseudocode without any external modules to generate the answer. LOGIC2VISION outperforms generative models in VISREAS (+4.82% over LLaVA-1.5; +12.23% over InstructBLIP) and achieves a significant gain in performance against the classification models.

The explainability of a robot's actions is crucial to its acceptance in social spaces. Explaining why a robot fails to complete a given task is particularly important for non-expert users to be aware of the robot's capabilities and limitations. So far, research on explaining robot failures has only considered generating textual explanations, even though several studies have shown the benefits of multimodal ones. However, a simple combination of multiple modalities may lead to semantic incoherence between the information across different modalities - a problem that is not well-studied. An incoherent multimodal explanation can be difficult to understand, and it may even become inconsistent with what the robot and the human observe and how they perform reasoning with the observations. Such inconsistencies may lead to wrong conclusions about the robot's capabilities. In this paper, we introduce an approach to generate coherent multimodal explanations by checking the logical coherence of explanations from different modalities, followed by refinements as required. We propose a classification approach for coherence assessment, where we evaluate if an explanation logically follows another. Our experiments suggest that fine-tuning a neural network that was pre-trained to recognize textual entailment, performs well for coherence assessment of multimodal explanations. Code & data: https://pradippramanick.github.io/coherent-explain/.

Large Language Models (LLMs) trained on massive corpora demonstrate impressive capabilities in a wide range of tasks. While there are ongoing efforts to adapt these models to languages beyond English, the attention given to their evaluation methodologies remains limited. Current multilingual benchmarks often rely on back translations or re-implementations of English tests, limiting their capacity to capture unique cultural and linguistic nuances. To bridge this gap for the Korean language, we introduce HAE-RAE Bench, a dataset curated to challenge models lacking Korean cultural and contextual depth. The dataset encompasses six downstream tasks across four domains: vocabulary, history, general knowledge, and reading comprehension. Contrary to traditional evaluation suites focused on token or sequence classification and specific mathematical or logical reasoning, HAE-RAE Bench emphasizes a model's aptitude for recalling Korean-specific knowledge and cultural contexts. Comparative analysis with prior Korean benchmarks indicates that the HAE-RAE Bench presents a greater challenge to non-native models, by disturbing abilities and knowledge learned from English being transferred.

The Legacy Survey of Space and Time (LSST) at the Vera C. Rubin Observatory will capture light curves (LCs) for 10 billion sources and produce millions of transient candidates per night, necessitating scalable, accurate, and efficient classification. To prepare the community for this scale of data, the Extended LSST Astronomical Time-Series Classification Challenge (ELAsTiCC) sought to simulate a diversity of LSST-like time-domain events. Using a small transformer-based model and refined light curve encoding logic, we present a new state of the art classification performance on ELAsTiCC, with 71.8% F1 on LC-only classifications, and 89.8% F1 on LC+metadata classifications. Previous state of the art was 65.5% F1 for LC-only, and for LC+metadata, 84% F1 with a different setup and 83.5% F1 with a directly comparable setup. Our model outperforms previous state-of-the-art models for fine-grained early detection at all time cutoffs, which should help prioritize candidate transients for follow-up observations. We demonstrate label-efficient training by removing labels from 90% of the training data (chosen uniformly at random), and compensate by leveraging regularization, bootstrap ensembling, and unsupervised pretraining. Even with only 10% of the labeled data, we achieve 67.4% F1 on LC-only and 87.1% F1 on LC+metadata, validating an approach that should help mitigate synthetic and observational data drift, and improve classification on tasks with less labeled data. We find that our base model is poorly calibrated via reliability diagrams, and correct it at a minimal cost to overall performance, enabling selections by classification precision. Finally, our GPU-optimized implementation is 9x faster than other state-of-the-art ELAsTiCC models, and can run inference at ~33000 LCs/s on a consumer-grade GPU, making it suitable for large-scale applications, and less expensive to train.

Recently, large language models (LLMs) have demonstrated outstanding reasoning capabilities on mathematical and coding tasks. However, their application to financial tasks-especially the most fundamental task of stock movement prediction-remains underexplored. We study a three-class classification problem (up, hold, down) and, by analyzing existing reasoning responses, observe that: (1) LLMs follow analysts' opinions rather than exhibit a systematic, independent analytical logic (CoTs). (2) LLMs list summaries from different sources without weighing adversarial evidence, yet such counterevidence is crucial for reliable prediction. It shows that the model does not make good use of its reasoning ability to complete the task. To address this, we propose Reflective Evidence Tuning (RETuning), a cold-start method prior to reinforcement learning, to enhance prediction ability. While generating CoT, RETuning encourages dynamically constructing an analytical framework from diverse information sources, organizing and scoring evidence for price up or down based on that framework-rather than on contextual viewpoints-and finally reflecting to derive the prediction. This approach maximally aligns the model with its learned analytical framework, ensuring independent logical reasoning and reducing undue influence from context. We also build a large-scale dataset spanning all of 2024 for 5,123 A-share stocks, with long contexts (32K tokens) and over 200K samples. In addition to price and news, it incorporates analysts' opinions, quantitative reports, fundamental data, macroeconomic indicators, and similar stocks. Experiments show that RETuning successfully unlocks the model's reasoning ability in the financial domain. Inference-time scaling still works even after 6 months or on out-of-distribution stocks, since the models gain valuable insights about stock movement prediction.

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns probability-based confidence scores to rules learned for a classification task. This allows users to know how confident they should be in a prediction made by the model. We present a confidence-based pruning algorithm that uses the unique structure of FOLD-RM rules to efficiently prune rules and prevent overfitting. Furthermore, CON-FOLD enables the user to provide pre-existing knowledge in the form of logic program rules that are either (fixed) background knowledge or (modifiable) initial rule candidates. The paper describes our method in detail and reports on practical experiments. We demonstrate the performance of the algorithm on benchmark datasets from the UCI Machine Learning Repository. For that, we introduce a new metric, Inverse Brier Score, to evaluate the accuracy of the produced confidence scores. Finally we apply this extension to a real world example that requires explainability: marking of student responses to a short answer question from the Australian Physics Olympiad.

In recent years, generative artificial intelligence (GenAI) has demonstrated remarkable capabilities in high-stakes domains such as molecular science. However, challenges related to the verifiability and structural privacy of its outputs remain largely unresolved. This paper focuses on the task of molecular toxicity repair. It proposes a structure-private verification framework - ToxiEval-ZKP - which, for the first time, introduces zero-knowledge proof (ZKP) mechanisms into the evaluation process of this task. The system enables model developers to demonstrate to external verifiers that the generated molecules meet multidimensional toxicity repair criteria, without revealing the molecular structures themselves. To this end, we design a general-purpose circuit compatible with both classification and regression tasks, incorporating evaluation logic, Poseidon-based commitment hashing, and a nullifier-based replay prevention mechanism to build a complete end-to-end ZK verification system. Experimental results demonstrate that ToxiEval-ZKP facilitates adequate validation under complete structural invisibility, offering strong circuit efficiency, security, and adaptability, thereby opening up a novel paradigm for trustworthy evaluation in generative scientific tasks.

This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing methods either suffer from the problem of searching in a large search space (e.g., neural logic programming) or ineffective optimization due to sparse rewards (e.g., techniques based on reinforcement learning). To address these limitations, this paper proposes a probabilistic model called RNNLogic. RNNLogic treats logic rules as a latent variable, and simultaneously trains a rule generator as well as a reasoning predictor with logic rules. We develop an EM-based algorithm for optimization. In each iteration, the reasoning predictor is first updated to explore some generated logic rules for reasoning. Then in the E-step, we select a set of high-quality rules from all generated rules with both the rule generator and reasoning predictor via posterior inference; and in the M-step, the rule generator is updated with the rules selected in the E-step. Experiments on four datasets prove the effectiveness of RNNLogic.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of symbolic approaches, where knowledge was explicitly represented by means of symbols and explicitly programmed rules. However, with the advent of machine learning, there has been a paradigm shift towards systems that can autonomously learn from data, requiring minimal human guidance. In light of this shift, in latest years, there has been increasing interest and efforts at endowing neural networks with the ability to reason, bridging the gap between data-driven learning and logical reasoning. Within this context, Neural Algorithmic Reasoning (NAR) stands out as a promising research field, aiming to integrate the structured and rule-based reasoning of algorithms with the adaptive learning capabilities of neural networks, typically by tasking neural models to mimic classical algorithms. In this dissertation, we provide theoretical and practical contributions to this area of research. We explore the connections between neural networks and tropical algebra, deriving powerful architectures that are aligned with algorithm execution. Furthermore, we discuss and show the ability of such neural reasoners to learn and manipulate complex algorithmic and combinatorial optimization concepts, such as the principle of strong duality. Finally, in our empirical efforts, we validate the real-world utility of NAR networks across different practical scenarios. This includes tasks as diverse as planning problems, large-scale edge classification tasks and the learning of polynomial-time approximate algorithms for NP-hard combinatorial problems. Through this exploration, we aim to showcase the potential integrating algorithmic reasoning in machine learning models.

Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main learning settings; describe the building blocks of an ILP system; compare several systems on several dimensions; describe four systems (Aleph, TILDE, ASPAL, and Metagol); highlight key application areas; and, finally, summarise current limitations and directions for future research.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

We present FOLD-SE, an efficient, explainable machine learning algorithm for classification tasks given tabular data containing numerical and categorical values. FOLD-SE generates a set of default rules-essentially a stratified normal logic program-as an (explainable) trained model. Explainability provided by FOLD-SE is scalable, meaning that regardless of the size of the dataset, the number of learned rules and learned literals stay quite small while good accuracy in classification is maintained. A model with smaller number of rules and literals is easier to understand for human beings. FOLD-SE is competitive with state-of-the-art machine learning algorithms such as XGBoost and Multi-Layer Perceptrons (MLP) wrt accuracy of prediction. However, unlike XGBoost and MLP, the FOLD-SE algorithm is explainable. The FOLD-SE algorithm builds upon our earlier work on developing the explainable FOLD-R++ machine learning algorithm for binary classification and inherits all of its positive features. Thus, pre-processing of the dataset, using techniques such as one-hot encoding, is not needed. Like FOLD-R++, FOLD-SE uses prefix sum to speed up computations resulting in FOLD-SE being an order of magnitude faster than XGBoost and MLP in execution speed. The FOLD-SE algorithm outperforms FOLD-R++ as well as other rule-learning algorithms such as RIPPER in efficiency, performance and scalability, especially for large datasets. A major reason for scalable explainability of FOLD-SE is the use of a literal selection heuristics based on Gini Impurity, as opposed to Information Gain used in FOLD-R++. A multi-category classification version of FOLD-SE is also presented.

Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being learned in these studies and introduce a simple domain specific language and a systematic translation from this language to first-order logic. By recasting the target representations in terms of classical logic, we aim to broaden the applicability of existing code datasets for investigating more complex natural language understanding and reasoning problems in the software domain.

Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However, formal language can cause systematic problems for inductive reasoning such as disability of handling raw input such as natural language, sensitiveness to mislabeled data, and incapacity to handle ambiguous input. To this end, we propose a new paradigm (task) for inductive reasoning, which is to induce natural language rules from natural language facts, and create a dataset termed DEER containing 1.2k rule-fact pairs for the task, where rules and facts are written in natural language. New automatic metrics are also proposed and analysed for the evaluation of this task. With DEER, we investigate a modern approach for inductive reasoning where we use natural language as representation for knowledge instead of formal language and use pretrained language models as ''reasoners''. Moreover, we provide the first and comprehensive analysis of how well pretrained language models can induce natural language rules from natural language facts. We also propose a new framework drawing insights from philosophy literature for this task, which we show in the experiment section that surpasses baselines in both automatic and human evaluations. We discuss about our future perspectives for inductive reasoning in Section 7. Dataset and code are available at https://github.com/ZonglinY/Inductive_Reasoning.

Progress in AI is hindered by the lack of a programming language with all the requisite features. Libraries like PyTorch and TensorFlow provide automatic differentiation and efficient GPU implementation, but are additions to Python, which was never intended for AI. Their lack of support for automated reasoning and knowledge acquisition has led to a long and costly series of hacky attempts to tack them on. On the other hand, AI languages like LISP an Prolog lack scalability and support for learning. This paper proposes tensor logic, a language that solves these problems by unifying neural and symbolic AI at a fundamental level. The sole construct in tensor logic is the tensor equation, based on the observation that logical rules and Einstein summation are essentially the same operation, and all else can be reduced to them. I show how to elegantly implement key forms of neural, symbolic and statistical AI in tensor logic, including transformers, formal reasoning, kernel machines and graphical models. Most importantly, tensor logic makes new directions possible, such as sound reasoning in embedding space. This combines the scalability and learnability of neural networks with the reliability and transparency of symbolic reasoning, and is potentially a basis for the wider adoption of AI.

There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing (NLP) and Image Classification (IC). However, scientific and engineering problems have their own unique characteristics and requirements raising new challenges for effective design and deployment of machine learning approaches. There is a strong need for further mathematical developments on the foundations of machine learning methods to increase the level of rigor of employed methods and to ensure more reliable and interpretable results. Also as reported in the recent literature on state-of-the-art results and indicated by the No Free Lunch Theorems of statistical learning theory incorporating some form of inductive bias and domain knowledge is essential to success. Consequently, even for existing and widely used methods there is a strong need for further mathematical work to facilitate ways to incorporate prior scientific knowledge and related inductive biases into learning frameworks and algorithms. We briefly discuss these topics and discuss some ideas proceeding in this direction.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of providing a system with explicit, general knowledge and having the system reason over that knowledge. However, expressing the knowledge in a formal (logical or probabilistic) representation has been a major obstacle to this research. This paper investigates a modern approach to this problem where the facts and rules are provided as natural language sentences, thus bypassing a formal representation. We train transformers to reason (or emulate reasoning) over these sentences using synthetically generated data. Our models, that we call RuleTakers, provide the first empirical demonstration that this kind of soft reasoning over language is learnable, can achieve high (99%) accuracy, and generalizes to test data requiring substantially deeper chaining than seen during training (95%+ scores). We also demonstrate that the models transfer well to two hand-authored rulebases, and to rulebases paraphrased into more natural language. These findings are significant as it suggests a new role for transformers, namely as limited "soft theorem provers" operating over explicit theories in language. This in turn suggests new possibilities for explainability, correctability, and counterfactual reasoning in question-answering.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

Recent advances in Hierarchical Multi-label Classification (HMC), particularly neurosymbolic-based approaches, have demonstrated improved consistency and accuracy by enforcing constraints on a neural model during training. However, such work assumes the existence of such constraints a-priori. In this paper, we relax this strong assumption and present an approach based on Error Detection Rules (EDR) that allow for learning explainable rules about the failure modes of machine learning models. We show that these rules are not only effective in detecting when a machine learning classifier has made an error but also can be leveraged as constraints for HMC, thereby allowing the recovery of explainable constraints even if they are not provided. We show that our approach is effective in detecting machine learning errors and recovering constraints, is noise tolerant, and can function as a source of knowledge for neurosymbolic models on multiple datasets, including a newly introduced military vehicle recognition dataset.

Rule-based models are attractive for various tasks because they inherently lead to interpretable and explainable decisions and can easily incorporate prior knowledge. However, such systems are difficult to apply to problems involving natural language, due to its linguistic variability. In contrast, neural models can cope very well with ambiguity by learning distributed representations of words and their composition from data, but lead to models that are difficult to interpret. In this paper, we describe a model combining neural networks with logic programming in a novel manner for solving multi-hop reasoning tasks over natural language. Specifically, we propose to use a Prolog prover which we extend to utilize a similarity function over pretrained sentence encoders. We fine-tune the representations for the similarity function via backpropagation. This leads to a system that can apply rule-based reasoning to natural language, and induce domain-specific rules from training data. We evaluate the proposed system on two different question answering tasks, showing that it outperforms two baselines -- BIDAF (Seo et al., 2016a) and FAST QA (Weissenborn et al., 2017b) on a subset of the WikiHop corpus and achieves competitive results on the MedHop data set (Welbl et al., 2017).

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

Machine learning classification problems are widespread in bioinformatics, but the technical knowledge required to perform model training, optimization, and inference can prevent researchers from utilizing this technology. This article presents an automated tool for machine learning classification problems to simplify the process of training models and producing results while providing informative visualizations and insights into the data. This tool supports both binary and multiclass classification problems, and it provides access to a variety of models and methods. Synthetic data can be generated within the interface to fill missing values, balance class labels, or generate entirely new datasets. It also provides support for feature evaluation and generates explainability scores to indicate which features influence the output the most. We present CLASSify, an open-source tool for simplifying the user experience of solving classification problems without the need for knowledge of machine learning.

