Let me tell you a bit more about it! The Wim Hof Wethod in Action: Increased Mental Clarity: By practicing the Wim Hof breathing exercises, you can oxygenate your body, improving blood flow and ...

Enhance Your Well-being and Boost Your Performance with the Wim Hof Method

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WETHOD

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Technical Overview of the UniswapX Protocol: Architecture, Integration Methods, and Order Execution

Digital Transformations Methodology - When Agile Can Fall Short in Cloud Procurement While agile methodology has revolutionized product/technology development and project management, it’s not always the perfect fit for cloud or SaaS solution implementations. Agile offers flexibility, quick iterations, and adaptability, which are critical in many IT projects. However, the nature of cloud migrations or implementations can sometimes conflict with Agile's principles, posing challenges that require careful consideration. Complexities of Cloud Solutions Cloud solutions in procurement, especially large-scale implementations, involve careful process design and integration with existing legacy systems. These projects require careful planning and alignment with long-term organizational goals. Agile’s emphasis on iterative sprints can sometimes lead to fragmented or misaligned outcomes in these complex environments. For instance, procurement transformations require upfront technical architectural decisions, including integration landscape and compliance standards, which can’t be easily changed in small iterative cycles. Without the appropriate planning phase, organizations may find themselves dealing with significant rework, leading to delays and increased costs. Catering to Business and Industry Requirements Cloud procurement implementations often involve multiple stakeholders from different areas of the organization such as finance, accounting, and IT, in addition to supply chain teams -, each with distinct needs and expectations. The problem arises when these requirements aren’t fully defined at the outset. While agile champions flexibility and responsiveness, cloud solutions typically demand a deeper understanding of the end-to-end requirements before configuration starts. Without a comprehensive design of the functional and technical requirements and how they align with the business, agile teams may struggle to make informed decisions during sprints. This lack of clarity can result in missed objectives, scope creep, or misalignment with business goals. Integration with Legacy Systems One of the major challenges in cloud procurement implementations is integrating with boundary systems such as planning solutions, ERPs, or HR systems. The technical architecture needs to be well established prior to beginning the design and development of integrations. Legacy systems can also present roadblocks that Agile’s short-cycle approach isn’t well-equipped to handle. While agile works well in environments where all components are relatively new and flexible, legacy systems require careful mapping, data migration strategies, and detailed data mapping, which might not fit well within agile's fast-paced, iterative process. The Case for a Hybrid Approach Given these challenges, many organizations are opting for a hybrid approach that combines agile principles with a more traditional, structured project management methodology. This approach allows teams to maintain agile's flexibility in execution while ensuring that the foundational elements of the cloud solution—such as architecture, compliance, and system integration—are fully planned and mapped out before implementation begins. For instance, a hybrid approach may involve initial phases of waterfall-style planning for architecture, compliance, and other critical decisions, followed by agile sprints for more granular tasks like development, testing, and deployment. This enables teams to strike a balance between the adaptability of agile and the structured requirements of a complex cloud solution. Conclusion While agile methodology offers a powerful framework for many types of IT projects, it may not always be the best approach for cloud procurement implementations. The complexity, integration requirements, and regulatory considerations of cloud migrations often require more upfront planning and structured project management. By adopting a hybrid methodology, organizations can leverage the strengths of agile while mitigating the risks that come with applying it too rigidly to cloud solutions. Feel free to reach out for any questions on digital transformations of enterprise operations. Disclaimer: The views in this article are my own and do not represent my current or prior employers. Digital Transformations Methodology - When Agile Can Fall Short in Cloud Procurement Digital Transformations Methodology - When Agile Can Fall Short in Cloud Procurement While agile methodology has revolutionized product/technology development and project management, it’s not always the perfect fit for cloud or SaaS solution implementations. Agile offers flexibility, quick iterations, and adaptability, which are critical in many IT projects. However, the nature of cloud migrations or implementations can sometimes conflict with Agile's principles, posing challenges that require careful consideration. Complexities of Cloud Solutions Cloud solutions in procurement, especially large-scale implementations, involve careful process design and integration with existing legacy systems. These projects require careful planning and alignment with long-term organizational goals. Agile’s emphasis on iterative sprints can sometimes lead to fragmented or misaligned outcomes in these complex environments. For instance, procurement transformations require upfront technical architectural decisions, including integration landscape and compliance standards, which can’t be easily changed in small iterative cycles. Without the appropriate planning phase, organizations may find themselves dealing with significant rework, leading to delays and increased costs. Catering to Business and Industry Requirements Cloud procurement implementations often involve multiple stakeholders from different areas of the organization such as finance, accounting, and IT, in addition to supply chain teams -, each with distinct needs and expectations. The problem arises when these requirements aren’t fully defined at the outset. While agile champions flexibility and responsiveness, cloud solutions typically demand a deeper understanding of the end-to-end requirements before configuration starts. Without a comprehensive design of the functional and technical requirements and how they align with the business, agile teams may struggle to make informed decisions during sprints. This lack of clarity can result in missed objectives, scope creep, or misalignment with business goals. Integration with Legacy Systems One of the major challenges in cloud procurement implementations is integrating with boundary systems such as planning solutions, ERPs, or HR systems. The technical architecture needs to be well established prior to beginning the design and development of integrations. Legacy systems can also present roadblocks that Agile’s short-cycle approach isn’t well-equipped to handle. While agile works well in environments where all components are relatively new and flexible, legacy systems require careful mapping, data migration strategies, and detailed data mapping, which might not fit well within agile's fast-paced, iterative process. The Case for a Hybrid Approach Given these challenges, many organizations are opting for a hybrid approach that combines agile principles with a more traditional, structured project management methodology. This approach allows teams to maintain agile's flexibility in execution while ensuring that the foundational elements of the cloud solution—such as architecture, compliance, and system integration—are fully planned and mapped out before implementation begins. For instance, a hybrid approach may involve initial phases of waterfall-style planning for architecture, compliance, and other critical decisions, followed by agile sprints for more granular tasks like development, testing, and deployment. This enables teams to strike a balance between the adaptability of agile and the structured requirements of a complex cloud solution. Conclusion While agile methodology offers a powerful framework for many types of IT projects, it may not always be the best approach for cloud procurement implementations. The complexity, integration requirements, and regulatory considerations of cloud migrations often require more upfront planning and structured project management. By adopting a hybrid methodology, organizations can leverage the strengths of agile while mitigating the risks that come with applying it too rigidly to cloud solutions. Feel free to reach out for any questions on digital transformations of enterprise operations. Disclaimer: The views in this article are my own and do not represent my current or prior employers. Disclaimer: The views in this article are my own and do not represent my current or prior employers.

