Daily Papers

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality correct solutions from advanced models, neglecting the value contained in error data, potentially hindering the model's reflective ability. Though some studies attempt to leverage error data, they often involve complex mechanisms, such as Monte Carlo Tree Search (MCTS) to explore error nodes. In this work, we propose to enhance LLMs' reasoning ability by Learning from Errors for Mathematical Advancement (LEMMA). LEMMA constructs data consisting of an incorrect solution with an erroneous step and a reflection connection to a correct solution for fine-tuning. Specifically, we systematically analyze the model-generated error types and introduce an error-type grounded mistake augmentation method to collect diverse and representative errors. Correct solutions are either from fixing the errors or generating a fresh start. Through a model-aware smooth reflection connection, the erroneous solution is transferred to the correct one. By fine-tuning on the constructed dataset, the model is able to self-correct errors autonomously within the generation process without relying on external critique models. Experimental results demonstrate that LEMMA achieves significant performance improvements over other strong baselines.

Lemmatization is still not a trivial task for morphologically rich languages. Previous studies showed that hybrid architectures usually work better for these languages and can yield great results. This paper presents a hybrid lemmatizer utilizing both a neural model, dictionaries and hand-crafted rules. We introduce a hybrid architecture along with empirical results on a widely used Hungarian dataset. The presented methods are published as three HuSpaCy models.

Lemmatization is a natural language processing (NLP) task which consists of producing, from a given inflected word, its canonical form or lemma. Lemmatization is one of the basic tasks that facilitate downstream NLP applications, and is of particular importance for high-inflected languages. Given that the process to obtain a lemma from an inflected word can be explained by looking at its morphosyntactic category, including fine-grained morphosyntactic information to train contextual lemmatizers has become common practice, without considering whether that is the optimum in terms of downstream performance. In order to address this issue, in this paper we empirically investigate the role of morphological information to develop contextual lemmatizers in six languages within a varied spectrum of morphological complexity: Basque, Turkish, Russian, Czech, Spanish and English. Furthermore, and unlike the vast majority of previous work, we also evaluate lemmatizers in out-of-domain settings, which constitutes, after all, their most common application use. The results of our study are rather surprising. It turns out that providing lemmatizers with fine-grained morphological features during training is not that beneficial, not even for agglutinative languages. In fact, modern contextual word representations seem to implicitly encode enough morphological information to obtain competitive contextual lemmatizers without seeing any explicit morphological signal. Moreover, our experiments suggest that the best lemmatizers out-of-domain are those using simple UPOS tags or those trained without morphology and, finally, that current evaluation practices for lemmatization are not adequate to clearly discriminate between models.

The original Grover's algorithm suffers from the souffle problem, which means that the success probability of quantum search decreases dramatically if the iteration time is too small or too large from the right time. To overcome the souffle problem, the fixed-point quantum search with an optimal number of queries was proposed [Phys. Rev. Lett. 113, 210501 (2014)], which always finds a marked state with a high probability when a lower bound of the proportion of marked states is given. The fixed-point quantum search relies on a key lemma regarding the explicit formula of recursive quasi-Chebyshev polynomials, but its proof is not given explicitly. In this work, we give a detailed proof of this lemma, thus providing a sound foundation for the correctness of the fixed-point quantum search. This lemma may be of independent interest as well, since it expands the mathematical form of the recursive relation of Chebyshev polynomials of the first kind, and it also constitutes a key component in overcoming the souffle problem of quantum walk-based search algorithms, for example, robust quantum walk search on complete bipartite graphs [Phys. Rev. A 106, 052207 (2022)]. Hopefully, more applications of the lemma will be found in the future.

We present LEMMING, a modular log-linear model that jointly models lemmatization and tagging and supports the integration of arbitrary global features. It is trainable on corpora annotated with gold standard tags and lemmata and does not rely on morphological dictionaries or analyzers. LEMMING sets the new state of the art in token-based statistical lemmatization on six languages; e.g., for Czech lemmatization, we reduce the error by 60%, from 4.05 to 1.58. We also give empirical evidence that jointly modeling morphological tags and lemmata is mutually beneficial.

We present GliLem -- a novel hybrid lemmatization system for Estonian that enhances the highly accurate rule-based morphological analyzer Vabamorf with an external disambiguation module based on GliNER -- an open vocabulary NER model that is able to match text spans with text labels in natural language. We leverage the flexibility of a pre-trained GliNER model to improve the lemmatization accuracy of Vabamorf by 10\% compared to its original disambiguation module and achieve an improvement over the token classification-based baseline. To measure the impact of improvements in lemmatization accuracy on the information retrieval downstream task, we first created an information retrieval dataset for Estonian by automatically translating the DBpedia-Entity dataset from English. We benchmark several token normalization approaches, including lemmatization, on the created dataset using the BM25 algorithm. We observe a substantial improvement in IR metrics when using lemmatization over simplistic stemming. The benefits of improving lemma disambiguation accuracy manifest in small but consistent improvement in the IR recall measure, especially in the setting of high k.

This study introduces the eFontes models for automatic linguistic annotation of Medieval Latin texts, focusing on lemmatization, part-of-speech tagging, and morphological feature determination. Using the Transformers library, these models were trained on Universal Dependencies (UD) corpora and the newly developed eFontes corpus of Polish Medieval Latin. The research evaluates the models' performance, addressing challenges such as orthographic variations and the integration of Latinized vernacular terms. The models achieved high accuracy rates: lemmatization at 92.60%, part-of-speech tagging at 83.29%, and morphological feature determination at 88.57%. The findings underscore the importance of high-quality annotated corpora and propose future enhancements, including extending the models to Named Entity Recognition.

This study evaluates three different lemmatization approaches to Estonian -- Generative character-level models, Pattern-based word-level classification models, and rule-based morphological analysis. According to our experiments, a significantly smaller Generative model consistently outperforms the Pattern-based classification model based on EstBERT. Additionally, we observe a relatively small overlap in errors made by all three models, indicating that an ensemble of different approaches could lead to improvements.

This paper describes our submission to CoNLL 2018 UD Shared Task. We have extended an LSTM-based neural network designed for sequence tagging to additionally generate character-level sequences. The network was jointly trained to produce lemmas, part-of-speech tags and morphological features. Sentence segmentation, tokenization and dependency parsing were handled by UDPipe 1.2 baseline. The results demonstrate the viability of the proposed multitask architecture, although its performance still remains far from state-of-the-art.

In this paper, we propose a weak regularity principle which is similar to both weak K\"onig's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.

Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the proofs in formal language can be challenging for humans and machines. The miniF2F benchmark has 20 IMO problems in its test set, yet formal proofs are available only for 6 of these problems (3 of which are only written by mathematicians). The model with best accuracy can only prove 2 of these 20 IMO problems, from 1950s and 60s, while its training set is a secret. In this work, we write complete, original formal proofs for the remaining IMO problems in Lean along with 3 extra problems from IMO 2022 and 2023. This effort expands the availability of proof currently in the public domain by creating 5,880 lines of Lean proof. The goal of the paper is to pave the way for developing AI models that can automatically write the formal proofs for all the IMO problems in miniF2F and beyond by providing an evaluation benchmark. In this pursuit, we devise a method to decompose the proofs of these problems into their building blocks, constructing a dataset of 1,329 lemmas with more than 40k lines of Lean code. These lemmas are not trivial, yet they are approachable, providing the opportunity to evaluate and diagnose the failures and successes of AI models. We evaluate the ability of the SOTA LLMs on our dataset and analyze their success and failure modes from different perspectives. Our dataset and code is available at: https://github.com/roozbeh-yz/IMO-Steps.