Futuristic DeFi landscape with AMM pools protected from MEV attacks.

Dynamic AMMs: How to Protect Your Investments from Multiblock MEV Attacks

Q: What conditions must multi-token trades satisfy in Temporal-Function Market Making (TFMM) pools to be accepted?

In Temporal-Function Market Making (TFMM) pools, multi-token trades, where traders exchange a set of tokens (vector A) for another set (vector A), must meet specific conditions to be accepted. The pool requires that for tokens i where ∆i > 0, Ai = 0, meaning tokens cannot be traded for themselves. Additionally, trades must account for fees (1 – γ), satisfying a condition that ensures the trade benefits the pool. This rigorous condition ensures the pool's integrity and prevents exploitative trades, though vulnerabilities related to Maximal Extractable Value (MEV) can still arise.

Mira Elwood in Tech & Innovation December 2025 • 4 min read.

"Discover the hidden vulnerabilities in dynamic Automated Market Makers (AMMs) and how innovative protections can safeguard your assets from sophisticated MEV exploits."

In the fast-evolving world of decentralized finance (DeFi), Automated Market Makers (AMMs) have become essential for trading digital assets. Unlike traditional markets that rely on order books, AMMs use mathematical formulas to determine the prices of assets. Constant Function Market Makers (CFMMs) are a common type of AMM, but dynamic AMMs, which include liquidity bootstrap pools (LBPs), Temporal-function market makers (TFMMs), and replicating market makers (RMMs), introduce new complexities and potential vulnerabilities.

One critical concern is the risk of Maximal Extractable Value (MEV) attacks, where malicious actors exploit blockchain mechanics to profit at the expense of other users. While MEV in CFMMs is relatively well understood, dynamic AMMs present novel attack vectors. This article explores how inter-block weight changes in dynamic AMMs can be exploited, leading to multiblock MEV attacks, and examines the protections needed to guard against these threats.

We'll delve into how attackers can manipulate pool weights across multiple blocks, similar to 'sandwich attacks,' but targeting liquidity providers (LPs) rather than individual traders. By understanding these vulnerabilities and the proposed guardrails, you can better protect your investments in dynamic AMMs.

Understanding Temporal-Function Market Making (TFMM)

Futuristic DeFi landscape with AMM pools protected from MEV attacks.

Temporal-Function Market Making (TFMM) pools differ from traditional AMMs by incorporating time-varying trading functions. In a TFMM pool, the portfolio vector, which represents the allocation of assets, changes from block to block. This dynamic adjustment responds to market information, creating arbitrage opportunities that incentivize external agents to rebalance the pool's holdings to match target allocations.

The trading function in a TFMM pool can be expressed as follows:

R_u(t) = k(t)
where ∑ w_i(t) = 1
and ∀i, 0 < w_i(t) < 1

This formula indicates that the reserves of each asset (R_i) depend on the time-varying weights (w_i(t)), and the pool's constant (k) also changes with time. Trades within a block must preserve or increase the value of k(t) at the time of the trade. The dynamic nature of TFMM pools allows them to adapt their positions, re-weighting assets based on market conditions and arbitrage opportunities.

Multi-token trades are permitted in TFMMs, where traders can exchange a set of tokens (represented by vector A) for another set (represented by vector A). The pool requires that for tokens i where ∆i > 0, A_i = 0, meaning tokens cannot be traded for themselves. To ensure acceptance, trades must also account for fees (1 – γ), satisfying the condition:

Future Directions for AMM Security

This analysis marks an initial step in understanding and addressing potential multi-block MEV attacks on dynamic AMMs. As the DeFi landscape evolves, ongoing research and development of robust defense mechanisms are crucial to ensuring the safety and economic viability of these systems. Continuous improvements in mathematical models, analytical methods, and practical guardrails will be essential to mitigate risks and foster a secure environment for decentralized finance participants.

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.2404.15489,

Title: Multiblock Mev Opportunities & Protections In Dynamic Amms

Subject: q-fin.tr

Authors: Matthew Willetts, Christian Harrington

Published: 23-04-2024

Everything You Need To Know

What are dynamic Automated Market Makers (AMMs) and how do they differ from Constant Function Market Makers (CFMMs)?

Dynamic AMMs, such as liquidity bootstrap pools (LBPs), Temporal-function market makers (TFMMs), and replicating market makers (RMMs), introduce complexities not found in Constant Function Market Makers (CFMMs). Unlike CFMMs, which use a fixed formula to determine asset prices, dynamic AMMs can adjust their parameters over time. For instance, Temporal-Function Market Making (TFMM) pools incorporate time-varying trading functions, allowing the pool's portfolio vector to change from block to block, responding to market information and arbitrage opportunities. This adaptability, however, also creates new vulnerabilities, particularly concerning Maximal Extractable Value (MEV) attacks.

What are Multiblock Maximal Extractable Value (MEV) attacks in the context of dynamic AMMs, and who do they target?

Multiblock Maximal Extractable Value (MEV) attacks in dynamic AMMs involve malicious actors exploiting blockchain mechanics across multiple blocks to extract profit at the expense of other users. In dynamic AMMs like Temporal-Function Market Making (TFMM) pools, attackers can manipulate pool weights over several blocks, similar to 'sandwich attacks'. However, unlike traditional sandwich attacks that target individual traders, these attacks are often aimed at liquidity providers (LPs). By understanding how attackers can manipulate pool weights, it becomes easier to implement guardrails to protect investments in dynamic AMMs.

How does Temporal-Function Market Making (TFMM) work, and what is the significance of the formula Ru(t) = k(t)?

Temporal-Function Market Making (TFMM) pools differ from traditional AMMs by incorporating time-varying trading functions. The formula Ru(t) = k(t), where ∑ wi(t) = 1 and ∀i, 0 < wi(t) < 1, signifies that the reserves of each asset (Ri) depend on the time-varying weights (wi(t)), and the pool's constant (k) also changes with time. This dynamic nature allows TFMM pools to adapt their positions by re-weighting assets based on market conditions and arbitrage opportunities. Trades within a block must preserve or increase the value of k(t) at the time of the trade. This adaptability introduces vulnerabilities that can be exploited, as portfolio vector changes can be exploited.

What conditions must multi-token trades satisfy in Temporal-Function Market Making (TFMM) pools to be accepted?

In Temporal-Function Market Making (TFMM) pools, multi-token trades, where traders exchange a set of tokens (vector A) for another set (vector A), must meet specific conditions to be accepted. The pool requires that for tokens i where ∆i > 0, Ai = 0, meaning tokens cannot be traded for themselves. Additionally, trades must account for fees (1 – γ), satisfying a condition that ensures the trade benefits the pool. This rigorous condition ensures the pool's integrity and prevents exploitative trades, though vulnerabilities related to Maximal Extractable Value (MEV) can still arise.

What future developments are necessary to enhance the security of dynamic AMMs and mitigate the risks of Multiblock Maximal Extractable Value (MEV) attacks?

To enhance the security of dynamic AMMs and mitigate the risks of Multiblock Maximal Extractable Value (MEV) attacks, ongoing research and development of robust defense mechanisms are essential. This includes continuous improvements in mathematical models, analytical methods, and practical guardrails. As the DeFi landscape evolves, addressing potential multiblock MEV attacks on dynamic AMMs like Temporal-Function Market Making (TFMM) pools requires continuous adaptation of defensive strategies. The goal is to foster a secure environment for decentralized finance participants.