Challenges in Implementing Agile Methodology for Cloud Solutions

Authors:
(1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch);
(2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch);
(3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.2 Anchor Regression 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation B Experiments 3 Anchor Data Augmentation In this section, we introduce Anchor Data Augmentation (ADA), a domain-independent data augmentation method inspired by AR. ADA does not require previous knowledge about the data invariances nor manually engineered transformations. As opposed to existing domain-agnostic data augmentation methods [10, 45, 46], we do not require training of an expensive generative model, and the augmentation only adds marginally to the computation complexity of the training. In addition, since ADA originates from a causal regression problem, it can be readily applied to regression problems. Even when ADA does not improve performance, its effect on performance remains minimal. This paper is available on arxiv under CC0 1.0 DEED license. Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Authors: Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.1 Data Augmentation 2.2 Anchor Regression 2.2 Anchor Regression 3 Anchor Data Augmentation 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation A Additional information for Anchor Data Augmentation B Experiments B Experiments 3 Anchor Data Augmentation In this section, we introduce Anchor Data Augmentation (ADA), a domain-independent data augmentation method inspired by AR. ADA does not require previous knowledge about the data invariances nor manually engineered transformations. As opposed to existing domain-agnostic data augmentation methods [10, 45, 46], we do not require training of an expensive generative model, and the augmentation only adds marginally to the computation complexity of the training. In addition, since ADA originates from a causal regression problem, it can be readily applied to regression problems. Even when ADA does not improve performance, its effect on performance remains minimal. This paper is available on arxiv under CC0 1.0 DEED license. This paper is available on arxiv under CC0 1.0 DEED license. available on arxiv

Anchor Data Augmentation (ADA): A Domain-Agnostic Method for Enhancing Regression Models

Authors:
(1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch);
(2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch);
(3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.2 Anchor Regression 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation B Experiments 2.1 Data Augmentation Many different data augmentation methods have been proposed in recent years with several applications in mind. Still most augmentations we mention here use human-designed transformations based on domain knowledge which leave the target variable invariant. For instance, Cutout [10] is an image-specific augmentation technique that is successfully used to train models on CIFAR10 and CIFAR100 [25], but was determined to be unsuitable for larger image datasets like ImageNet with higher resolution [9]. Other augmentation methods for images such as random crop, horizontal or vertical mirroring, random rotation, or translation [29, 43] may similarly apply to a certain group of image datasets while being inapplicable to others, e.g. datasets of digits and letters. In an attempt to automate the augmentation process and reduce human involvement, policy or searchbased automated augmentation methods were developed. In AutoAugment [7] a neural network is trained with Reinforcement Learning (RL) to combine an assortment of transformations in varying strengths to apply on samples of a given dataset and improve the model accuracy. Methods such as RandAugment [8], Fast AutoAugment [30], UniformAugment [32] and TrivialAugment [36] aim at reducing the cost of the pretraining search phase in automated augmentation with randomized transformations and reduced search space. Alternatively, in order to adapt the augmentation policy to the model during training, PopulationBased Augmentation [16] and Online Hyperparameter Learning [31] use multiple data augmentation workers that are updated using evolutionary strategies and RL, respectively. Adversarial AutoAugment [53] and AugMax [47] optimize for the augmentation policy that deteriorates the training accuracy and improves its robustness. DivAug [34] finds the policy which maximizes the diversity of the augmented data. Having a separate search phase for optimal augmentation policy is computationally expensive and may exceed the required computation to train the downstream model [8, 48]. In addition, these methods and their online counterparts need to be trained separately on every single dataset. While OnlineAugment [44] and DDAS exploit meta-learning to avoid this problem, they still rely on a set of predefined class invariant transformations that require domain-specific information. Generic transformations such as Gaussian or adversarial noise [10, 28, 45] and dropout [3] are also effective in expanding the training dataset. Generative models such as Generative Adversarial Networks (GAN) [13] and Variational Auto-Encoders (VAE) [22] are trained in [1, 6, 44] to synthesize samples close to the low dimensional manifold of the data for classification. Mixup [51] is a popular data augmentation using a convex combination of pairs of samples from different classes and their softened labels for augmentation. Mixup is only evaluated on classification problems, even though it is claimed that the application to regression is straightforward. Various extensions of Mixup have been proposed to prevent data manifold intrusion [46], use more complex mixing strategies [33, 50] or account for saliency in augmented samples [20, 21]. These methods were predominantly designed to excel in classification tasks. In particular, Mixup for regression was studied in [5, 18, 49, 52] but it was reported to adversely impact the predictions in regression problems when misleading augmented samples are generated from a pair of faraway samples. This paper is available on arxiv under CC0 1.0 DEED license. Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Authors: Authors: (1) Nora Schneider, Computer Science Department, ETH Zurich, Zurich, Switzerland (nschneide@student.ethz.ch); (2) Shirin Goshtasbpour, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (shirin.goshtasbpour@inf.ethz.ch); (3) Fernando Perez-Cruz, Computer Science Department, ETH Zurich, Zurich, Switzerland and Swiss Data Science Center, Zurich, Switzerland (fernando.perezcruz@sdsc.ethz.ch). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Background 2.1 Data Augmentation 2.1 Data Augmentation 2.2 Anchor Regression 2.2 Anchor Regression 3 Anchor Data Augmentation 3 Anchor Data Augmentation 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.1 Comparison to C-Mixup and 3.2 Preserving nonlinear data structure 3.3 Algorithm 3.3 Algorithm 4 Experiments and 4.1 Linear synthetic data 4 Experiments and 4.1 Linear synthetic data 4.2 Housing nonlinear regression 4.2 Housing nonlinear regression 4.3 In-distribution Generalization 4.3 In-distribution Generalization 4.4 Out-of-distribution Robustness 4.4 Out-of-distribution Robustness 5 Conclusion, Broader Impact, and References 5 Conclusion, Broader Impact, and References A Additional information for Anchor Data Augmentation A Additional information for Anchor Data Augmentation B Experiments B Experiments 2.1 Data Augmentation Many different data augmentation methods have been proposed in recent years with several applications in mind. Still most augmentations we mention here use human-designed transformations based on domain knowledge which leave the target variable invariant. For instance, Cutout [10] is an image-specific augmentation technique that is successfully used to train models on CIFAR10 and CIFAR100 [25], but was determined to be unsuitable for larger image datasets like ImageNet with higher resolution [9]. Other augmentation methods for images such as random crop, horizontal or vertical mirroring, random rotation, or translation [29, 43] may similarly apply to a certain group of image datasets while being inapplicable to others, e.g. datasets of digits and letters. In an attempt to automate the augmentation process and reduce human involvement, policy or searchbased automated augmentation methods were developed. In AutoAugment [7] a neural network is trained with Reinforcement Learning (RL) to combine an assortment of transformations in varying strengths to apply on samples of a given dataset and improve the model accuracy. Methods such as RandAugment [8], Fast AutoAugment [30], UniformAugment [32] and TrivialAugment [36] aim at reducing the cost of the pretraining search phase in automated augmentation with randomized transformations and reduced search space. Alternatively, in order to adapt the augmentation policy to the model during training, PopulationBased Augmentation [16] and Online Hyperparameter Learning [31] use multiple data augmentation workers that are updated using evolutionary strategies and RL, respectively. Adversarial AutoAugment [53] and AugMax [47] optimize for the augmentation policy that deteriorates the training accuracy and improves its robustness. DivAug [34] finds the policy which maximizes the diversity of the augmented data. Having a separate search phase for optimal augmentation policy is computationally expensive and may exceed the required computation to train the downstream model [8, 48]. In addition, these methods and their online counterparts need to be trained separately on every single dataset. While OnlineAugment [44] and DDAS exploit meta-learning to avoid this problem, they still rely on a set of predefined class invariant transformations that require domain-specific information. Generic transformations such as Gaussian or adversarial noise [10, 28, 45] and dropout [3] are also effective in expanding the training dataset. Generative models such as Generative Adversarial Networks (GAN) [13] and Variational Auto-Encoders (VAE) [22] are trained in [1, 6, 44] to synthesize samples close to the low dimensional manifold of the data for classification. Mixup [51] is a popular data augmentation using a convex combination of pairs of samples from different classes and their softened labels for augmentation. Mixup is only evaluated on classification problems, even though it is claimed that the application to regression is straightforward. Various extensions of Mixup have been proposed to prevent data manifold intrusion [46], use more complex mixing strategies [33, 50] or account for saliency in augmented samples [20, 21]. These methods were predominantly designed to excel in classification tasks. In particular, Mixup for regression was studied in [5, 18, 49, 52] but it was reported to adversely impact the predictions in regression problems when misleading augmented samples are generated from a pair of faraway samples. This paper is available on arxiv under CC0 1.0 DEED license. This paper is available on arxiv under CC0 1.0 DEED license. available on arxiv