Reasoning is central to human intelligence. However, fallacious arguments are common, and some exacerbate problems such as spreading misinformation about climate change. In this paper, we propose the task of logical fallacy detection, and provide a new dataset (Logic) of logical fallacies generally found in text, together with an additional challenge set for detecting logical fallacies in climate change claims (LogicClimate). Detecting logical fallacies is a hard problem as the model must understand the underlying logical structure of the argument. We find that existing pretrained large language models perform poorly on this task. In contrast, we show that a simple structure-aware classifier outperforms the best language model by 5.46% on Logic and 4.51% on LogicClimate. We encourage future work to explore this task as (a) it can serve as a new reasoning challenge for language models, and (b) it can have potential applications in tackling the spread of misinformation. Our dataset and code are available at https://github.com/causalNLP/logical-fallacy

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we use 14 large language models and investigate their syllogistic reasoning capabilities in terms of symbolic inferences as well as natural language understanding. Even though this reasoning mechanism is not a uniform emergent property across LLMs, the perfect symbolic performances in certain models make us wonder whether LLMs are becoming more and more formal reasoning mechanisms, rather than making explicit the nuances of human reasoning.

Large-scale datasets for natural language inference are created by presenting crowd workers with a sentence (premise), and asking them to generate three new sentences (hypotheses) that it entails, contradicts, or is logically neutral with respect to. We show that, in a significant portion of such data, this protocol leaves clues that make it possible to identify the label by looking only at the hypothesis, without observing the premise. Specifically, we show that a simple text categorization model can correctly classify the hypothesis alone in about 67% of SNLI (Bowman et. al, 2015) and 53% of MultiNLI (Williams et. al, 2017). Our analysis reveals that specific linguistic phenomena such as negation and vagueness are highly correlated with certain inference classes. Our findings suggest that the success of natural language inference models to date has been overestimated, and that the task remains a hard open problem.

Recent advances in semi-supervised semantic segmentation have been heavily reliant on pseudo labeling to compensate for limited labeled data, disregarding the valuable relational knowledge among semantic concepts. To bridge this gap, we devise LogicDiag, a brand new neural-logic semi-supervised learning framework. Our key insight is that conflicts within pseudo labels, identified through symbolic knowledge, can serve as strong yet commonly ignored learning signals. LogicDiag resolves such conflicts via reasoning with logic-induced diagnoses, enabling the recovery of (potentially) erroneous pseudo labels, ultimately alleviating the notorious error accumulation problem. We showcase the practical application of LogicDiag in the data-hungry segmentation scenario, where we formalize the structured abstraction of semantic concepts as a set of logic rules. Extensive experiments on three standard semi-supervised semantic segmentation benchmarks demonstrate the effectiveness and generality of LogicDiag. Moreover, LogicDiag highlights the promising opportunities arising from the systematic integration of symbolic reasoning into the prevalent statistical, neural learning approaches.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions provided are not consistent with how LMs are trained, process information, and generate new tokens. To illustrate this incommensurability we assume the view that transformer-based LMs implement an implicit finite-order Markov kernel mapping contexts to conditional token distributions. In this view, reasoning-like outputs correspond to statistical regularities and approximate statistical invariances in the learned kernel rather than the implementation of explicit logical mechanisms. This view is illustrative of the claim that LMs are "statistical pattern matchers"" and not genuine reasoners and provides a perspective that clarifies why reasoning-like outputs arise in LMs without any guarantees of logical consistency. This distinction is fundamental to how epistemic uncertainty is evaluated in LMs. We invite a discussion on the importance of how the computational processes of the systems we build and analyze in NLP research are described.

In this thesis, I evaluate the performance of Large Language Models (LLMs) on the Law School Admissions Test (LSAT), specifically the Logic Games section of the test. I focus on this section because it presents a complex logical reasoning task and thus is a valuable source of data for evaluating how modern, increasingly capable LLMs can handle hard logical reasoning tasks. I construct a dataset of LSAT logic games and their associated metadata, and extensively evaluate LLMs' performance in a Chain-of-Thought prompting setting. Given the weak performance in this setting, I explore other prompting frameworks on a smaller subset of the dataset, adapting ideas from Reflexion to this task. This results in a substantially improved accuracy of 70 percent for GPT-4 and 46 percent for GPT-3.5 on this data subset, highlighting the capacity of LLMs to revise their logical errors, despite initially weak performance. Finally, I analyze the types of logic games that models perform better or worse on, as well as the types of logical errors I observe from human annotation, providing detailed insights on the logical reasoning capabilities of LLMs.

These handouts are designed for people who is just starting involved with the topic artificial neural networks. We show how it works a single artificial neuron (McCulloch & Pitt model), mathematically and graphically. We do explain the delta rule, a learning algorithm to find the neuron weights. We also present some examples in MATLAB/Octave. There are examples for classification task for lineal and non-lineal problems. At the end, we present an artificial neural network, a feed-forward neural network along its learning algorithm backpropagation. ----- Estos apuntes est\'an dise\~nados para personas que por primera vez se introducen en el tema de las redes neuronales artificiales. Se muestra el funcionamiento b\'asico de una neurona, matem\'aticamente y gr\'aficamente. Se explica la Regla Delta, algoritmo deaprendizaje para encontrar los pesos de una neurona. Tambi\'en se muestran ejemplos en MATLAB/Octave. Hay ejemplos para problemas de clasificaci\'on, para problemas lineales y no-lineales. En la parte final se muestra la arquitectura de red neuronal artificial conocida como backpropagation.

Logic reasoning in natural language has been recognized as an important measure of human intelligence for Large Language Models (LLMs). Popular benchmarks may entangle multiple reasoning skills and thus provide unfaithful evaluations on the logic reasoning skill. Meanwhile, existing logic reasoning benchmarks are limited in language diversity and their distributions are deviated from the distribution of an ideal logic reasoning benchmark, which may lead to biased evaluation results. This paper thereby proposes a new classical logic benchmark DivLogicEval, consisting of natural sentences composed of diverse statements in a counterintuitive way. To ensure a more reliable evaluation, we also introduce a new evaluation metric that mitigates the influence of bias and randomness inherent in LLMs. Through experiments, we demonstrate the extent to which logical reasoning is required to answer the questions in DivLogicEval and compare the performance of different popular LLMs in conducting logical reasoning.

Dense retrieval, which aims to encode the semantic information of arbitrary text into dense vector representations or embeddings, has emerged as an effective and efficient paradigm for text retrieval, consequently becoming an essential component in various natural language processing systems. These systems typically focus on optimizing the embedding space by attending to the relevance of text pairs, while overlooking the Boolean logic inherent in language, which may not be captured by current training objectives. In this work, we first investigate whether current retrieval systems can comprehend the Boolean logic implied in language. To answer this question, we formulate the task of Boolean Dense Retrieval and collect a benchmark dataset, BoolQuestions, which covers complex queries containing basic Boolean logic and corresponding annotated passages. Through extensive experimental results on the proposed task and benchmark dataset, we draw the conclusion that current dense retrieval systems do not fully understand Boolean logic in language, and there is a long way to go to improve our dense retrieval systems. Furthermore, to promote further research on enhancing the understanding of Boolean logic for language models, we explore Boolean operation on decomposed query and propose a contrastive continual training method that serves as a strong baseline for the research community.

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if P and Q, then R" for some propositions P, Q, and R. Next, we prove that although small transformers can faithfully follow such rules, maliciously crafted prompts can still mislead both theoretical constructions and models learned from data. Furthermore, we demonstrate that popular attack algorithms on LLMs find adversarial prompts and induce attention patterns that align with our theory. Our novel logic-based framework provides a foundation for studying LLMs in rule-based settings, enabling a formal analysis of tasks like logical reasoning and jailbreak attacks.

Most positive and unlabeled data is subject to selection biases. The labeled examples can, for example, be selected from the positive set because they are easier to obtain or more obviously positive. This paper investigates how learning can be ena BHbled in this setting. We propose and theoretically analyze an empirical-risk-based method for incorporating the labeling mechanism. Additionally, we investigate under which assumptions learning is possible when the labeling mechanism is not fully understood and propose a practical method to enable this. Our empirical analysis supports the theoretical results and shows that taking into account the possibility of a selection bias, even when the labeling mechanism is unknown, improves the trained classifiers.

As machine learning systems become ubiquitous, there has been a surge of interest in interpretable machine learning: systems that provide explanation for their outputs. These explanations are often used to qualitatively assess other criteria such as safety or non-discrimination. However, despite the interest in interpretability, there is very little consensus on what interpretable machine learning is and how it should be measured. In this position paper, we first define interpretability and describe when interpretability is needed (and when it is not). Next, we suggest a taxonomy for rigorous evaluation and expose open questions towards a more rigorous science of interpretable machine learning.

