2026-01-19 06:00:03
Convex Relaxation Techniques for Hyperbolic SVMs
Discussions, Acknowledgements, and References
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B. Solution Extraction in Relaxed Formulation
C. On Moment Sum-of-Squares Relaxation Hierarchy
E. Detailed Experimental Results
F. Robust Hyperbolic Support Vector Machine
In this section, we propose the robust version of hyperbolic support vector machine without implemention. This is different from the practice of adversarial training that searches for adversarial samples on the fly used in the machine learning community, such as Weber et al. [7]. Rather, we predefine an uncertainty structure for data features and attempt to write down the corresponding optimization formulation, which we call the robust counterpart, as described in [42, 43].
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\ Then, by adding the uncertainty set to the constraints, we have
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\ where the last step is a rewriting into the robust counterpart (RC). We present the 𝑙∞ norm bounded robust HSVM as follows,
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\ Note that since 𝑦𝑖 ∈ {−1, 1}, we may drop the 𝑦𝑖 term in the norm and subsequently write down the SDP relaxation to this non-convex QCQP problem and solve it efficiently with
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\ For the implementation in MOSEK, we linearize the 𝑙1 norm term by introducing extra auxiliary variables, which we do not show here. The moment relaxation can be implemented likewise, since this is constraint-wise uncertainty and we preserve the same sparsity pattern so that the same sparse moment relaxation applies.
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:::info Authors:
(1) Sheng Yang, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA ([email protected]);
(2) Peihan Liu, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA ([email protected]);
(3) Cengiz Pehlevan, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, Center for Brain Science, Harvard University, Cambridge, MA, and Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA ([email protected]).
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:::info This paper is available on arxiv under CC by-SA 4.0 Deed (Attribution-Sharealike 4.0 International) license.
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2026-01-19 05:54:48
The IT economy still relies heavily on COBOL (Common Business-Oriented Language), which powers 70% of global data processing—from banking and ATM transactions to tax processing and healthcare. With over 800 billion lines of code in active production, these systems form a critical foundation, yet they are increasingly at risk.
However, as the original engineers retire, organizations face a dangerous knowledge gap; modern developers find COBOL's procedural logic nearly impenetrable. To prevent these systems from becoming "black boxes," industry leaders are deploying AI Agents for legacy COBOL modernization. These agents function as translators, decoding legacy COBOL and converting it into modern, maintainable code, bridging the 60-year gap between mainframes and today’s software stack.
In this blog, we’ll explore AI coding agents, such as GitHub Copilot, to address the skills gap crisis, reverse-engineer opaque business logic, and de-risk the transition from legacy mainframes to modern cloud architectures.
According to Julia Kordick, a Microsoft Global Black Belt, COBOL or mainframe modernization can be done without learning COBOL. Sounds remarkable, yet confusing?
She emphasized a structured legacy system modernization approach that leverages AI coding agents to support all mainframe modernization projects, including COBOL.
COBOL modernization begins with understanding what the legacy code does—a problem that every organization faces. Even though they are still using legacy code and building workflows around it, they’ve lost sight of its purpose. AI agents reverse-engineering legacy systems
This is where AI Agents reverse-engineer legacy systems. They:
Here is a sample of business logic and preliminary analysis generated by GitHub Copilot: \n 
For further processing, this analysis/understanding is supplemented with additional content to help other AI coding agents better understand your requirement. This could require:
Translation: AI coding agents are better with English context. If your COBOL code contains other languages, use GitHub Copilot to translate it. Structural Changes: COBOL systems follow specific patterns that can be deduced even without knowing this language. You can instruct GitHub Copilot to follow the same
Ask AI coding agents, such as GitHub Copilot, to map these divisions. This is achievable by using prompts like: \n 
Save the enriched context as markdown files for future reference.
The Plus Point: GitHub Copilot is highly verbose. Straightforward prompts like “enrich with total sales data or add annual revenue details” are almost self-documenting.
Once you have understood the business logic and enriched it with context, shift from using GitHub Copilot as a conversational assistant to relying on it as an AI coding agent that builds mainframe modernization workflows.
Use multiple AI coding agents and manage them using Microsoft Semantic Kernel. Assign specific tasks to each AI Agent:
While the above process is pretty much automated, always have a human expert validate and approve the modernized code generated by GitHub Copilot or any other AI coding agent.
Benefits of Deploying AI Agents for Legacy COBOL Modernization**Deploying AI coding agents like GitHub Copilot brings several benefits:
Traditional discovery timelines, in which developers manually analyzed legacy code to understand system behavior, averaged 8-12 months. This comes down to a few days and weeks when you use AI coding agents for COBOL modernization.
The biggest fear in a mainframe modernization project is that the new system won't "act" like the old one. But AI coding agents like GitHub Copilot excel at generating comprehensive unit tests based on inferred legacy logic. Modernized COBOL code that passes these tests serves as a safety net and ultimately the modern counterpart.
Most companies partner with a legacy application modernization company or hire consultants for legacy work because in-house teams often lack COBOL skills. However, when you leverage AI agents for COBOL modernization, you get digital co-workers who act as force multipliers.
Basic AI legacy system tools work as simple translators. However, AI coding agents re-architect legacy logic from scratch and often refactor it into reversible units or microservices. This architectural upgrade enhances your IT system and does not merely translate the code.
Although AI coding agents like GitHub Copilot automate the mainframe modernization process, some steps still require manual, strategic navigation. This is because:
While AI coding agents read legacy COBOL, they cannot read the purpose. Several legacy COBOL systems have functions and logic that’s undocument and based on ‘workarounds’ that are probably 30 years old.
Literal translation of COBOL code often results in JOBOL—Java code that follows COBOL patterns line-by-line. Without proper validation and specific structural changes, this code becomes as challenging to maintain as the original mainframe code. [Source: IBM Research]
Currently, AI Agents are designed to handle multi-step transactions as “continuous workflows” without a transaction coordinator (TC) to manage estate transactions for each task in the chain. If the AI coding agent crashes mid-task, the entire chain breaks, and the consequences can be adverse and irreversible.
According to Google Research, this is only resolved when atomicity/granularity are emphasized as Agentic AI infrastructure requirements. Until then, there must be guardrails to undo Agentic actions and convert the entire multi-step process into reversible tasks.
Key Takeaways:
The COBOL problem has persisted for years and is often viewed as a ticking time bomb, especially when you lack COBOL fluency. But with AI coding agents, you don’t need this level of fluency for COBOL modernization. These AI Agents can analyze outdated code, extract legacy logic, and rewrite it in any modern programming language of your choice.
Using AI agents for COBOL modernization will not only help you survive in the modern tech space but also help you reclaim decades of business intelligence, making it accessible to the newer generation of engineers who will manage your systems in the future. You can either integrate agents like GitHub Copilot or hire AI Agent developers to build custom agents for your modernization project.
2026-01-19 05:40:37
WOW Exchange is a pre-launch crypto trading platform built to address transparency, security, and intelligence gaps through high-performance infrastructure and AI-driven analytics.
2026-01-19 05:24:01
Traditional CI/CD pipelines are collapsing under tool sprawl, static logic, and coordination overhead. Agentic DevOps replaces brittle scripts with AI systems that adapt, automate toil, and reshape how software ships—at a cost.
2026-01-19 05:11:18
This article explains how Android processes work, how they manage memory and threads, how components map to processes, and how the system monitors and terminates apps.
2026-01-19 05:11:12
Android is built on the Linux kernel, which handles power management, hardware control, and secure communication between apps and system services. While most developers never touch it directly, understanding the kernel explains many core Android behaviors and system-level interactions.