A Comprehensive Overview of Data Augmentation Methods

Authors:
(1) Zhaoqing Wang, The University of Sydney and AI2Robotics;
(2) Xiaobo Xia, The University of Sydney;
(3) Ziye Chen, The University of Melbourne;
(4) Xiao He, AI2Robotics;
(5) Yandong Guo, AI2Robotics;
(6) Mingming Gong, The University of Melbourne and Mohamed bin Zayed University of Artificial Intelligence;
(7) Tongliang Liu, The University of Sydney. Table of Links Abstract and 1. Introduction 2. Related works 3. Method and 3.1. Problem definition 3.2. Baseline and 3.3. Uni-OVSeg framework 4. Experiments 4.1. Implementation details 4.2. Main results 4.3. Ablation study 5. Conclusion 6. Broader impacts and References A. Framework details B. Promptable segmentation C. Visualisation 4.2. Main results Open-vocabulary semantic segmentation. As demonstrated in Tab. 1, our study presents a comprehensive comparison of our Uni-OVSeg against previous works across a range of benchmarks. These include ADE20K (encompassing both 150 and 847 class variants), PASCAL Context (459 and 59 class variants), PASCAL VOC (with 20 and 21 class categories), and Cityscapes. Compared to weakly-supervised methods, Uni-OVSeg exhibits remarkable performance improvements across all evaluated datasets. Specifically, in the more challenging datasets of PASCAL Context-459, Uni-OVSeg not only surpasses its weakly-supervised counterparts but also outperforms the cutting-edge fully-supervised methods, e.g., FC-CLIP. This is indicative of Uni-OVSeg’s superior capability in categorizing a diverse array of semantic classes. Furthermore, in the PASCAL VOC benchmarks (20 and 21 classes), Uni-OVSeg demonstrates a substantial enhancement over state-of-the-art weakly-supervised methods, achieving improvements of 18.3% and 12.2% mIoU, respectively, which demonstrates our Uni-OVSeg captures fine-grained spatial structures. These results elevate the practical applicability of weakly-supervised open-vocabulary segmentation to new heights. Open-vocabulary panoptic segmentation. For openvocabulary panoptic segmentation, we zero-shot evaluate our model on the COCO, ADE20K, and Cityscapes datasets, shown in Tab. 2. Existing weakly-supervised methods only use text supervision, which causes a challenge to discriminate different instances with the same semantic class. To the best of our knowledge, we are the first to learn open-vocabulary panoptic segmentation with weak supervision. Compared to unsupervised methods, we obviously outperform U2Seg by 1.9% PQ, 1.5%SQ, and 4.4% RQ on COCO datasets. Unfortunately, our used image-mask pairs contain multiple granularity masks, such as object-wise and part-wise masks, which is different with the panoptic segmentation datasets. This discrepancy leads to a number of false positive results, limiting our performance. Promptable segmentation. To evaluate the segmentation efficacy of Uni-OVSeg in scenarios involving interactive point and box prompts, we conduct comparative analyses with the SAM-ViT/L model across a range of datasets from diverse domains. For visual prompts, we implement a uniform 20×20 point grid as the interactive point prompt and utilise the actual bounding boxes as box prompts. The segmentation performance is measured using the 1-pt IoU (Oracle) metric across all datasets. The results, as demonstrated in Fig. 3, indicate that Uni-OVSeg exceeds SAM in most datasets when employing point and box prompts. In particular, Uni-OVSeg significantly surpasses SAM in terms of IoU by 31.1%, 20.1%, and 43.2% on the TimberSeg, COCO instance, and PIDray datasets, respectively. Additionally, we provide a visualisation of the segmentation results of both SAM and Uni-OVSeg in Fig. 4. The visualisation reveals that SAM tends to miss larger masks and erroneously categorise areas with unclear boundaries. In contrast, UniOVSeg demonstrates exceptional precision in segmenting objects of varying scales and different stuff. More experimental results are visualisation can be found in the Appendix B and C. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Zhaoqing Wang, The University of Sydney and AI2Robotics; (2) Xiaobo Xia, The University of Sydney; (3) Ziye Chen, The University of Melbourne; (4) Xiao He, AI2Robotics; (5) Yandong Guo, AI2Robotics; (6) Mingming Gong, The University of Melbourne and Mohamed bin Zayed University of Artificial Intelligence; (7) Tongliang Liu, The University of Sydney. Authors: Authors: (1) Zhaoqing Wang, The University of Sydney and AI2Robotics; (2) Xiaobo Xia, The University of Sydney; (3) Ziye Chen, The University of Melbourne; (4) Xiao He, AI2Robotics; (5) Yandong Guo, AI2Robotics; (6) Mingming Gong, The University of Melbourne and Mohamed bin Zayed University of Artificial Intelligence; (7) Tongliang Liu, The University of Sydney. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Related works 2. Related works 3. Method and 3.1. Problem definition 3. Method and 3.1. Problem definition 3.2. Baseline and 3.3. Uni-OVSeg framework 3.2. Baseline and 3.3. Uni-OVSeg framework 4. Experiments 4.1. Implementation details 4.1. Implementation details 4.2. Main results 4.2. Main results 4.3. Ablation study 4.3. Ablation study 5. Conclusion 5. Conclusion 6. Broader impacts and References 6. Broader impacts and References A. Framework details A. Framework details B. Promptable segmentation B. Promptable segmentation C. Visualisation C. Visualisation 4.2. Main results Open-vocabulary semantic segmentation. As demonstrated in Tab. 1, our study presents a comprehensive comparison of our Uni-OVSeg against previous works across a range of benchmarks. These include ADE20K (encompassing both 150 and 847 class variants), PASCAL Context (459 and 59 class variants), PASCAL VOC (with 20 and 21 class categories), and Cityscapes. Compared to weakly-supervised methods, Uni-OVSeg exhibits remarkable performance improvements across all evaluated datasets. Specifically, in the more challenging datasets of PASCAL Context-459, Uni-OVSeg not only surpasses its weakly-supervised counterparts but also outperforms the cutting-edge fully-supervised methods, e.g., FC-CLIP. This is indicative of Uni-OVSeg’s superior capability in categorizing a diverse array of semantic classes. Furthermore, in the PASCAL VOC benchmarks (20 and 21 classes), Uni-OVSeg demonstrates a substantial enhancement over state-of-the-art weakly-supervised methods, achieving improvements of 18.3% and 12.2% mIoU, respectively, which demonstrates our Uni-OVSeg captures fine-grained spatial structures. These results elevate the practical applicability of weakly-supervised open-vocabulary segmentation to new heights. Open-vocabulary semantic segmentation. Open-vocabulary panoptic segmentation. For openvocabulary panoptic segmentation, we zero-shot evaluate our model on the COCO, ADE20K, and Cityscapes datasets, shown in Tab. 2. Existing weakly-supervised methods only use text supervision, which causes a challenge to discriminate different instances with the same semantic class. To the best of our knowledge, we are the first to learn open-vocabulary panoptic segmentation with weak supervision. Compared to unsupervised methods, we obviously outperform U2Seg by 1.9% PQ, 1.5%SQ, and 4.4% RQ on COCO datasets. Unfortunately, our used image-mask pairs contain multiple granularity masks, such as object-wise and part-wise masks, which is different with the panoptic segmentation datasets. This discrepancy leads to a number of false positive results, limiting our performance. Open-vocabulary panoptic segmentation. Promptable segmentation. To evaluate the segmentation efficacy of Uni-OVSeg in scenarios involving interactive point and box prompts, we conduct comparative analyses with the SAM-ViT/L model across a range of datasets from diverse domains. For visual prompts, we implement a uniform 20×20 point grid as the interactive point prompt and utilise the actual bounding boxes as box prompts. The segmentation performance is measured using the 1-pt IoU (Oracle) metric across all datasets. The results, as demonstrated in Fig. 3, indicate that Uni-OVSeg exceeds SAM in most Promptable segmentation. datasets when employing point and box prompts. In particular, Uni-OVSeg significantly surpasses SAM in terms of IoU by 31.1%, 20.1%, and 43.2% on the TimberSeg, COCO instance, and PIDray datasets, respectively. Additionally, we provide a visualisation of the segmentation results of both SAM and Uni-OVSeg in Fig. 4. The visualisation reveals that SAM tends to miss larger masks and erroneously categorise areas with unclear boundaries. In contrast, UniOVSeg demonstrates exceptional precision in segmenting objects of varying scales and different stuff. More experimental results are visualisation can be found in the Appendix B and C. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Uni-OVSeg Outperforms Weakly-Supervised and Fully-Supervised Methods in Open-Vocabulary Segmentation

