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Peer analysis is a critical component of investment management, often relying on expert-provided categorization systems. These systems' consistency is questioned when they do not align with cohorts from unsupervised clustering algorithms optimized for various metrics. We investigate whether unsupervised clustering can reproduce ground truth classes in a labeled dataset, showing that success depends on feature selection and the chosen distance metric. Using toy datasets and fund categorization as real-world examples we demonstrate that accurately reproducing ground truth classes is challenging. We also highlight the limitations of standard clustering evaluation metrics in identifying the optimal number of clusters relative to the ground truth classes. We then show that if appropriate features are available in the dataset, and a proper distance metric is known (e.g., using a supervised Random Forest-based distance metric learning method), then an unsupervised clustering can indeed reproduce the ground truth classes as distinct clusters., Comment: 9 pages, 4 tables 28 figures

The explainability of black-box machine learning algorithms, commonly known as Explainable Artificial Intelligence (XAI), has become crucial for financial and other regulated industrial applications due to regulatory requirements and the need for transparency in business practices. Among the various paradigms of XAI, Explainable Case-Based Reasoning (XCBR) stands out as a pragmatic approach that elucidates the output of a model by referencing actual examples from the data used to train or test the model. Despite its potential, XCBR has been relatively underexplored for many algorithms such as tree-based models until recently. We start by observing that most XCBR methods are defined based on the distance metric learned by the algorithm. By utilizing a recently proposed technique to extract the distance metric learned by Random Forests (RFs), which is both geometry- and accuracy-preserving, we investigate various XCBR methods. These methods amount to identify special points from the training datasets, such as prototypes, critics, counter-factuals, and semi-factuals, to explain the predictions for a given query of the RF. We evaluate these special points using various evaluation metrics to assess their explanatory power and effectiveness., Comment: 8 pages, 2 figures, 5 tables

Extraction and interpretation of intricate information from unstructured text data arising in financial applications, such as earnings call transcripts, present substantial challenges to large language models (LLMs) even using the current best practices to use Retrieval Augmented Generation (RAG) (referred to as VectorRAG techniques which utilize vector databases for information retrieval) due to challenges such as domain specific terminology and complex formats of the documents. We introduce a novel approach based on a combination, called HybridRAG, of the Knowledge Graphs (KGs) based RAG techniques (called GraphRAG) and VectorRAG techniques to enhance question-answer (Q&A) systems for information extraction from financial documents that is shown to be capable of generating accurate and contextually relevant answers. Using experiments on a set of financial earning call transcripts documents which come in the form of Q&A format, and hence provide a natural set of pairs of ground-truth Q&As, we show that HybridRAG which retrieves context from both vector database and KG outperforms both traditional VectorRAG and GraphRAG individually when evaluated at both the retrieval and generation stages in terms of retrieval accuracy and answer generation. The proposed technique has applications beyond the financial domain, Comment: 9 pages, 2 figures, 5 tables

In many real-world classification or recognition tasks, it is often difficult to collect training examples that exhaust all possible classes due to, for example, incomplete knowledge during training or ever changing regimes. Therefore, samples from unknown/novel classes may be encountered in testing/deployment. In such scenarios, the classifiers should be able to i) perform classification on known classes, and at the same time, ii) identify samples from unknown classes. This is known as open-set recognition. Although random forest has been an extremely successful framework as a general-purpose classification (and regression) method, in practice, it usually operates under the closed-set assumption and is not able to identify samples from new classes when run out of the box. In this work, we propose a novel approach to enabling open-set recognition capability for random forest classifiers by incorporating distance metric learning and distance-based open-set recognition. The proposed method is validated on both synthetic and real-world datasets. The experimental results indicate that the proposed approach outperforms state-of-the-art distance-based open-set recognition methods.

We initiate a novel approach to explain the predictions and out of sample performance of random forest (RF) regression and classification models by exploiting the fact that any RF can be mathematically formulated as an adaptive weighted K nearest-neighbors model. Specifically, we employ a recent result that, for both regression and classification tasks, any RF prediction can be rewritten exactly as a weighted sum of the training targets, where the weights are RF proximities between the corresponding pairs of data points. We show that this linearity facilitates a local notion of explainability of RF predictions that generates attributions for any model prediction across observations in the training set, and thereby complements established feature-based methods like SHAP, which generate attributions for a model prediction across input features. We show how this proximity-based approach to explainability can be used in conjunction with SHAP to explain not just the model predictions, but also out-of-sample performance, in the sense that proximities furnish a novel means of assessing when a given model prediction is more or less likely to be correct. We demonstrate this approach in the modeling of US corporate bond prices and returns in both regression and classification cases., Comment: 5 pages, 6 figures

