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Classic stochastic volatility models assume volatility is unobservable. We use the VIX for consider it observable, and use the Volatility Index: S\&P 500 VIX. This index was designed to measure volatility of S&P 500. We apply it to a different segment: Corporate bond markets. We fit time series models for spreads between corporate and 10-year Treasury bonds. Next, we divide residuals by VIX. Our main idea is such division makes residuals closer to the ideal case of a Gaussian white noise. This is remarkable, since these residuals and VIX come from separate market segments. We also discuss total returns of Bank of America corporate bonds. We conclude with the analysis of long-term behavior of these models.

Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully proves 162 theorems previously unproved by humans across 23 diverse Lean repositories, many from advanced mathematics. It performs significantly better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem-proving performance.

Transformers have had tremendous impact for several sequence related tasks, largely due to their ability to retrieve from any part of the sequence via softmax based dot-product attention. This mechanism plays a crucial role in Transformer's performance. We analyze the gradients backpropagated through the softmax operation in the attention mechanism and observe that these gradients can often be small. This poor gradient signal backpropagation can lead to inefficient learning of parameters preceeding the attention operations. To this end, we introduce a new attention mechanism called LASER, which we analytically show to admit a larger gradient signal. We show that LASER Attention can be implemented by making small modifications to existing attention implementations. We conduct experiments on autoregressive large language models (LLMs) with upto 2.2 billion parameters where we show upto 3.38% and an average of ~1% improvement over standard attention on downstream evaluations. Using LASER gives the following relative improvements in generalization performance across a variety of tasks (vision, text and speech): 4.67% accuracy in Vision Transformer (ViT) on Imagenet, 2.25% error rate in Conformer on the Librispeech speech-to-text and 0.93% fraction of incorrect predictions in BERT with 2.2 billion parameters.

The ability of intelligent systems to predict human behaviors is crucial, particularly in fields such as autonomous vehicle navigation and social robotics. However, the complexity of human motion have prevented the development of a standardized dataset for human motion prediction, thereby hindering the establishment of pre-trained models. In this paper, we address these limitations by integrating multiple datasets, encompassing both trajectory and 3D pose keypoints, to propose a pre-trained model for human motion prediction. We merge seven distinct datasets across varying modalities and standardize their formats. To facilitate multimodal pre-training, we introduce Multi-Transmotion, an innovative transformer-based model designed for cross-modality pre-training. Additionally, we present a novel masking strategy to capture rich representations. Our methodology demonstrates competitive performance across various datasets on several downstream tasks, including trajectory prediction in the NBA and JTA datasets, as well as pose prediction in the AMASS and 3DPW datasets. The code is publicly available: //github.com/vita-epfl/multi-transmotion

Recently, there has been increasing interest in using Large Language Models (LLMs) to construct complex multi-agent systems to perform tasks such as compiling literature reviews, drafting consumer reports, and planning vacations. Many tools and libraries exist for helping create such systems, however none support recursive multi-agent systems -- where the models themselves flexibly decide when to delegate tasks and how to organize their delegation structure. In this work, we introduce ReDel: a toolkit for recursive multi-agent systems that supports custom tool-use, delegation schemes, event-based logging, and interactive replay in an easy-to-use web interface. We show that, using ReDel, we are able to easily identify potential areas of improvements through the visualization and debugging tools. Our code, documentation, and PyPI package are open-source and free to use under the MIT license at //github.com/zhudotexe/redel.

More than one hundred benchmarks have been developed to test the commonsense knowledge and commonsense reasoning abilities of artificial intelligence (AI) systems. However, these benchmarks are often flawed and many aspects of common sense remain untested. Consequently, we do not currently have any reliable way of measuring to what extent existing AI systems have achieved these abilities. This paper surveys the development and uses of AI commonsense benchmarks. We discuss the nature of common sense; the role of common sense in AI; the goals served by constructing commonsense benchmarks; and desirable features of commonsense benchmarks. We analyze the common flaws in benchmarks, and we argue that it is worthwhile to invest the work needed ensure that benchmark examples are consistently high quality. We survey the various methods of constructing commonsense benchmarks. We enumerate 139 commonsense benchmarks that have been developed: 102 text-based, 18 image-based, 12 video based, and 7 simulated physical environments. We discuss the gaps in the existing benchmarks and aspects of commonsense reasoning that are not addressed in any existing benchmark. We conclude with a number of recommendations for future development of commonsense AI benchmarks.