Deep neural networks have proved to be a very effective way to perform classification tasks. They excel when the input data is high dimensional, the relationship between the input and the output is complicated, and the number of labeled training examples is large. But it is hard to explain why a learned network makes a particular classification decision on a particular test case. This is due to their reliance on distributed hierarchical representations. If we could take the knowledge acquired by the neural net and express the same knowledge in a model that relies on hierarchical decisions instead, explaining a particular decision would be much easier. We describe a way of using a trained neural net to create a type of soft decision tree that generalizes better than one learned directly from the training data.

In this paper, we present a new theoretical approach for enabling domain knowledge acquisition by intelligent systems. We introduce a hybrid model that starts with minimal input knowledge in the form of an upper ontology of concepts, stores and reasons over this knowledge through a knowledge graph database and learns new information through a Logic Neural Network. We study the behavior of this architecture when handling new data and show that the final system is capable of enriching its current knowledge as well as extending it to new domains.

Machine reading is a fundamental task for testing the capability of natural language understanding, which is closely related to human cognition in many aspects. With the rising of deep learning techniques, algorithmic models rival human performances on simple QA, and thus increasingly challenging machine reading datasets have been proposed. Though various challenges such as evidence integration and commonsense knowledge have been integrated, one of the fundamental capabilities in human reading, namely logical reasoning, is not fully investigated. We build a comprehensive dataset, named LogiQA, which is sourced from expert-written questions for testing human Logical reasoning. It consists of 8,678 QA instances, covering multiple types of deductive reasoning. Results show that state-of-the-art neural models perform by far worse than human ceiling. Our dataset can also serve as a benchmark for reinvestigating logical AI under the deep learning NLP setting. The dataset is freely available at https://github.com/lgw863/LogiQA-dataset

Large language models (LLMs) are susceptible to a variety of risks, from non-faithful output to biased and toxic generations. Due to several limiting factors surrounding LLMs (training cost, API access, data availability, etc.), it may not always be feasible to impose direct safety constraints on a deployed model. Therefore, an efficient and reliable alternative is required. To this end, we present our ongoing efforts to create and deploy a library of detectors: compact and easy-to-build classification models that provide labels for various harms. In addition to the detectors themselves, we discuss a wide range of uses for these detector models - from acting as guardrails to enabling effective AI governance. We also deep dive into inherent challenges in their development and discuss future work aimed at making the detectors more reliable and broadening their scope.

We present a new approach for mitigating unfairness in learned classifiers. In particular, we focus on binary classification tasks over individuals from two populations, where, as our criterion for fairness, we wish to achieve similar false positive rates in both populations, and similar false negative rates in both populations. As a proof of concept, we implement our approach and empirically evaluate its ability to achieve both fairness and accuracy, using datasets from the fields of criminal risk assessment, credit, lending, and college admissions.

We present a new logic-based inference engine for natural language inference (NLI) called MonaLog, which is based on natural logic and the monotonicity calculus. In contrast to existing logic-based approaches, our system is intentionally designed to be as lightweight as possible, and operates using a small set of well-known (surface-level) monotonicity facts about quantifiers, lexical items and tokenlevel polarity information. Despite its simplicity, we find our approach to be competitive with other logic-based NLI models on the SICK benchmark. We also use MonaLog in combination with the current state-of-the-art model BERT in a variety of settings, including for compositional data augmentation. We show that MonaLog is capable of generating large amounts of high-quality training data for BERT, improving its accuracy on SICK.

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

This paper introduces a new approach to using Large Language Models (LLMs) for classification tasks, which are typically handled using Machine Learning (ML) models. Unlike ML models that rely heavily on data cleaning and feature engineering, this method streamlines the process using LLMs. This paper proposes a new concept called "Language Model Learning (LML)" powered by a new method called "Data-Augmented Prediction (DAP)". The classification is performed by LLMs using a method similar to humans manually exploring and understanding the data and deciding classifications using data as a reference. Training data is summarized and evaluated to determine the features that lead to the classification of each label the most. In the process of DAP, the system uses the data summary to automatically create a query, which is used to retrieve relevant rows from the dataset. A classification is generated by the LLM using data summary and relevant rows, ensuring satisfactory accuracy even with complex data. Usage of data summary and similar data in DAP ensures context-aware decision-making. The proposed method uses the words "Act as an Explainable Machine Learning Model" in the prompt to enhance the interpretability of the predictions by allowing users to review the logic behind each prediction. In some test cases, the system scored an accuracy above 90%, proving the effectiveness of the system and its potential to outperform conventional ML models in various scenarios. The code is available at https://github.com/Pro-GenAI/LML-DAP

1. The popularity of Machine learning (ML), Deep learning (DL), and Artificial intelligence (AI) has risen sharply in recent years. Despite this spike in popularity, the inner workings of ML and DL algorithms are often perceived as opaque, and their relationship to classical data analysis tools remains debated. 2. Although it is often assumed that ML and DL excel primarily at making predictions, ML and DL can also be used for analytical tasks traditionally addressed with statistical models. Moreover, most recent discussions and reviews on ML focus mainly on DL, missing out on synthesizing the wealth of ML algorithms with different advantages and general principles. 3. Here, we provide a comprehensive overview of the field of ML and DL, starting by summarizing its historical developments, existing algorithm families, differences to traditional statistical tools, and universal ML principles. We then discuss why and when ML and DL models excel at prediction tasks and where they could offer alternatives to traditional statistical methods for inference, highlighting current and emerging applications for ecological problems. Finally, we summarize emerging trends such as scientific and causal ML, explainable AI, and responsible AI that may significantly impact ecological data analysis in the future. 4. We conclude that ML and DL are powerful new tools for predictive modeling and data analysis. The superior performance of ML and DL algorithms compared to statistical models can be explained by their higher flexibility and automatic data-dependent complexity optimization. However, their use for causal inference is still disputed as the focus of ML and DL methods on predictions creates challenges for the interpretation of these models. Nevertheless, we expect ML and DL to become an indispensable tool in E&E, comparable to other traditional statistical tools.

Recent advances in Large Vision-Language models (LVLM) have spurred significant progress in document parsing task. Compared to traditional pipeline-based methods, end-to-end paradigms have shown their excellence in converting PDF images into structured outputs through integrated Optical Character Recognition (OCR), table recognition, mathematical formula recognition and so on. However, the absence of explicit analytical stages for document layouts and reading orders limits the LVLM's capability in handling complex document types such as multi-column newspapers or posters. To address this limitation, we propose in this report Logics-Parsing: an end-to-end LVLM-based model augmented with reinforcement learning. Our model incorporates meticulously designed reward mechanisms to optimize complex layout analysis and reading order inference. In addition, we expand the model's versatility by incorporating diverse data types such as chemical formulas and handwritten Chinese characters into supervised fine-tuning. Finally, to enable rigorous evaluation of our approach, we introduce LogicsParsingBench, a curated set of 1,078 page-level PDF images spanning nine major categories and over twenty sub-categories, which will be released later. Comprehensive experiments conducted on LogicsParsingBench have validated the efficacy and State-of-the-art (SOTA) performance of our proposed model across diverse document analysis scenarios. Project Page: https://github.com/alibaba/Logics-Parsing

Parallel neurosymbolic architectures have been applied effectively in NLP by distilling knowledge from a logic theory into a deep model.However, prior art faces several limitations including supporting restricted forms of logic theories and relying on the assumption of independence between the logic and the deep network. We present Concordia, a framework overcoming the limitations of prior art. Concordia is agnostic both to the deep network and the logic theory offering support for a wide range of probabilistic theories. Our framework can support supervised training of both components and unsupervised training of the neural component. Concordia has been successfully applied to tasks beyond NLP and data classification, improving the accuracy of state-of-the-art on collective activity detection, entity linking and recommendation tasks.

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the automated dialog thread to stay focussed on the task by synthesizing a prompt that summarizes the depth-first steps taken so far. Our algorithm is derived from a simple recursive descent implementation of a Horn Clause interpreter, except that we accommodate our logic engine to fit the natural language reasoning patterns LLMs have been trained on. Semantic similarity to ground-truth facts or oracle advice from another LLM instance is used to restrict the search space and validate the traces of justification steps returned as answers. At the end, the unique minimal model of a generated Horn Clause program collects the results of the reasoning process. As applications, we sketch implementations of consequence predictions, causal explanations, recommendation systems and topic-focussed exploration of scientific literature.