For a financial analyst, the question and answer (Q\&A) segment of the company financial report is a crucial piece of information for various analysis and investment decisions. However, extracting valuable insights from the Q\&A section has posed considerable challenges as the conventional methods such as detailed reading and note-taking lack scalability and are susceptible to human errors, and Optical Character Recognition (OCR) and similar techniques encounter difficulties in accurately processing unstructured transcript text, often missing subtle linguistic nuances that drive investor decisions. Here, we demonstrate the utilization of Large Language Models (LLMs) to efficiently and rapidly extract information from earnings report transcripts while ensuring high accuracy transforming the extraction process as well as reducing hallucination by combining retrieval-augmented generation technique as well as metadata. We evaluate the outcomes of various LLMs with and without using our proposed approach based on various objective metrics for evaluating Q\&A systems, and empirically demonstrate superiority of our method., Comment: 4 pages + references. Accepted for publication in Workshop on Generative AI at the 3rd International Conference on AI-ML Systems 2023, Bengaluru, India

Identifying companies with similar profiles is a core task in finance with a wide range of applications in portfolio construction, asset pricing and risk attribution. When a rigorous definition of similarity is lacking, financial analysts usually resort to 'traditional' industry classifications such as Global Industry Classification System (GICS) which assign a unique category to each company at different levels of granularity. Due to their discrete nature, though, GICS classifications do not allow for ranking companies in terms of similarity. In this paper, we explore the ability of pre-trained and finetuned large language models (LLMs) to learn company embeddings based on the business descriptions reported in SEC filings. We show that we can reproduce GICS classifications using the embeddings as features. We also benchmark these embeddings on various machine learning and financial metrics and conclude that the companies that are similar according to the embeddings are also similar in terms of financial performance metrics including return correlation., Comment: 8 pages, 2 figures, 2 tables

Mutual fund categorization has become a standard tool for the investment management industry and is extensively used by allocators for portfolio construction and manager selection, as well as by fund managers for peer analysis and competitive positioning. As a result, a (unintended) miscategorization or lack of precision can significantly impact allocation decisions and investment fund managers. Here, we aim to quantify the effect of miscategorization of funds utilizing a machine learning based approach. We formulate the problem of miscategorization of funds as a distance-based outlier detection problem, where the outliers are the data-points that are far from the rest of the data-points in the given feature space. We implement and employ a Random Forest (RF) based method of distance metric learning, and compute the so-called class-wise outlier measures for each data-point to identify outliers in the data. We test our implementation on various publicly available data sets, and then apply it to mutual fund data. We show that there is a strong relationship between the outlier measures of the funds and their future returns and discuss the implications of our findings., Comment: 8 pages, 5 tables, 8 figures

In this paper we consider three-dimensional steady water waves with vorticity, under the action of gravity and surface tension; in particular we consider so-called Beltrami flows, for which the velocity field and the vorticity are collinear. We discuss a recent variational formulation of the problem which involves a generalisation of the classical Dirichlet-Neumann operator. We study this operator in detail, extending some well-known results for the classical Dirichlet-Neumann operator, such as the Taylor expansion in homogeneous powers of the wave profile, the computation of its differential and the asymptotic expansion of its associated symbol. A new formulation of the problem as a single equation for the wave profile is also presented and discussed in a similar vein. As an application of these results we rigorously prove existence of doubly periodic gravity-capillary steady waves and construct approximate doubly periodic gravity steady waves.

Large language models (LLMs) have significantly advanced the field of natural language processing (NLP), providing a highly useful, task-agnostic foundation for a wide range of applications. However, directly applying LLMs to solve sophisticated problems in specific domains meets many hurdles, caused by the heterogeneity of domain data, the sophistication of domain knowledge, the uniqueness of domain objectives, and the diversity of the constraints (e.g., various social norms, cultural conformity, religious beliefs, and ethical standards in the domain applications). Domain specification techniques are key to make large language models disruptive in many applications. Specifically, to solve these hurdles, there has been a notable increase in research and practices conducted in recent years on the domain specialization of LLMs. This emerging field of study, with its substantial potential for impact, necessitates a comprehensive and systematic review to better summarize and guide ongoing work in this area. In this article, we present a comprehensive survey on domain specification techniques for large language models, an emerging direction critical for large language model applications. First, we propose a systematic taxonomy that categorizes the LLM domain-specialization techniques based on the accessibility to LLMs and summarizes the framework for all the subcategories as well as their relations and differences to each other. Second, we present an extensive taxonomy of critical application domains that can benefit dramatically from specialized LLMs, discussing their practical significance and open challenges. Last, we offer our insights into the current research status and future trends in this area.

We study analytically the dynamics of a $d$-dimensional Klein-Gordon lattice with periodic boundary conditions, for $d \leq 3$. We consider initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation, the resonant normal form of the system is given by a small-dispersion nonlinear Schr\"odinger (NLS) equation. By exploiting a result about the growth of Sobolev norms for solutions of small-dispersion NLS, we are able to describe an energy cascade phenomenon for the Klein-Gordon lattice, where part of the energy is transferred to modes associated to higher frequencies. Such phenomenon holds within the time-scale for which we can ensure the validity of the continuous approximation., Comment: Changes with respect to previous version: changes to the presentation of the main result in Section 2 and in Section 6, changes to Section 3 and Appendix A, some comments added, some typos corrected. arXiv admin note: text overlap with arXiv:1911.12648