Authors:
(1) Zhaoqing Wang, The University of Sydney and AI2Robotics;
(2) Xiaobo Xia, The University of Sydney;
(3) Ziye Chen, The University of Melbourne;
(4) Xiao He, AI2Robotics;
(5) Yandong Guo, AI2Robotics;
(6) Mingming Gong, The University of Melbourne and Mohamed bin Zayed University of Artificial Intelligence;
(7) Tongliang Liu, The University of Sydney. Table of Links Abstract and 1. Introduction 2. Related works 3. Method and 3.1. Problem definition 3.2. Baseline and 3.3. Uni-OVSeg framework 4. Experiments 4.1. Implementation details 4.2. Main results 4.3. Ablation study 5. Conclusion 6. Broader impacts and References A. Framework details B. Promptable segmentation C. Visualisation 4.1. Implementation details Datasets. During training, we randomly sample the 30% subset from the SA-1B dataset [34], which contains ∼ 3 million images and ∼ 0.3 billion masks. Although this supervision provides diverse binary masks, it lacks the semantic class for each mask. In addition, following Chen et al. [8], we collect about 1.3 million image-text pairs and use a large vision-language model to refine them. Afterward, we use the ChatGPT-based parser to extract entities with descriptive words from these text descriptions. Evaluation & metrics. We evaluate our model mainly on three tasks, including open-vocabulary semantic segmentation, open-vocabulary panoptic segmentation, and promptable segmentation. Following previous work [76], we adopt prompt engineering from [21, 66] and prompt templates from [22, 37]. For open-vocabulary semantic segmentation, we zero-shot evaluate the model on the COCO [40], ADE20K [84], PASCAL [18] datasets. The open-vocabulary semantic segmentation results are evaluated with the mean Intersection-over-Union (mIoU). For open-vocabulary panoptic segmentation, we evaluate the model on the COCO, ADE20K, and Cityscapes [15] datasets. We report the panoptic quality (PQ), semantic quality (SQ), and recognition quality (RQ) for open-vocabulary panoptic segmentation. For promptable segmentation, we report the 1-Point and 1-Box IoU (Oracle) on a wide range of datasets. Oracle denotes that we select the output mask with the max IoU by calculating the IoU between the prediction and target mask. More details can be found in Appendix B. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Zhaoqing Wang, The University of Sydney and AI2Robotics; (2) Xiaobo Xia, The University of Sydney; (3) Ziye Chen, The University of Melbourne; (4) Xiao He, AI2Robotics; (5) Yandong Guo, AI2Robotics; (6) Mingming Gong, The University of Melbourne and Mohamed bin Zayed University of Artificial Intelligence; (7) Tongliang Liu, The University of Sydney. Authors: Authors: (1) Zhaoqing Wang, The University of Sydney and AI2Robotics; (2) Xiaobo Xia, The University of Sydney; (3) Ziye Chen, The University of Melbourne; (4) Xiao He, AI2Robotics; (5) Yandong Guo, AI2Robotics; (6) Mingming Gong, The University of Melbourne and Mohamed bin Zayed University of Artificial Intelligence; (7) Tongliang Liu, The University of Sydney. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Related works 2. Related works 3. Method and 3.1. Problem definition 3. Method and 3.1. Problem definition 3.2. Baseline and 3.3. Uni-OVSeg framework 3.2. Baseline and 3.3. Uni-OVSeg framework 4. Experiments 4.1. Implementation details 4.1. Implementation details 4.2. Main results 4.2. Main results 4.3. Ablation study 4.3. Ablation study 5. Conclusion 5. Conclusion 6. Broader impacts and References 6. Broader impacts and References A. Framework details A. Framework details B. Promptable segmentation B. Promptable segmentation C. Visualisation C. Visualisation 4.1. Implementation details Datasets . During training, we randomly sample the 30% subset from the SA-1B dataset [34], which contains ∼ 3 million images and ∼ 0.3 billion masks. Although this supervision provides diverse binary masks, it lacks the semantic class for each mask. In addition, following Chen et al. [8], we collect about 1.3 million image-text pairs and use a large vision-language model to refine them. Afterward, we use the ChatGPT-based parser to extract entities with descriptive words from these text descriptions. Datasets Evaluation & metrics. We evaluate our model mainly on three tasks, including open-vocabulary semantic segmentation, open-vocabulary panoptic segmentation, and promptable segmentation. Following previous work [76], we adopt prompt engineering from [21, 66] and prompt templates from [22, 37]. For open-vocabulary semantic segmentation, we zero-shot evaluate the model on the COCO [40], ADE20K [84], PASCAL [18] datasets. The open-vocabulary semantic segmentation results are evaluated with the mean Intersection-over-Union (mIoU). For open-vocabulary panoptic segmentation, we evaluate the model on the COCO, ADE20K, and Cityscapes [15] datasets. We report the panoptic quality (PQ), semantic quality (SQ), and recognition quality (RQ) for open-vocabulary panoptic segmentation. For promptable segmentation, we report the 1-Point and 1-Box IoU (Oracle) on a wide range of datasets. Oracle denotes that we select the output mask with the max IoU by calculating the IoU between the prediction and target mask. More details can be found in Appendix B. Evaluation & metrics. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Datasets and Evaluation Methods for Open-Vocabulary Segmentation Tasks