In this research. we analyze the potential of Feature Density (HD) as a way to comparatively estimate machine learning (ML) classifier performance prior to training. The goal of the study is to aid in solving the problem of resource-intensive training of ML models which is becoming a serious issue due to continuously increasing dataset sizes and the ever rising popularity of Deep Neural Networks (DNN). The issue of constantly increasing demands for more powerful computational resources is also affecting the environment, as training large-scale ML models are causing alarmingly-growing amounts of CO2, emissions. Our approach 1s to optimize the resource-intensive training of ML models for Natural Language Processing to reduce the number of required experiments iterations. We expand on previous attempts on improving classifier training efficiency with FD while also providing an insight to the effectiveness of various linguistically-backed feature preprocessing methods for dialog classification, specifically cyberbullying detection.

Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalizes the structural interplay between residuals and parameters in supervised learning. The present paper focuses on the multiple linear regression model, which represents the most basic form of supervised learning. By defining two concrete categories corresponding to parameters and data, along with an adjoint pair of functors between them, we introduce our categorical formulation of supervised learning. We show that the essential structure of this framework is captured by what we call the Gauss-Markov Adjunction. Within this setting, the dual flow of information can be explicitly described as a correspondence between variations in parameters and residuals. The ordinary least squares estimator for the parameters and the minimum residual are related via the preservation of limits by the right adjoint functor. Furthermore, we position this formulation as an instance of extended denotational semantics for supervised learning, and propose applying a semantic perspective developed in theoretical computer science as a formal foundation for Explicability in AI.

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct a systematic study of the inductive reasoning capabilities of LMs through iterative hypothesis refinement, a technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs a three-step process: proposing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal hypothesis proposers (i.e., generating candidate rules), and when coupled with a (task-specific) symbolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling inductive reasoners, showing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.e., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks.

Logical reasoning is a fundamental task in natural language processing that presents significant challenges to Large Language Models (LLMs). The inherent characteristics of logical reasoning makes it well-suited for symbolic representations such as first-order logic (FOL). Research in symbolic logical reasoning explored FOL generation using state-of-the-art LLMs (i.e., GPT-4) to produce FOL translations of natural language (NL) statements, but errors in translation are usually not the focus. We address this by categorizing the translation errors in FOL statements generated by LLMs. To make progress towards improving the quality of FOL translations for smaller language models such as LLaMA-2 13B and Mistral 7B, we create ProofFOL, a high-quality FOL-annotated subset of ProofWriter dataset using GPT-4o. The models fine-tuned on this silver standard data achieve a significant gain in performance when compared to larger language models such as LLaMA-2 70B. In addition to improving the model using large data, we also tackle the issue of data scarcity and introduce an incremental framework encompassing of data augmentation and verification steps. In the augmentation process, a single pair of (premises, conclusion) is split into multiple new instances based on the predicates and FOLs. This data is used for fine-tuning, and the inference on this model generates FOLs with fewer errors over the model trained on the original data. Our investigation on the translation errors leads to generation of a perturbation dataset, which is used to train a verifier that corrects potential syntactic and semantic FOL translation errors. We demonstrate an efficient method for making the most of a limited existing human-annotated dataset. Our results show state-of-the-art performance for ProofWriter and ProntoQA datasets using ProofFOL on LLaMA-2 and Mistral models.

Despite their linguistic competence, Large Language models (LLMs) often exhibit limitations in their ability to reason reliably and flexibly. To address this, we propose a neurosymbolic approach that prompts LLMs to extract and encode all relevant information from a problem statement as logical code statements, and then use a logic programming language (Prolog) to conduct the iterative computations of explicit deductive reasoning. Our approach significantly enhances the performance of LLMs on the standard mathematical reasoning benchmark, GSM8k, and the Navigate dataset from the BIG-bench dataset. Additionally, we introduce a novel dataset, the Non-Linear Reasoning (NLR) dataset, consisting of 55 unique word problems that target the shortcomings of the next token prediction paradigm of LLMs and require complex non-linear reasoning but only basic arithmetic skills to solve. Our findings demonstrate that the integration of Prolog enables LLMs to achieve high performance on the NLR dataset, which even the most advanced language models (including GPT4) fail to solve using text only.

Legislation can be viewed as a body of prescriptive rules expressed in natural language. The application of legislation to facts of a case we refer to as statutory reasoning, where those facts are also expressed in natural language. Computational statutory reasoning is distinct from most existing work in machine reading, in that much of the information needed for deciding a case is declared exactly once (a law), while the information needed in much of machine reading tends to be learned through distributional language statistics. To investigate the performance of natural language understanding approaches on statutory reasoning, we introduce a dataset, together with a legal-domain text corpus. Straightforward application of machine reading models exhibits low out-of-the-box performance on our questions, whether or not they have been fine-tuned to the legal domain. We contrast this with a hand-constructed Prolog-based system, designed to fully solve the task. These experiments support a discussion of the challenges facing statutory reasoning moving forward, which we argue is an interesting real-world task that can motivate the development of models able to utilize prescriptive rules specified in natural language.

Most applications of machine learning to classification assume a closed set of balanced classes. This is at odds with the real world, where class occurrence statistics often follow a long-tailed power-law distribution and it is unlikely that all classes are seen in a single sample. Nonparametric Bayesian models naturally capture this phenomenon, but have significant practical barriers to widespread adoption, namely implementation complexity and computational inefficiency. To address this, we present a method for extracting the inductive bias from a nonparametric Bayesian model and transferring it to an artificial neural network. By simulating data with a nonparametric Bayesian prior, we can metalearn a sequence model that performs inference over an unlimited set of classes. After training, this "neural circuit" has distilled the corresponding inductive bias and can successfully perform sequential inference over an open set of classes. Our experimental results show that the metalearned neural circuit achieves comparable or better performance than particle filter-based methods for inference in these models while being faster and simpler to use than methods that explicitly incorporate Bayesian nonparametric inference.

Internet is one of the important inventions and a large number of persons are its users. These persons use this for different purposes. There are different social media platforms that are accessible to these users. Any user can make a post or spread the news through the online platforms. These platforms do not verify the users or their posts. So some of the users try to spread fake news through these platforms. These news can be propaganda against an individual, society, organization or political party. A human being is unable to detect all these fake news. So there is a need for machine learning classifiers that can detect these fake news automatically. Use of machine learning classifiers for detecting fake news is described in this systematic literature review.

Retrieval-Augmented Generation (RAG) systems have shown promise in enhancing the performance of Large Language Models (LLMs). However, these systems face challenges in effectively integrating external knowledge with the LLM's internal knowledge, often leading to issues with misleading or unhelpful information. This work aims to provide a systematic study on knowledge checking in RAG systems. We conduct a comprehensive analysis of LLM representation behaviors and demonstrate the significance of using representations in knowledge checking. Motivated by the findings, we further develop representation-based classifiers for knowledge filtering. We show substantial improvements in RAG performance, even when dealing with noisy knowledge databases. Our study provides new insights into leveraging LLM representations for enhancing the reliability and effectiveness of RAG systems.

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary, limiting the generalizability of acquired reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. Then, using the proposed corpora, which we name FLD (Formal Logic Deduction), we first evaluate and analyze the logical reasoning ability of the latest LLMs. Even GPT-4 can solve only half of the problems, suggesting that pure logical reasoning isolated from knowledge is still challenging for the LLMs, and additional training specialized in logical reasoning is indeed essential. We next empirically verify that LMs trained on FLD corpora acquire more generalizable reasoning ability. Furthermore, we identify the aspects of reasoning ability on which deduction corpora can enhance LMs and those on which they cannot, and discuss future directions on each aspect. The released corpora serve both as learning resources and as challenging benchmarks.

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive) in its questions. We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of state-of-the-art MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. These findings highlight the critical limitations and performance imbalances of current MLLMs in diverse logical reasoning scenarios, providing comprehensive and systematic insights into the understanding and evaluation of reasoning capabilities.

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

Users increasingly rely on Large Language Models (LLMs) for Deep Research, using them to synthesize diverse sources into structured reports that support understanding and action. In this context, the practical reliability of such reports hinges on logical quality: whether the report's claims and arguments are explicitly supported and can be trusted as a basis for downstream use, rather than merely appearing fluent or informative. However, current evaluation frameworks largely overlook this requirement. To bridge this gap, we introduce ReportLogic, a benchmark that quantifies report-level logical quality through a reader-centric lens of auditability. Specifically, ReportLogic adopts a hierarchical taxonomy that evaluates whether readers can (1) trace an on-topic report structure with a unified analytical arc (Macro-Logic), (2) understand the progression with necessary context (Expositional-Logic), and (3) verify conclusions via explicit claim--support (Structural-Logic). Based on this taxonomy, we construct a human-annotated rubric-guided dataset and train an open-source LogicJudge for scalable evaluation. We further evaluate judge robustness via adversarial attacks, showing that off-the-shelf LLM judges are frequently influenced by superficial cues (e.g., verbosity), and reasoning modes can mask broken support relations. Overall, our results provide actionable guidance for building more robust logic evaluators and improving the logical reliability of LLM-generated reports.

Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties. While translating FOL into human-readable English is relatively straightforward, the inverse problem, converting NL to FOL (NL-FOL translation), has remained a longstanding challenge, for both humans and machines. Although the emergence of Large Language Models (LLMs) promised a breakthrough, recent literature provides contrasting results on their ability to perform NL-FOL translation. In this work, we provide a threefold contribution. First, we critically examine existing datasets and protocols for evaluating NL-FOL translation performance, revealing key limitations that may cause a misrepresentation of LLMs' actual capabilities. Second, to overcome these shortcomings, we propose a novel evaluation protocol explicitly designed to distinguish genuine semantic-level logical understanding from superficial pattern recognition, memorization, and dataset contamination. Third, using this new approach, we show that state-of-the-art, dialogue-oriented LLMs demonstrate strong NL-FOL translation skills and a genuine grasp of sentence-level logic, whereas embedding-centric models perform markedly worse.

Interpretability in machine learning (ML) is crucial for high stakes decisions and troubleshooting. In this work, we provide fundamental principles for interpretable ML, and dispel common misunderstandings that dilute the importance of this crucial topic. We also identify 10 technical challenge areas in interpretable machine learning and provide history and background on each problem. Some of these problems are classically important, and some are recent problems that have arisen in the last few years. These problems are: (1) Optimizing sparse logical models such as decision trees; (2) Optimization of scoring systems; (3) Placing constraints into generalized additive models to encourage sparsity and better interpretability; (4) Modern case-based reasoning, including neural networks and matching for causal inference; (5) Complete supervised disentanglement of neural networks; (6) Complete or even partial unsupervised disentanglement of neural networks; (7) Dimensionality reduction for data visualization; (8) Machine learning models that can incorporate physics and other generative or causal constraints; (9) Characterization of the "Rashomon set" of good models; and (10) Interpretable reinforcement learning. This survey is suitable as a starting point for statisticians and computer scientists interested in working in interpretable machine learning.

Large language models (LLMs) have shown incredible performance in completing various real-world tasks. The current knowledge learning paradigm of LLMs is mainly based on learning from examples, in which LLMs learn the internal rule implicitly from a certain number of supervised examples. However, this learning paradigm may not well learn those complicated rules, especially when the training examples are limited. We are inspired that humans can learn the new tasks or knowledge in another way by learning from rules. That is, humans can learn new tasks or grasps new knowledge quickly and generalize well given only a detailed rule and a few optional examples. Therefore, in this paper, we aim to explore the feasibility of this new learning paradigm, which targets on encoding rule-based knowledge into LLMs. We further propose rule distillation, which first uses the strong in-context abilities of LLMs to extract the knowledge from the textual rules, and then explicitly encode the knowledge into the parameters of LLMs by learning from the above in-context signals produced inside the model. Our experiments show that making LLMs learn from rules by our method is much more efficient than example-based learning in both the sample size and generalization ability. Warning: This paper may contain examples with offensive content.

Courts must justify their decisions, but systematically analyzing judicial reasoning at scale remains difficult. This study tests claims about formalistic judging in Central and Eastern Europe (CEE) by developing automated methods to detect and classify judicial reasoning in decisions of Czech Supreme Courts using state-of-the-art natural language processing methods. We create the MADON dataset of 272 decisions from two Czech Supreme Courts with expert annotations of 9,183 paragraphs with eight argument types and holistic formalism labels for supervised training and evaluation. Using a corpus of 300,511 Czech court decisions, we adapt transformer LLMs to Czech legal domain through continued pretraining and we experiment with methods to address dataset imbalance including asymmetric loss and class weighting. The best models can detect argumentative paragraphs (82.6% Bal-F1), classify traditional types of legal argument (77.5% Bal-F1), and classify decisions as formalistic/non-formalistic (83.8% Bal-F1). Our three-stage pipeline combining ModernBERT, Llama 3.1, and traditional feature-based machine learning achieves promising results for decision classification while reducing computational costs and increasing explainability. Empirically, we challenge prevailing narratives about CEE formalism. We demonstrate that legal argument mining enables promising judicial philosophy classification and highlight its potential for other important tasks in computational legal studies. Our methodology can be used across jurisdictions, and our entire pipeline, datasets, guidelines, models, and source codes are available at https://github.com/trusthlt/madon.

Large Language Models (LLMs) have shown remarkable abilities in structured reasoning and symbolic tasks, with coding emerging as a particular area of strength. This success has sparked growing interest in applying LLMs to mathematics, both in informal problem-solving and formal theorem proving. However, progress in formal mathematics has proven to be significantly more difficult, despite surface-level similarities between programming and proof construction. This discrepancy raises important questions about how LLMs ``reason'', how they are supervised, and whether they internally track a notion of computational or deductive state. In this article, we address the state-of-the-art of the discipline, focusing on recent models and benchmarks, and explore three central issues at the intersection of machine learning and mathematical cognition: (i) the trade-offs between formal and informal mathematics as training domains; (ii) the deeper reasons why proof generation remains more brittle than code synthesis; (iii) and the question of whether LLMs represent, or merely mimic, a notion of evolving logical state. Our goal is not to draw hard boundaries, but to identify where the current limits lie, and how they might be extended.

We contribute a theoretical and operational framework for neurosymbolic AI called DeepLog. DeepLog introduces building blocks and primitives for neurosymbolic AI that make abstraction of commonly used representations and computational mechanisms used in neurosymbolic AI. DeepLog can represent and emulate a wide range of neurosymbolic systems. It consists of two key components. The first is the DeepLog language for specifying neurosymbolic models and inference tasks. This language consists of an annotated neural extension of grounded first-order logic, and makes abstraction of the type of logic, e.g. boolean, fuzzy or probabilistic, and whether logic is used in the architecture or in the loss function. The second DeepLog component is situated at the computational level and uses extended algebraic circuits as computational graphs. Together these two components are to be considered as a neurosymbolic abstract machine, with the DeepLog language as the intermediate level of abstraction and the circuits level as the computational one. DeepLog is implemented in software, relies on the latest insights in implementing algebraic circuits on GPUs, and is declarative in that it is easy to obtain different neurosymbolic models by making different choices for the underlying algebraic structures and logics. The generality and efficiency of the DeepLog neurosymbolic machine is demonstrated through an experimental comparison between 1) different fuzzy and probabilistic logics, 2) between using logic in the architecture or in the loss function, and 3) between a standalone CPU-based implementation of a neurosymbolic AI system and a DeepLog GPU-based one.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Despite alarm over the reliance of machine learning systems on so-called spurious patterns, the term lacks coherent meaning in standard statistical frameworks. However, the language of causality offers clarity: spurious associations are due to confounding (e.g., a common cause), but not direct or indirect causal effects. In this paper, we focus on natural language processing, introducing methods and resources for training models less sensitive to spurious patterns. Given documents and their initial labels, we task humans with revising each document so that it (i) accords with a counterfactual target label; (ii) retains internal coherence; and (iii) avoids unnecessary changes. Interestingly, on sentiment analysis and natural language inference tasks, classifiers trained on original data fail on their counterfactually-revised counterparts and vice versa. Classifiers trained on combined datasets perform remarkably well, just shy of those specialized to either domain. While classifiers trained on either original or manipulated data alone are sensitive to spurious features (e.g., mentions of genre), models trained on the combined data are less sensitive to this signal. Both datasets are publicly available.

Machine learning has opened up new tools for financial fraud detection. Using a sample of annotated transactions, a machine learning classification algorithm learns to detect frauds. With growing credit card transaction volumes and rising fraud percentages there is growing interest in finding appropriate machine learning classifiers for detection. However, fraud data sets are diverse and exhibit inconsistent characteristics. As a result, a model effective on a given data set is not guaranteed to perform on another. Further, the possibility of temporal drift in data patterns and characteristics over time is high. Additionally, fraud data has massive and varying imbalance. In this work, we evaluate sampling methods as a viable pre-processing mechanism to handle imbalance and propose a data-driven classifier selection strategy for characteristic highly imbalanced fraud detection data sets. The model derived based on our selection strategy surpasses peer models, whilst working in more realistic conditions, establishing the effectiveness of the strategy.