Understanding non-linear relationships among financial instruments has various applications in investment processes ranging from risk management, portfolio construction and trading strategies. Here, we focus on interconnectedness among stocks based on their correlation matrix which we represent as a network with the nodes representing individual stocks and the weighted links between pairs of nodes representing the corresponding pair-wise correlation coefficients. The traditional network science techniques, which are extensively utilized in financial literature, require handcrafted features such as centrality measures to understand such correlation networks. However, manually enlisting all such handcrafted features may quickly turn out to be a daunting task. Instead, we propose a new approach for studying nuances and relationships within the correlation network in an algorithmic way using a graph machine learning algorithm called Node2Vec. In particular, the algorithm compresses the network into a lower dimensional continuous space, called an embedding, where pairs of nodes that are identified as similar by the algorithm are placed closer to each other. By using log returns of S&P 500 stock data, we show that our proposed algorithm can learn such an embedding from its correlation network. We define various domain specific quantitative (and objective) and qualitative metrics that are inspired by metrics used in the field of Natural Language Processing (NLP) to evaluate the embeddings in order to identify the optimal one. Further, we discuss various applications of the embeddings in investment management., Comment: 8 pages, 2 column format, 3 figure, 7 tables

Categorization of mutual funds or Exchange-Traded-funds (ETFs) have long served the financial analysts to perform peer analysis for various purposes starting from competitor analysis, to quantifying portfolio diversification. The categorization methodology usually relies on fund composition data in the structured format extracted from the Form N-1A. Here, we initiate a study to learn the categorization system directly from the unstructured data as depicted in the forms using natural language processing (NLP). Positing as a multi-class classification problem with the input data being only the investment strategy description as reported in the form and the target variable being the Lipper Global categories, and using various NLP models, we show that the categorization system can indeed be learned with high accuracy. We discuss implications and applications of our findings as well as limitations of existing pre-trained architectures in applying them to learn fund categorization., Comment: 8 pages, 5 figures, 2-column format

Financial literature consists of ample research on similarity and comparison of financial assets and securities such as stocks, bonds, mutual funds, etc. However, going beyond correlations or aggregate statistics has been arduous since financial datasets are noisy, lack useful features, have missing data and often lack ground truth or annotated labels. However, though similarity extrapolated from these traditional models heuristically may work well on an aggregate level, such as risk management when looking at large portfolios, they often fail when used for portfolio construction and trading which require a local and dynamic measure of similarity on top of global measure. In this paper we propose a supervised similarity framework for corporate bonds which allows for inference based on both local and global measures. From a machine learning perspective, this paper emphasis that random forest (RF), which is usually viewed as a supervised learning algorithm, can also be used as a similarity learning (more specifically, a distance metric learning) algorithm. In addition, this framework proposes a novel metric to evaluate similarities, and analyses other metrics which further demonstrate that RF outperforms all other methods experimented with, in this work., Comment: A few minor typos corrected, 1 figure added. Conclusions unchanged. Matching with the accepted version

The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on the 2-dimensional torus exchanging energy among Fourier modes in a \emph{chaotic-like} way. We say that a transition of energy is \emph{chaotic-like} if either the choice of activated modes or the time spent in each transfer can be chosen randomly. We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations. The key point of the construction of the special solutions is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form of those equations., Comment: arXiv admin note: substantial text overlap with arXiv:2006.09309

We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on $T^2$ and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be considered \emph{chaotic-like} since either the choice of activated modes or the time spent in each transfer can be chosen randomly. The key point of the construction of those orbits is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form truncation of those equations.

We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation, the resonant normal form of the system is given by integrable PDEs. We exploit the normal form result in order to prove the existence of metastability phenomena for the lattices. More precisely, we show that the energy spectrum of the normal modes attains a distribution in which the energy is shared among a packet of low-frequencies modes; such distribution remains unchanged up to the time-scale of validity of the continuous approximation.

We consider the dispersive Degasperis-Procesi equation $u_t-u_{x x t}-\mathtt{c} u_{xxx}+4 \mathtt{c} u_x-u u_{xxx}-3 u_x u_{xx}+4 u u_x=0$ with $\mathtt{c}\neq 0$. In \cite{Deg} the authors proved that this equation possesses infinitely many conserved quantities. We prove that, in a neighborhood of the origin, there are infinitely many of such constants of motion which control the Sobolev norms and which are analytic in a neighborhood of the origin of some $H^s$ Sobolev space, both on $\mathbb{R}$ and $\mathbb{T}$. By the analysis of these conserved quantities we deduce a result of global well-posedness for solutions with small initial data and we show that, on the circle, the formal Birkhoff normal form of the Degasperis-Procesi at any order is action-preserving.

We study the the nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity. In particular, we consider an order-$r$ normalized approximation of NLKG (which corresponds to the NLS at order $r=1$), and prove that when $M=\mathbb{R}^d$, $d \geq 2$, small radiation solutions of the order-$r$ normalized equation approximate solutions of the nonlinear NLKG up to times of order $\mathcal{O}(c^{2(r-1)})$., Comment: more details added to the proof of Proposition 5.4 ; some typos corrected

We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small $H^s$ norm remain small for long times. The result is uniform with respect to $c \geq 1$, which however has to belong to a set of large measure., Comment: Some typos corrected