A digital illustration of a blockchain network with a glowing ellipse at its center, representing the future of DeFi security.

DeFi's Next Frontier: Can Automated Market Makers Outsmart Front-Running?

Elliot Brynn in Tech & Innovation August 2025 • 4 min read.

"Explore the evolution of Automated Market Makers (AMMs) and how innovative models like constant ellipse functions could revolutionize DeFi security and efficiency."

Decentralized Finance (DeFi) is transforming the financial world by creating smart contracts, or DApps, that are stored on public blockchains. These contracts automate financial instruments and digital assets, ensuring transparency and security. However, the DeFi landscape is not without its challenges.

One of the most pressing issues is the vulnerability of DeFi platforms to front-running attacks. In a blockchain system, transactions are visible in the network's mempool before they are processed. Malicious actors can exploit this visibility by inserting their own transactions before or after observed ones to extract profit, a concept known as Miner Extractable Value (MEV).

This article delves into the mathematical models that underpin Automated Market Makers (AMMs), the backbone of many DeFi applications. We'll explore how these models can be optimized to resist front-running attacks and reduce gas costs, paving the way for a more secure and efficient DeFi ecosystem.

Understanding Automated Market Makers (AMMs): The Key Models

A digital illustration of a blockchain network with a glowing ellipse at its center, representing the future of DeFi security.

Automated Market Makers (AMMs) are decentralized exchanges that use mathematical equations to determine the prices of assets. Unlike traditional exchanges that rely on order books, AMMs use liquidity pools, where users deposit tokens to provide trading liquidity. These pools operate according to predefined algorithms, making them accessible and automated.

Several mathematical models drive AMMs, each with its strengths and weaknesses:

Logarithmic Market Scoring Rule (LMSR): An early model that adjusts prices based on the total availability of assets.
Liquidity Sensitive LMSR (LS-LMSR): An enhancement of LMSR that considers the liquidity of the market to reduce sensitivity to large trades.
Constant Product/Mean/Sum: Popularized by Uniswap, this model maintains a constant product of the quantities of tokens in a pool.
Constant Ellipse: A newer model that uses an ellipse-based cost function to provide a balance between price stability and gas efficiency.

Each of these models has implications for transaction costs, price slippage, and resistance to front-running attacks. The choice of model can significantly impact the user experience and security of a DeFi platform.

The Future of AMMs: Enhanced Security and Efficiency

The evolution of AMM models is critical to the future of DeFi. As the DeFi ecosystem grows, addressing vulnerabilities such as front-running attacks and high gas costs becomes increasingly important. Innovations like constant ellipse functions and other advanced mathematical models hold the promise of creating more secure, efficient, and user-friendly decentralized exchanges. By understanding and optimizing these models, we can unlock the full potential of decentralized finance.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2009.01676,

Title: Automated Market Makers For Decentralized Finance (Defi)

Subject: q-fin.tr cs.dm cs.gt

Authors: Yongge Wang

Published: 03-09-2020

Everything You Need To Know

What are Automated Market Makers (AMMs) and how do they differ from traditional exchanges?

Automated Market Makers (AMMs) are decentralized exchanges that utilize mathematical equations to set asset prices. Unlike traditional exchanges that depend on order books, AMMs use liquidity pools. Users deposit tokens into these pools to provide trading liquidity. These pools function according to predefined algorithms, making them automated and accessible. Traditional exchanges rely on human order books, which can be prone to manipulation and offer less transparency than AMMs.

What is front-running and why is it a problem in Decentralized Finance (DeFi)?

Front-running is a malicious tactic in DeFi where actors exploit the visibility of transactions in the mempool before they are processed on the blockchain. Because transactions are public before they are executed, bad actors can insert their own trades before or after observed transactions to profit. This practice is known as Miner Extractable Value (MEV). This is a major issue because it leads to unfair trading practices, increased costs for users, and undermines the trust and integrity of DeFi platforms.

Can you explain the key mathematical models used by Automated Market Makers (AMMs)?

Several mathematical models drive Automated Market Makers (AMMs), each with its own characteristics. These include the Logarithmic Market Scoring Rule (LMSR), which adjusts prices based on total asset availability. Another is Liquidity Sensitive LMSR (LS-LMSR), which improves upon LMSR by considering market liquidity. Constant Product/Mean/Sum, a model popularized by Uniswap, maintains a constant product of token quantities. The Constant Ellipse model uses an ellipse-based cost function to balance price stability and gas efficiency. Each model influences transaction costs, price slippage, and the resistance to front-running attacks.

How can innovations like constant ellipse functions improve the security and efficiency of AMMs?

Innovations like constant ellipse functions can significantly enhance the security and efficiency of Automated Market Makers (AMMs). Constant ellipse functions offer a balance between price stability and gas efficiency compared to earlier models. By optimizing these mathematical models, developers can reduce the impact of front-running attacks and lower gas costs. This leads to a more secure, efficient, and user-friendly experience on decentralized exchanges, supporting the broader growth of the DeFi ecosystem.

What are the implications of choosing different Automated Market Maker (AMM) models?

The choice of Automated Market Maker (AMM) model significantly impacts a DeFi platform's performance and user experience. Each model, such as Logarithmic Market Scoring Rule (LMSR), Liquidity Sensitive LMSR (LS-LMSR), Constant Product/Mean/Sum, and Constant Ellipse, has unique characteristics. These affect transaction costs, including gas fees, and the degree of price slippage, the difference between the expected price and the actual price when a trade is executed. Furthermore, different models offer varying levels of resistance to front-running attacks. The selection of an AMM model influences how a platform handles these factors, directly affecting the platform's efficiency, security, and overall appeal to users.