The aim of Logic2Text is to generate controllable and faithful texts conditioned on tables and logical forms, which not only requires a deep understanding of the tables and logical forms, but also warrants symbolic reasoning over the tables. State-of-the-art methods based on pre-trained models have achieved remarkable performance on the standard test dataset. However, we question whether these methods really learn how to perform logical reasoning, rather than just relying on the spurious correlations between the headers of the tables and operators of the logical form. To verify this hypothesis, we manually construct a set of counterfactual samples, which modify the original logical forms to generate counterfactual logical forms with rarely co-occurred table headers and logical operators. SOTA methods give much worse results on these counterfactual samples compared with the results on the original test dataset, which verifies our hypothesis. To deal with this problem, we firstly analyze this bias from a causal perspective, based on which we propose two approaches to reduce the model's reliance on the shortcut. The first one incorporates the hierarchical structure of the logical forms into the model. The second one exploits automatically generated counterfactual data for training. Automatic and manual experimental results on the original test dataset and the counterfactual dataset show that our method is effective to alleviate the spurious correlation. Our work points out the weakness of previous methods and takes a further step toward developing Logic2Text models with real logical reasoning ability.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

Interpretable machine learning aims to provide transparent models whose decision-making processes can be readily understood by humans. Recent advances in rule-based approaches, such as expressive Boolean formulas (BoolXAI), offer faithful and compact representations of model behavior. However, for non-technical stakeholders, main challenges remain in practice: (i) selecting semantically meaningful features and (ii) translating formal logical rules into accessible explanations. In this work, we propose BoolXLLM , as a hybrid framework that integrates Large Language Models (LLMs) into the end-to-end pipeline of Boolean rule learning. We augment BoolXAI , an expressive Boolean rule-based classifier, with LLMs at three critical stages: (1) feature selection, where LLMs guide the identification of domain-relevant variables; (2) threshold recommendation, where LLMs propose semantically meaningful discretization strategies for numerical features; and (3) rule compression and interpretation, where Boolean rules are translated into natural language explanations at both global and local levels. This integration bridges formal, faithful explanations with human-understandable narratives. This allows build an explainable AI system that is both theoretically grounded and accessible to non-experts. Early empirical results demonstrate that LLM-assisted pipelines improve interpretability while maintaining competitive predictive performance. Our work highlights the promise of combining symbolic reasoning with language-based models for human-centered explainability.

Reviewing contracts is a time-consuming procedure that incurs large expenses to companies and social inequality to those who cannot afford it. In this work, we propose "document-level natural language inference (NLI) for contracts", a novel, real-world application of NLI that addresses such problems. In this task, a system is given a set of hypotheses (such as "Some obligations of Agreement may survive termination.") and a contract, and it is asked to classify whether each hypothesis is "entailed by", "contradicting to" or "not mentioned by" (neutral to) the contract as well as identifying "evidence" for the decision as spans in the contract. We annotated and release the largest corpus to date consisting of 607 annotated contracts. We then show that existing models fail badly on our task and introduce a strong baseline, which (1) models evidence identification as multi-label classification over spans instead of trying to predict start and end tokens, and (2) employs more sophisticated context segmentation for dealing with long documents. We also show that linguistic characteristics of contracts, such as negations by exceptions, are contributing to the difficulty of this task and that there is much room for improvement.

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage parametric knowledge in formal reasoning despite their inconsistency? We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic. We provide experimental evidence for the feasibility of the method by evaluating the function using datasets created from several short-form factuality benchmarks. Unlike prior work, our method offers a theoretical framework for neuro-symbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

E-commerce platforms categorize their products into a multi-level taxonomy tree with thousands of leaf categories. Conventional methods for product categorization are typically based on machine learning classification algorithms. These algorithms take product information as input (e.g., titles and descriptions) to classify a product into a leaf category. In this paper, we propose a new paradigm based on machine translation. In our approach, we translate a product's natural language description into a sequence of tokens representing a root-to-leaf path in a product taxonomy. In our experiments on two large real-world datasets, we show that our approach achieves better predictive accuracy than a state-of-the-art classification system for product categorization. In addition, we demonstrate that our machine translation models can propose meaningful new paths between previously unconnected nodes in a taxonomy tree, thereby transforming the taxonomy into a directed acyclic graph (DAG). We discuss how the resultant taxonomy DAG promotes user-friendly navigation, and how it is more adaptable to new products.

Explaining Artificial Intelligence (AI) decisions is a major challenge nowadays in AI, in particular when applied to sensitive scenarios like medicine and law. However, the need to explain the rationale behind decisions is a main issue also for human-based deliberation as it is important to justify why a certain decision has been taken. Resident medical doctors for instance are required not only to provide a (possibly correct) diagnosis, but also to explain how they reached a certain conclusion. Developing new tools to aid residents to train their explanation skills is therefore a central objective of AI in education. In this paper, we follow this direction, and we present, to the best of our knowledge, the first multilingual dataset for Medical Question Answering where correct and incorrect diagnoses for a clinical case are enriched with a natural language explanation written by doctors. These explanations have been manually annotated with argument components (i.e., premise, claim) and argument relations (i.e., attack, support), resulting in the Multilingual CasiMedicos-Arg dataset which consists of 558 clinical cases in four languages (English, Spanish, French, Italian) with explanations, where we annotated 5021 claims, 2313 premises, 2431 support relations, and 1106 attack relations. We conclude by showing how competitive baselines perform over this challenging dataset for the argument mining task.

Medical applications challenge today's text categorization techniques by demanding both high accuracy and ease-of-interpretation. Although deep learning has provided a leap ahead in accuracy, this leap comes at the sacrifice of interpretability. To address this accuracy-interpretability challenge, we here introduce, for the first time, a text categorization approach that leverages the recently introduced Tsetlin Machine. In all brevity, we represent the terms of a text as propositional variables. From these, we capture categories using simple propositional formulae, such as: if "rash" and "reaction" and "penicillin" then Allergy. The Tsetlin Machine learns these formulae from a labelled text, utilizing conjunctive clauses to represent the particular facets of each category. Indeed, even the absence of terms (negated features) can be used for categorization purposes. Our empirical comparison with Na\"ive Bayes, decision trees, linear support vector machines (SVMs), random forest, long short-term memory (LSTM) neural networks, and other techniques, is quite conclusive. The Tsetlin Machine either performs on par with or outperforms all of the evaluated methods on both the 20 Newsgroups and IMDb datasets, as well as on a non-public clinical dataset. On average, the Tsetlin Machine delivers the best recall and precision scores across the datasets. Finally, our GPU implementation of the Tsetlin Machine executes 5 to 15 times faster than the CPU implementation, depending on the dataset. We thus believe that our novel approach can have a significant impact on a wide range of text analysis applications, forming a promising starting point for deeper natural language understanding with the Tsetlin Machine.

Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying language, facilitating communication between different scientific disciplines. It is therefore unsurprising that there is a burgeoning interest in applying category theory to machine learning. We aim to document the motivations, goals and common themes across these applications. We touch on gradient-based learning, probability, and equivariant learning.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

We propose DISC-LawLLM, an intelligent legal system utilizing large language models (LLMs) to provide a wide range of legal services. We adopt legal syllogism prompting strategies to construct supervised fine-tuning datasets in the Chinese Judicial domain and fine-tune LLMs with legal reasoning capability. We augment LLMs with a retrieval module to enhance models' ability to access and utilize external legal knowledge. A comprehensive legal benchmark, DISC-Law-Eval, is presented to evaluate intelligent legal systems from both objective and subjective dimensions. Quantitative and qualitative results on DISC-Law-Eval demonstrate the effectiveness of our system in serving various users across diverse legal scenarios. The detailed resources are available at https://github.com/FudanDISC/DISC-LawLLM.

Current advances in Artificial Intelligence (AI) and Machine Learning (ML) have achieved unprecedented impact across research communities and industry. Nevertheless, concerns about trust, safety, interpretability and accountability of AI were raised by influential thinkers. Many have identified the need for well-founded knowledge representation and reasoning to be integrated with deep learning and for sound explainability. Neural-symbolic computing has been an active area of research for many years seeking to bring together robust learning in neural networks with reasoning and explainability via symbolic representations for network models. In this paper, we relate recent and early research results in neurosymbolic AI with the objective of identifying the key ingredients of the next wave of AI systems. We focus on research that integrates in a principled way neural network-based learning with symbolic knowledge representation and logical reasoning. The insights provided by 20 years of neural-symbolic computing are shown to shed new light onto the increasingly prominent role of trust, safety, interpretability and accountability of AI. We also identify promising directions and challenges for the next decade of AI research from the perspective of neural-symbolic systems.