Following unprecedented success on the natural language tasks, Transformers have been successfully applied to several computer vision problems, achieving state-of-the-art results and prompting researchers to reconsider the supremacy of convolutional neural networks (CNNs) as {de facto} operators. Capitalizing on these advances in computer vision, the medical imaging field has also witnessed growing interest for Transformers that can capture global context compared to CNNs with local receptive fields. Inspired from this transition, in this survey, we attempt to provide a comprehensive review of the applications of Transformers in medical imaging covering various aspects, ranging from recently proposed architectural designs to unsolved issues. Specifically, we survey the use of Transformers in medical image segmentation, detection, classification, reconstruction, synthesis, registration, clinical report generation, and other tasks. In particular, for each of these applications, we develop taxonomy, identify application-specific challenges as well as provide insights to solve them, and highlight recent trends. Further, we provide a critical discussion of the field's current state as a whole, including the identification of key challenges, open problems, and outlining promising future directions. We hope this survey will ignite further interest in the community and provide researchers with an up-to-date reference regarding applications of Transformer models in medical imaging. Finally, to cope with the rapid development in this field, we intend to regularly update the relevant latest papers and their open-source implementations at \url{//github.com/fahadshamshad/awesome-transformers-in-medical-imaging}.

Knowledge graphs are important resources for many artificial intelligence tasks but often suffer from incompleteness. In this work, we propose to use pre-trained language models for knowledge graph completion. We treat triples in knowledge graphs as textual sequences and propose a novel framework named Knowledge Graph Bidirectional Encoder Representations from Transformer (KG-BERT) to model these triples. Our method takes entity and relation descriptions of a triple as input and computes scoring function of the triple with the KG-BERT language model. Experimental results on multiple benchmark knowledge graphs show that our method can achieve state-of-the-art performance in triple classification, link prediction and relation prediction tasks.

With the capability of modeling bidirectional contexts, denoising autoencoding based pretraining like BERT achieves better performance than pretraining approaches based on autoregressive language modeling. However, relying on corrupting the input with masks, BERT neglects dependency between the masked positions and suffers from a pretrain-finetune discrepancy. In light of these pros and cons, we propose XLNet, a generalized autoregressive pretraining method that (1) enables learning bidirectional contexts by maximizing the expected likelihood over all permutations of the factorization order and (2) overcomes the limitations of BERT thanks to its autoregressive formulation. Furthermore, XLNet integrates ideas from Transformer-XL, the state-of-the-art autoregressive model, into pretraining. Empirically, XLNet outperforms BERT on 20 tasks, often by a large margin, and achieves state-of-the-art results on 18 tasks including question answering, natural language inference, sentiment analysis, and document ranking.

Explainable Recommendation refers to the personalized recommendation algorithms that address the problem of why -- they not only provide the user with the recommendations, but also make the user aware why such items are recommended by generating recommendation explanations, which help to improve the effectiveness, efficiency, persuasiveness, and user satisfaction of recommender systems. In recent years, a large number of explainable recommendation approaches -- especially model-based explainable recommendation algorithms -- have been proposed and adopted in real-world systems. In this survey, we review the work on explainable recommendation that has been published in or before the year of 2018. We first high-light the position of explainable recommendation in recommender system research by categorizing recommendation problems into the 5W, i.e., what, when, who, where, and why. We then conduct a comprehensive survey of explainable recommendation itself in terms of three aspects: 1) We provide a chronological research line of explanations in recommender systems, including the user study approaches in the early years, as well as the more recent model-based approaches. 2) We provide a taxonomy for explainable recommendation algorithms, including user-based, item-based, model-based, and post-model explanations. 3) We summarize the application of explainable recommendation in different recommendation tasks, including product recommendation, social recommendation, POI recommendation, etc. We devote a chapter to discuss the explanation perspectives in the broader IR and machine learning settings, as well as their relationship with explainable recommendation research. We end the survey by discussing potential future research directions to promote the explainable recommendation research area.