Table of Links Abstract and 1. Introduction 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution Literature Review
Methodology 3.1 Model Assumption 3.2 Theorems and Model Discussion Result Analysis
Conclusion and References 5. CONCLUSION The research findings have demonstrated that finite difference methods offer a powerful tool for approximating option prices and hedging parameters, especially in cases where closed-form solutions are unavailable or impractical. The asymptotic analysis conducted in this study has provided valuable insights into the convergence properties and accuracy of finite difference approximations, shedding light on the optimal choice of discretization schemes and grid sizes for different option contracts. Furthermore, the combination of finite difference methods and Monte Carlo simulation with variance reduction techniques offers a comprehensive approach to hedge error analysis in option pricing. By leveraging the strengths of both methodologies, financial practitioners can obtain more robust and reliable estimates of option prices and hedge parameters, thereby enhancing their risk management capabilities and decision-making processes. It is important to acknowledge the limitations of this study and areas for future research. While the asymptotic analysis provides valuable theoretical insights, further empirical validation is warranted to assess the robustness of the findings across different market conditions and asset classes. Additionally, exploring alternative variance reduction techniques and incorporating more sophisticated models of market dynamics could yield further improvements in hedge error analysis and option pricing accuracy. this study has advanced our understanding of the factors influencing hedge errors and provided practical tools for mitigating their impact on derivative pricing and risk management. As financial markets continue to evolve, the insights gained from this research will remain valuable for academics, practitioners, and policymakers striving to enhance the efficiency and stability of global financial systems. REFERENCES [1] C. W. Smith, “Option pricing. A review,” J. financ. econ., vol. 3, no. 1–2, pp. 3–51, 1976, doi: 10.1016/0304-405X(76)90019-2. [2] S. Guernsey, “an Introduction To the Black-Scholes Pde Model,” 2013. [3] B. Peeters, C. L. Dert, and A. Lucas, “Black Scholes for Portfolios of Options in Discrete Time,” SSRN Electron. J., no. 03, 2005, doi: 10.2139/ssrn.469022. [4] J. He, “A Study on Analytical and Numerical Solutions of Three Types of Black-Scholes Models,” Int. J. Trade, Econ. Financ., vol. 13, no. 2, 2022, doi: 10.18178/ijtef.2022.13.2.720. [5] A. S. Shinde and K. C. Takale, “Study of BlackScholes model and its applications,” Procedia Eng., vol. 38, pp. 270–279, 2012, doi: 10.1016/j.proeng.2012.06.035. [6] Y. Zhang, “The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives,” PLoS One, vol. 15, no. 2, pp. 1–13, 2020, doi: 10.1371/journal.pone.0229737. [7] P. L. Bonate, “A brief introduction to Monte Carlo simulation,” Clin. Pharmacokinet., vol. 40, no. 1, pp. 15–22, 2001, doi: 10.2165/00003088- 200140010-00002. [8] D. R. Tobergte and S. Curtis, “Importance sampling for high speed statistical Monte-Carlo simulations,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [9] E. C. Anderson and M. Stephens, “Importance Sampling and (MC)^3,” Sisg 2020, vol. 2, no. July, pp. 1–29, 2020. [10] I. N. Medvedev, “Vector estimators of the Monte Carlo method with a finite variance,” Russ. J. Numer. Anal. Math. Model., vol. 28, no. 3, pp. 231– 244, 2013, doi: 10.1515/rnam-2013-0014. [11] E. Saliby and R. J. Paul, “A farewell to the use of antithetic variates in monte carlo simulation,” J. Oper. Res. Soc., vol. 60, no. 7, pp. 1026–1035, 2009, doi: 10.1057/palgrave.jors.2602645. [12] P. W. Glynn and R. Szechtman, “Some New Perspectives on the Method of Control Variates,” Monte Carlo Quasi-Monte Carlo Methods 2000, pp. 27–49, 2002, doi: 10.1007/978-3-642-56046-0_3. [13] W. Gustafsson, “Evaluating the Longstaff-Schwartz method for pricing of American options,” 2015. [14] L. Andersen and M. Broadie, “Primal-dual simulation algorithm for pricing multidimensional American options,” Manage. Sci., vol. 50, no. 9, pp. 1222–1234, 2004, doi: 10.1287/mnsc.1040.0258. [15] E. Wipplinger, Jim Gatheral: The volatility surface, a practitioner’s guide, vol. 22, no. 1. 2008. doi: 10.1007/s11408-007-0072-4. [16] M. Avellaneda and S. Stoikov, “High-frequency trading in a limit order book,” Quant. Financ., vol. 8, no. 3, pp. 217–224, 2008, doi: 10.1080/14697680701381228. [17] S. Mayoral, D. Moreno, and A. Zareei, “Using a hedging network to minimize portfolio risk,” Financ. Res. Lett., vol. 44, no. April, p. 102044, 2022, doi: 10.1016/j.frl.2021.102044. [18] S. Gayathri Devi, K. Selvam, and S. P. Rajagopalan, “An abstract to calculate big o factors of time and space complexity of machine code,” IET Conf. Publ., vol. 2011, no. 583 CP, pp. 844–847, 2011, doi: 10.1049/cp.2011.0483. [19] M. S. H. Mojumder, M. N. Haque, and M. J. Alam, “Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation,” J. Appl. Math. Phys., vol. 11, no. 10, pp. 3099–3123, 2023, doi: 10.4236/jamp.2023.1110204. [20] I. R. Khan and R. Ohba, “Taylor series based finite difference approximations of higher-degree derivatives,” J. Comput. Appl. Math., vol. 154, no. 1, pp. 115–124, 2003, doi: 10.1016/S0377- 0427(02)00816-6. [21] S. Danho, “Pricing Financial Derivatives with the Finite Difference Method,” p. 237, 2017. [22] G. Connor and T. Lasarte, “An Introduction to Hedge Funds Strategies. Introductory Guide,” pp. 1–16, 2004, [Online]. Available: http://eprints.lse.ac.uk/24675/1/dp477.pdf [23] M. Nurul Anwar and L. Sazzad Andallah, “A Study on Numerical Solution of Black-Scholes Model,” J. Math. Financ., vol. 08, no. 02, pp. 372–381, 2018, doi: 10.4236/jmf.2018.82024. [24] J. Akahori, F. Barsotti, and Y. Imamura, “Hedging error as generalized timing risk,” Quant. Financ., vol. 23, no. 4, pp. 693–703, 2023, doi: 10.1080/14697688.2022.2154255. [25] R. C. A. Oomen and G. J. Jiang, “Hedging Derivatives Risks - A Simulation Study,” SSRN Electron. J., no. May, 2005, doi: 10.2139/ssrn.302525. [26] K. A. Froot, “Hedging Portfolios with Real Assets,” J. Portf. Manag., vol. 21, no. 4, pp. 60–77, 1995, doi: 10.3905/jpm.1995.409527. [27] H. E. LELAND, “Option Pricing and Replication with Transactions Costs,” J. Finance, vol. 40, no. 5, pp. 1283–1301, 1985, doi: 10.1111/j.1540- 6261.1985.tb02383.x. [28] T. Hayashi and P. A. Mykland, “Evaluating hedging errors: An asymptotic approach,” Math. Financ., vol. 15, no. 2, pp. 309–343, 2005, doi: 10.1111/j.0960-1627.2005.00221.x. [29] J.-L. Prigent, R. Hentati, and A. Kaffel, “Dynamic versus static optimization of hedge fund portfolios: the relevance of performance measures,” Int. J. Bus., vol. 15, no. 156, pp. 1–17, 2010. [30] R. A. Jarrow, D. Lando, and F. Yu, “Default Risk and Diversification : Theory and Empirical Implications * Default Risk and Diversification: Theory and Empirical Implications Abstract,” no. 607, 2003. [31] S. Kim, D. Jeong, C. Lee, and J. Kim, “Finite difference method for the multi-asset black-scholes equations,” Mathematics, vol. 8, no. 3, pp. 1–17, 2020, doi: 10.3390/math8030391. [32] D. Jeong, M. Yoo, and J. Kim, “Finite Difference Method for the Black–Scholes Equation Without Boundary Conditions,” Comput. Econ., vol. 51, no. 4, pp. 961–972, 2018, doi: 10.1007/s10614-017- 9653-0. [33] T. Guo, Black-Scholes Process and Monte Carlo Simulation-Based Options Pricing. Atlantis Press International BV, 2023. doi: 10.2991/978-94-6463- 010-7_75. [34] P. Glasserman, “Monte Carlo Methods in Financial Engineerring,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [35] Q. Jiang*, “Comparison of Black–Scholes Model and Monte-Carlo Simulation on Stock Price Modeling,” vol. 109, no. Icemci, pp. 135–137, 2020, doi: 10.2991/aebmr.k.191217.025. [36] E. Derman and E. K, “Stochastic Caclulus for Finance,” pp. 1–63, 2000. Authors:
(1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com);
(2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in);