This thesis explores open-sourced machine learning (ML) model explanation tools to understand whether these tools can allow a layman to visualize, understand, and suggest intuitive remedies to unfairness in ML-based decision-support systems. Machine learning models trained on datasets biased against minority groups are increasingly used to guide life-altering social decisions, prompting the urgent need to study their logic for unfairness. Due to this problem's impact on vast populations of the general public, it is critical for the layperson -- not just subject matter experts in social justice or machine learning experts -- to understand the nature of unfairness within these algorithms and the potential trade-offs. Existing research on fairness in machine learning focuses mostly on the mathematical definitions and tools to understand and remedy unfair models, with some directly citing user-interactive tools as necessary for future work. This thesis presents FairLay-ML, a proof-of-concept GUI integrating some of the most promising tools to provide intuitive explanations for unfair logic in ML models by integrating existing research tools (e.g. Local Interpretable Model-Agnostic Explanations) with existing ML-focused GUI (e.g. Python Streamlit). We test FairLay-ML using models of various accuracy and fairness generated by an unfairness detector tool, Parfait-ML, and validate our results using Themis. Our study finds that the technology stack used for FairLay-ML makes it easy to install and provides real-time black-box explanations of pre-trained models to users. Furthermore, the explanations provided translate to actionable remedies.

A recent paper (van Rooij et al. 2024) claims to have proved that achieving human-like intelligence using learning from data is intractable in a complexity-theoretic sense. We identify that the proof relies on an unjustified assumption about the distribution of (input, output) pairs to the system. We briefly discuss that assumption in the context of two fundamental barriers to repairing the proof: the need to precisely define ``human-like," and the need to account for the fact that a particular machine learning system will have particular inductive biases that are key to the analysis.

Recent powerful pre-trained language models have achieved remarkable performance on most of the popular datasets for reading comprehension. It is time to introduce more challenging datasets to push the development of this field towards more comprehensive reasoning of text. In this paper, we introduce a new Reading Comprehension dataset requiring logical reasoning (ReClor) extracted from standardized graduate admission examinations. As earlier studies suggest, human-annotated datasets usually contain biases, which are often exploited by models to achieve high accuracy without truly understanding the text. In order to comprehensively evaluate the logical reasoning ability of models on ReClor, we propose to identify biased data points and separate them into EASY set while the rest as HARD set. Empirical results show that state-of-the-art models have an outstanding ability to capture biases contained in the dataset with high accuracy on EASY set. However, they struggle on HARD set with poor performance near that of random guess, indicating more research is needed to essentially enhance the logical reasoning ability of current models.

We present Logics-STEM, a state-of-the-art reasoning model fine-tuned on Logics-STEM-SFT-Dataset, a high-quality and diverse dataset at 10M scale that represents one of the largest-scale open-source long chain-of-thought corpora. Logics-STEM targets reasoning tasks in the domains of Science, Technology, Engineering, and Mathematics (STEM), and exhibits exceptional performance on STEM-related benchmarks with an average improvement of 4.68% over the next-best model at 8B scale. We attribute the gains to our data-algorithm co-design engine, where they are jointly optimized to fit a gold-standard distribution behind reasoning. Data-wise, the Logics-STEM-SFT-Dataset is constructed from a meticulously designed data curation engine with 5 stages to ensure the quality, diversity, and scalability, including annotation, deduplication, decontamination, distillation, and stratified sampling. Algorithm-wise, our failure-driven post-training framework leverages targeted knowledge retrieval and data synthesis around model failure regions in the Supervised Fine-tuning (SFT) stage to effectively guide the second-stage SFT or the reinforcement learning (RL) for better fitting the target distribution. The superior empirical performance of Logics-STEM reveals the vast potential of combining large-scale open-source data with carefully designed synthetic data, underscoring the critical role of data-algorithm co-design in enhancing reasoning capabilities through post-training. We make both the Logics-STEM models (8B and 32B) and the Logics-STEM-SFT-Dataset (10M and downsampled 2.2M versions) publicly available to support future research in the open-source community.

Natural language inference (NLI) is critical for complex decision-making in biomedical domain. One key question, for example, is whether a given biomedical mechanism is supported by experimental evidence. This can be seen as an NLI problem but there are no directly usable datasets to address this. The main challenge is that manually creating informative negative examples for this task is difficult and expensive. We introduce a novel semi-supervised procedure that bootstraps an NLI dataset from existing biomedical dataset that pairs mechanisms with experimental evidence in abstracts. We generate a range of negative examples using nine strategies that manipulate the structure of the underlying mechanisms both with rules, e.g., flip the roles of the entities in the interaction, and, more importantly, as perturbations via logical constraints in a neuro-logical decoding system. We use this procedure to create a novel dataset for NLI in the biomedical domain, called BioNLI and benchmark two state-of-the-art biomedical classifiers. The best result we obtain is around mid 70s in F1, suggesting the difficulty of the task. Critically, the performance on the different classes of negative examples varies widely, from 97% F1 on the simple role change negative examples, to barely better than chance on the negative examples generated using neuro-logic decoding.

Logical reasoning is of vital importance to natural language understanding. Previous studies either employ graph-based models to incorporate prior knowledge about logical relations, or introduce symbolic logic into neural models through data augmentation. These methods, however, heavily depend on annotated training data, and thus suffer from over-fitting and poor generalization problems due to the dataset sparsity. To address these two problems, in this paper, we propose MERIt, a MEta-path guided contrastive learning method for logical ReasonIng of text, to perform self-supervised pre-training on abundant unlabeled text data. Two novel strategies serve as indispensable components of our method. In particular, a strategy based on meta-path is devised to discover the logical structure in natural texts, followed by a counterfactual data augmentation strategy to eliminate the information shortcut induced by pre-training. The experimental results on two challenging logical reasoning benchmarks, i.e., ReClor and LogiQA, demonstrate that our method outperforms the SOTA baselines with significant improvements.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths, while systematic evaluations of these capabilities are still limited. In this paper, we aim to conduct a comprehensive evaluation of LLMs across various logical reasoning problems utilizing formal languages. From the perspective of three dimensions, i.e., spectrum of LLMs, taxonomy of tasks, and format of trajectories, our key findings are: 1) Thinking models significantly outperform Instruct models, especially when formal language is employed; 2) All LLMs exhibit limitations in inductive reasoning capability, irrespective of whether they use a formal language; 3) Data with PoT format achieves the best generalization performance across other languages. Additionally, we also curate the formal-relative training data to further enhance the small language models, and the experimental results indicate that a simple rejected fine-tuning method can better enable LLMs to generalize across formal languages and achieve the best overall performance. Our codes and reports are available at https://github.com/jiangjin1999/FormalEval.

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose Additional Logic Training (ALT), which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples. We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights. Then, based on these principles, we construct a synthetic corpus named Formal Logic Deduction Diverse (FLD^{times 2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors. Finally, we empirically show that ALT on FLD^{times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B. Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

We present the design and implementation of a custom discrete optimization technique for building rule lists over a categorical feature space. Our algorithm produces rule lists with optimal training performance, according to the regularized empirical risk, with a certificate of optimality. By leveraging algorithmic bounds, efficient data structures, and computational reuse, we achieve several orders of magnitude speedup in time and a massive reduction of memory consumption. We demonstrate that our approach produces optimal rule lists on practical problems in seconds. Our results indicate that it is possible to construct optimal sparse rule lists that are approximately as accurate as the COMPAS proprietary risk prediction tool on data from Broward County, Florida, but that are completely interpretable. This framework is a novel alternative to CART and other decision tree methods for interpretable modeling.

This paper presents our system description and error analysis of our entry for NLLP 2024 shared task on Legal Natural Language Inference (L-NLI) hagag2024legallenssharedtask2024. The task required classifying these relationships as entailed, contradicted, or neutral, indicating any association between the review and the complaint. Our system emerged as the winning submission, significantly outperforming other entries with a substantial margin and demonstrating the effectiveness of our approach in legal text analysis. We provide a detailed analysis of the strengths and limitations of each model and approach tested, along with a thorough error analysis and suggestions for future improvements. This paper aims to contribute to the growing field of legal NLP by offering insights into advanced techniques for natural language inference in legal contexts, making it accessible to both experts and newcomers in the field.