(3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Abstract and 1. Introduction 1.1 Option Pricing 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.3 Finite Difference 1.4 The Black-Schole Model 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution 1.6 Our Contribution Literature Review Methodology Literature Review Literature Review Literature Review Methodology Methodology 3.1 Model Assumption 3.1 Model Assumption 3.2 Theorems and Model Discussion 3.2 Theorems and Model Discussion Result Analysis Conclusion and References Result Analysis Result Analysis Result Analysis Conclusion and References Conclusion and References Conclusion and References 5. CONCLUSION The research findings have demonstrated that finite difference methods offer a powerful tool for approximating option prices and hedging parameters, especially in cases where closed-form solutions are unavailable or impractical. The asymptotic analysis conducted in this study has provided valuable insights into the convergence properties and accuracy of finite difference approximations, shedding light on the optimal choice of discretization schemes and grid sizes for different option contracts. Furthermore, the combination of finite difference methods and Monte Carlo simulation with variance reduction techniques offers a comprehensive approach to hedge error analysis in option pricing. By leveraging the strengths of both methodologies, financial practitioners can obtain more robust and reliable estimates of option prices and hedge parameters, thereby enhancing their risk management capabilities and decision-making processes. It is important to acknowledge the limitations of this study and areas for future research. While the asymptotic analysis provides valuable theoretical insights, further empirical validation is warranted to assess the robustness of the findings across different market conditions and asset classes. Additionally, exploring alternative variance reduction techniques and incorporating more sophisticated models of market dynamics could yield further improvements in hedge error analysis and option pricing accuracy. this study has advanced our understanding of the factors influencing hedge errors and provided practical tools for mitigating their impact on derivative pricing and risk management. As financial markets continue to evolve, the insights gained from this research will remain valuable for academics, practitioners, and policymakers striving to enhance the efficiency and stability of global financial systems. REFERENCES [1] C. W. Smith, “Option pricing. A review,” J. financ. econ., vol. 3, no. 1–2, pp. 3–51, 1976, doi: 10.1016/0304-405X(76)90019-2. [2] S. Guernsey, “an Introduction To the Black-Scholes Pde Model,” 2013. [3] B. Peeters, C. L. Dert, and A. Lucas, “Black Scholes for Portfolios of Options in Discrete Time,” SSRN Electron. J., no. 03, 2005, doi: 10.2139/ssrn.469022. [4] J. He, “A Study on Analytical and Numerical Solutions of Three Types of Black-Scholes Models,” Int. J. Trade, Econ. Financ., vol. 13, no. 2, 2022, doi: 10.18178/ijtef.2022.13.2.720. [5] A. S. Shinde and K. C. Takale, “Study of BlackScholes model and its applications,” Procedia Eng., vol. 38, pp. 270–279, 2012, doi: 10.1016/j.proeng.2012.06.035. [6] Y. Zhang, “The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives,” PLoS One, vol. 15, no. 2, pp. 1–13, 2020, doi: 10.1371/journal.pone.0229737. [7] P. L. Bonate, “A brief introduction to Monte Carlo simulation,” Clin. Pharmacokinet., vol. 40, no. 1, pp. 15–22, 2001, doi: 10.2165/00003088- 200140010-00002. [8] D. R. Tobergte and S. Curtis, “Importance sampling for high speed statistical Monte-Carlo simulations,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [9] E. C. Anderson and M. Stephens, “Importance Sampling and (MC)^3,” Sisg 2020, vol. 2, no. July, pp. 1–29, 2020. [10] I. N. Medvedev, “Vector estimators of the Monte Carlo method with a finite variance,” Russ. J. Numer. Anal. Math. Model., vol. 28, no. 3, pp. 231– 244, 2013, doi: 10.1515/rnam-2013-0014. [11] E. Saliby and R. J. Paul, “A farewell to the use of antithetic variates in monte carlo simulation,” J. Oper. Res. Soc., vol. 60, no. 7, pp. 1026–1035, 2009, doi: 10.1057/palgrave.jors.2602645. [12] P. W. Glynn and R. Szechtman, “Some New Perspectives on the Method of Control Variates,” Monte Carlo Quasi-Monte Carlo Methods 2000, pp. 27–49, 2002, doi: 10.1007/978-3-642-56046-0_3. [13] W. Gustafsson, “Evaluating the Longstaff-Schwartz method for pricing of American options,” 2015. [14] L. Andersen and M. Broadie, “Primal-dual simulation algorithm for pricing multidimensional American options,” Manage. Sci., vol. 50, no. 9, pp. 1222–1234, 2004, doi: 10.1287/mnsc.1040.0258. [15] E. Wipplinger, Jim Gatheral: The volatility surface, a practitioner’s guide, vol. 22, no. 1. 2008. doi: 10.1007/s11408-007-0072-4. [16] M. Avellaneda and S. Stoikov, “High-frequency trading in a limit order book,” Quant. Financ., vol. 8, no. 3, pp. 217–224, 2008, doi: 10.1080/14697680701381228. [17] S. Mayoral, D. Moreno, and A. Zareei, “Using a hedging network to minimize portfolio risk,” Financ. Res. Lett., vol. 44, no. April, p. 102044, 2022, doi: 10.1016/j.frl.2021.102044. [18] S. Gayathri Devi, K. Selvam, and S. P. Rajagopalan, “An abstract to calculate big o factors of time and space complexity of machine code,” IET Conf. Publ., vol. 2011, no. 583 CP, pp. 844–847, 2011, doi: 10.1049/cp.2011.0483. [19] M. S. H. Mojumder, M. N. Haque, and M. J. Alam, “Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation,” J. Appl. Math. Phys., vol. 11, no. 10, pp. 3099–3123, 2023, doi: 10.4236/jamp.2023.1110204. [20] I. R. Khan and R. Ohba, “Taylor series based finite difference approximations of higher-degree derivatives,” J. Comput. Appl. Math., vol. 154, no. 1, pp. 115–124, 2003, doi: 10.1016/S0377- 0427(02)00816-6. [21] S. Danho, “Pricing Financial Derivatives with the Finite Difference Method,” p. 237, 2017. [22] G. Connor and T. Lasarte, “An Introduction to Hedge Funds Strategies. Introductory Guide,” pp. 1–16, 2004, [Online]. Available: http://eprints.lse.ac.uk/24675/1/dp477.pdf http://eprints.lse.ac.uk/24675/1/dp477.pdf [23] M. Nurul Anwar and L. Sazzad Andallah, “A Study on Numerical Solution of Black-Scholes Model,” J. Math. Financ., vol. 08, no. 02, pp. 372–381, 2018, doi: 10.4236/jmf.2018.82024. [24] J. Akahori, F. Barsotti, and Y. Imamura, “Hedging error as generalized timing risk,” Quant. Financ., vol. 23, no. 4, pp. 693–703, 2023, doi: 10.1080/14697688.2022.2154255. [25] R. C. A. Oomen and G. J. Jiang, “Hedging Derivatives Risks - A Simulation Study,” SSRN Electron. J., no. May, 2005, doi: 10.2139/ssrn.302525. [26] K. A. Froot, “Hedging Portfolios with Real Assets,” J. Portf. Manag., vol. 21, no. 4, pp. 60–77, 1995, doi: 10.3905/jpm.1995.409527. [27] H. E. LELAND, “Option Pricing and Replication with Transactions Costs,” J. Finance, vol. 40, no. 5, pp. 1283–1301, 1985, doi: 10.1111/j.1540- 6261.1985.tb02383.x. [28] T. Hayashi and P. A. Mykland, “Evaluating hedging errors: An asymptotic approach,” Math. Financ., vol. 15, no. 2, pp. 309–343, 2005, doi: 10.1111/j.0960-1627.2005.00221.x. [29] J.-L. Prigent, R. Hentati, and A. Kaffel, “Dynamic versus static optimization of hedge fund portfolios: the relevance of performance measures,” Int. J. Bus., vol. 15, no. 156, pp. 1–17, 2010. [30] R. A. Jarrow, D. Lando, and F. Yu, “Default Risk and Diversification : Theory and Empirical Implications * Default Risk and Diversification: Theory and Empirical Implications Abstract,” no. 607, 2003. [31] S. Kim, D. Jeong, C. Lee, and J. Kim, “Finite difference method for the multi-asset black-scholes equations,” Mathematics, vol. 8, no. 3, pp. 1–17, 2020, doi: 10.3390/math8030391. [32] D. Jeong, M. Yoo, and J. Kim, “Finite Difference Method for the Black–Scholes Equation Without Boundary Conditions,” Comput. Econ., vol. 51, no. 4, pp. 961–972, 2018, doi: 10.1007/s10614-017- 9653-0. [33] T. Guo, Black-Scholes Process and Monte Carlo Simulation-Based Options Pricing. Atlantis Press International BV, 2023. doi: 10.2991/978-94-6463- 010-7_75. [34] P. Glasserman, “Monte Carlo Methods in Financial Engineerring,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [35] Q. Jiang*, “Comparison of Black–Scholes Model and Monte-Carlo Simulation on Stock Price Modeling,” vol. 109, no. Icemci, pp. 135–137, 2020, doi: 10.2991/aebmr.k.191217.025. [36] E. Derman and E. K, “Stochastic Caclulus for Finance,” pp. 1–63, 2000. Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). Authors: Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv

Harnessing Finite Difference Methods for Enhanced Option Pricing

Comparative Analysis of Option Pricing Methods: FDM, Monte Carlo Simulation, and Variance Reduction 

Table of Links Abstract and 1. Introduction 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution Literature Review
Methodology 3.1 Model Assumption 3.2 Theorems and Model Discussion Result Analysis
Conclusion and References 1.3 FINITE DIFFERENCE Finite difference methods are numerical techniques used to approximate derivatives and solve differential equations by discretizing the domain into a grid of points. This approach is based on Taylor series expansions, where derivatives are expressed as combinations of function values at nearby points. Consider a function 𝑓(𝑥) and its derivative 𝑓′(𝑥) then finite difference approximation of the derivative at a point 𝑥𝑖 is given by: In this plot, the tangent line represents the true derivative 𝑓 ′ (𝑥0) , Meanwhile, the secant line represents the finite difference approximation. As the step size ℎ decreases, the secant line becomes closer to the tangent line, demonstrating the convergence of the finite difference approximation to the true derivative as ℎ approaches zero. The application of finite difference methods in option pricing allows for more accurate simulations of market dynamics and estimation of option prices. These methods enable practitioners to account for various factors affecting option values, such as changes in asset prices, volatility, and interest rates. Finite difference methods offer flexibility and scalability, making them suitable for pricing various types of options and constructing hedging strategies. Despite their computational complexity, advancements in numerical algorithms and computing power have made finite difference methods increasingly accessible and efficient for option pricing applications [4]. Authors:
(1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com);
(2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in);
(3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Abstract and 1. Introduction 1.1 Option Pricing 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.3 Finite Difference 1.4 The Black-Schole Model 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution 1.6 Our Contribution Literature Review Methodology Literature Review Literature Review Literature Review Methodology Methodology 3.1 Model Assumption 3.1 Model Assumption 3.2 Theorems and Model Discussion 3.2 Theorems and Model Discussion Result Analysis Conclusion and References Result Analysis Result Analysis Result Analysis Conclusion and References Conclusion and References Conclusion and References 1.3 FINITE DIFFERENCE Finite difference methods are numerical techniques used to approximate derivatives and solve differential equations by discretizing the domain into a grid of points. This approach is based on Taylor series expansions, where derivatives are expressed as combinations of function values at nearby points. Consider a function 𝑓(𝑥) and its derivative 𝑓′(𝑥) then finite difference approximation of the derivative at a point 𝑥𝑖 is given by: In this plot, the tangent line represents the true derivative 𝑓 ′ (𝑥0) , Meanwhile, the secant line represents the finite difference approximation. As the step size ℎ decreases, the secant line becomes closer to the tangent line, demonstrating the convergence of the finite difference approximation to the true derivative as ℎ approaches zero. The application of finite difference methods in option pricing allows for more accurate simulations of market dynamics and estimation of option prices. These methods enable practitioners to account for various factors affecting option values, such as changes in asset prices, volatility, and interest rates. Finite difference methods offer flexibility and scalability, making them suitable for pricing various types of options and constructing hedging strategies. Despite their computational complexity, advancements in numerical algorithms and computing power have made finite difference methods increasingly accessible and efficient for option pricing applications [4]. Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). Authors: Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv

Finite Difference Methods: A Numerical Approach to Option Pricing and Derivatives

Authors:
(1) Qian Yang, Zhejiang University, Equal contribution. This work was conducted during Qian Yang’s internship at Alibaba Group;
(2) Jin Xu, Alibaba Group, Equal contribution;
(3) Wenrui Liu, Zhejiang University;
(4) Yunfei Chu, Alibaba Group;
(5) Xiaohuan Zhou, Alibaba Group;
(6) Yichong Leng, Alibaba Group;
(7) Yuanjun Lv, Alibaba Group;
(8) Zhou Zhao, Alibaba Group and Corresponding to Zhou Zhao (zhaozhou@zju.edu.cn);
(9) Yichong Leng, Zhejiang University
(10) Chang Zhou, Alibaba Group and Corresponding to Chang Zhou (ericzhou.zc@alibaba-inc.com);
(11) Jingren Zhou, Alibaba Group. Table of Links Abstract and 1. Introduction 2 Related Work 3 AIR-Bench and 3.1 Overview 3.2 Foundation Benchmark 3.3 Chat Benchmark 3.4 Evaluation Strategy 4 Experiments 4.1 Models 4.2 Main Results 4.3 Human Evaluation and 4.4 Ablation Study of Positional Bias 5 Conclusion and References A Detailed Results of Foundation Benchmark 3.4 Evaluation Strategy In this paper, we leverage a unified evaluation method, as shown in Fig. 3, by viewing both the single-choice question in the foundation benchmark, and the open-ended question in the chat benchmark, as the generation tasks for the purpose of better alignment with actual use case scenarios of LALMs. That is, given audio and questions, LALMs are required to directly generate the answers as hypotheses, rather than comparing the perplexity on the probability of different reference answers via teacher forcing. Automated and accurate evaluation of open-ended generation is a challenging problem. Traditional automatic metrics such as WER, ROUGE (Lin, 2004), METEOR (Banerjee and Lavie, 2005) have been shown low correlation with human judgements (Liu et al., 2023a). Recently, LLM-based evaluation, such as GPT-4, shows better human preference alignment (Zheng et al., 2023; Liu et al., 2023a). In this work, we adopt reference-based GPT-4 evaluators to judge the generation quality of LALMs in the audio domain. However, GPT-4 cannot be directly used as an evaluator since it cannot receive audio inputs. To address this limitation, we offer the GPT-4 model rich meta-information of audio to replace audio input. Subsequently, we present questions and employ GPT-4 to evaluate the hypotheses produced by LALMs. To ensure consistency and fairness for evaluation, each model’s answer is compared against the same reference answer for scoring. For the foundation benchmark, the reference answer is the golden choice, and we prompt the evaluator to determine whether the hypothesis is correct or not. For the chat benchmark, the reference answer is generated by GPT-4, and we prompt the evaluator to provide a score ranging from 1 to 10, based on the assessment of usefulness, relevance, accuracy, and comprehensiveness of the hypothesis. Note that for the chat benchmark, the role of the reference is not to serve as the ground truth answer, but rather as a reference for scoring by GPT-4, in order to stabilize its scoring. Additionally, to mitigate any potential position bias resulting from the order of hypothesis and reference, following Bai et al. (2023b), we perform a second scoring round by swapping their positions and then compute the average of the two scores. Unless otherwise specified, the GPT-4 evaluator is GPT-4 Turbo, the gpt-4- 0125-preview version [2]. This paper is available on arxiv under CC BY 4.0 DEED license. [2] https://platform.openai.com/docs/models/gpt-4-and-gpt4-turbo Authors: (1) Qian Yang, Zhejiang University, Equal contribution. This work was conducted during Qian Yang’s internship at Alibaba Group; (2) Jin Xu, Alibaba Group, Equal contribution; (3) Wenrui Liu, Zhejiang University; (4) Yunfei Chu, Alibaba Group; (5) Xiaohuan Zhou, Alibaba Group; (6) Yichong Leng, Alibaba Group; (7) Yuanjun Lv, Alibaba Group; (8) Zhou Zhao, Alibaba Group and Corresponding to Zhou Zhao (zhaozhou@zju.edu.cn); (9) Yichong Leng, Zhejiang University (10) Chang Zhou, Alibaba Group and Corresponding to Chang Zhou (ericzhou.zc@alibaba-inc.com); (11) Jingren Zhou, Alibaba Group. Authors: Authors: (1) Qian Yang, Zhejiang University, Equal contribution. This work was conducted during Qian Yang’s internship at Alibaba Group; (2) Jin Xu, Alibaba Group, Equal contribution; (3) Wenrui Liu, Zhejiang University; (4) Yunfei Chu, Alibaba Group; (5) Xiaohuan Zhou, Alibaba Group; (6) Yichong Leng, Alibaba Group; (7) Yuanjun Lv, Alibaba Group; (8) Zhou Zhao, Alibaba Group and Corresponding to Zhou Zhao (zhaozhou@zju.edu.cn); (9) Yichong Leng, Zhejiang University (10) Chang Zhou, Alibaba Group and Corresponding to Chang Zhou (ericzhou.zc@alibaba-inc.com); (11) Jingren Zhou, Alibaba Group. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2 Related Work 2 Related Work 3 AIR-Bench and 3.1 Overview 3 AIR-Bench and 3.1 Overview 3.2 Foundation Benchmark 3.2 Foundation Benchmark 3.3 Chat Benchmark 3.3 Chat Benchmark 3.4 Evaluation Strategy 3.4 Evaluation Strategy 4 Experiments 4.1 Models 4.1 Models 4.2 Main Results 4.2 Main Results 4.3 Human Evaluation and 4.4 Ablation Study of Positional Bias 4.3 Human Evaluation and 4.4 Ablation Study of Positional Bias 5 Conclusion and References 5 Conclusion and References A Detailed Results of Foundation Benchmark A Detailed Results of Foundation Benchmark 3.4 Evaluation Strategy In this paper, we leverage a unified evaluation method, as shown in Fig. 3, by viewing both the single-choice question in the foundation benchmark, and the open-ended question in the chat benchmark, as the generation tasks for the purpose of better alignment with actual use case scenarios of LALMs. That is, given audio and questions, LALMs are required to directly generate the answers as hypotheses, rather than comparing the perplexity on the probability of different reference answers via teacher forcing. Automated and accurate evaluation of open-ended generation is a challenging problem. Traditional automatic metrics such as WER, ROUGE (Lin, 2004), METEOR (Banerjee and Lavie, 2005) have been shown low correlation with human judgements (Liu et al., 2023a). Recently, LLM-based evaluation, such as GPT-4, shows better human preference alignment (Zheng et al., 2023; Liu et al., 2023a). In this work, we adopt reference-based GPT-4 evaluators to judge the generation quality of LALMs in the audio domain. However, GPT-4 cannot be directly used as an evaluator since it cannot receive audio inputs. To address this limitation, we offer the GPT-4 model rich meta-information of audio to replace audio input. Subsequently, we present questions and employ GPT-4 to evaluate the hypotheses produced by LALMs. To ensure consistency and fairness for evaluation, each model’s answer is compared against the same reference answer for scoring. For the foundation benchmark, the reference answer is the golden choice, and we prompt the evaluator to determine whether the hypothesis is correct or not. For the chat benchmark, the reference answer is generated by GPT-4, and we prompt the evaluator to provide a score ranging from 1 to 10, based on the assessment of usefulness, relevance, accuracy, and comprehensiveness of the hypothesis. Note that for the chat benchmark, the role of the reference is not to serve as the ground truth answer, but rather as a reference for scoring by GPT-4, in order to stabilize its scoring. Additionally, to mitigate any potential position bias resulting from the order of hypothesis and reference, following Bai et al. (2023b), we perform a second scoring round by swapping their positions and then compute the average of the two scores. Unless otherwise specified, the GPT-4 evaluator is GPT-4 Turbo, the gpt-4- 0125-preview version [2]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv [2] https://platform.openai.com/docs/models/gpt-4-and-gpt4-turbo

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