SAMM: Sharded Automated Market Maker

arXiv:2406.05568 · cs.DC, cs.CR · Submitted 2024-06-08 · Read on arXiv

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Introduction to the show: ident: Security Radio. Generated commentary on the latest security and cryptography papers.

Nadia: Today's paper: "SAMM: Sharded Automated Market Maker".

Elias: As a diligent researcher, I have thoroughly analyzed both provided texts concerning the "SAMM: Sharded Automated Market Maker" paper.

Nadia: First, who's behind it and why it matters.

Paper summary: Nadia: So, we're looking at the "SAMM: Sharded Automated Market Maker" paper, which tackles the scaling issues with existing AMMs by using multiple shards running in parallel on the same blockchain. Elias, can you give us the quick rundown of what they are actually proposing with this architecture?

Elias: Certainly. The core thesis of "SAMM: Sharded Automated Market Maker" is that traditional AMMs struggle because their execution isn't parallelizable when demand grows, which limits how much trading the system can handle. They propose building an AMM structure where multiple shards operate independently on the same chain, which allows trades to happen simultaneously across those shards. This addresses the scaling bottleneck by enabling true parallel execution <ref:2406.05568#pg0>.

Priya: So, if I understand correctly, they are focusing on how this sharding mechanism solves the throughput problem we see with current AMM architectures? What is the main claim they are making about its necessity?

Nadia: Exactly. The paper argues that existing architectures simply can't meet projected demand by two thousand twenty-nine because of this non-parallelizable execution <ref:2406.05568#pg0>. SAMM claims its independence across shards is the solution for meeting that demand through parallel execution.

Elias: And it goes further by claiming that the system's security isn't just about technical sharding, but rather about incentive compatibility derived from game theory <ref:2406.05568#pg1>. They claim this design prevents attacks by making misbehavior unprofitable for participants, which is a significant shift in how they secure these systems.

Priya: That sounds interesting because security in decentralized systems often hinges on economic incentives rather than just code structure. Could you elaborate on what they mean by relying on game-theoretic security specifically?

Nadia: The authors model the system as having two types of rational users, traders and liquidity providers, and they use a Subgame-Perfect Nash Equilibrium analysis to show how their fee design encourages the right behavior <ref:2406.05568#pg1>. This is where they argue that the incentive structure itself provides the robustness for the sharded AMM.

Elias: Precisely. They specifically identify a fillup strategy for liquidity providers based on this analysis, which ensures they actively rebalance their liquidity across all shards, preventing imbalances <ref:2406.05568#pg0>. This is key to overcoming potential destabilization attacks that might otherwise occur in a single pool setting.

Priya: It sounds like the focus is heavily on maintaining system balance through these strategic interactions between traders and LPs. What kind of data are they using to back up these theoretical claims?

Paper summary: Nadia: They validate their game-theoretic analysis with simulations run using real trade data, which confirms the effects of SAMM’s incentive design in practice <ref:2406.05568#pg2>. This moves the discussion from pure theory into something that reflects how it behaves when actual users are involved.

Elias: And they also specifically address potential weaknesses, such as sandwich attacks and losses due to price fluctuations, showing that sharding actually reduces the profitability of those attacks compared to a single pool <ref:2406.05568#pg2>. This is a concrete result they present regarding system resilience.

Priya: So, beyond the throughput gains mentioned earlier, what are the real-world economic implications of this paper for how we view decentralized exchange scaling?

Nadia: The paper suggests that SAMM can be employed not just for direct usage but also as a component within larger DeFi contracts <ref:2406.05568#pg2>. This implies that scaling AMMs isn't just about making one pool bigger; it could mean designing entire DeFi applications around this sharded structure.

Elias: And they introduce a specific mathematical tool, the bounded-ratio polynomial function, to handle the trading fees in a way that supports these scaling properties <ref:2406.05568#pg3>. This new fee design is what enables those desired c-properties mentioned in their analysis.

Priya: That new mathematical formulation sounds like the technical mechanism that allows for the theoretical guarantees they claim regarding the trading dynamics to hold up under stress. It’s interesting how much of this stability rests on these specific functions.

Nadia: And when we look at the performance metrics they cite, it shows a five times increase in throughput on Sui and a sixteen times increase on Solana <ref:2406.05568#pg2>. Those numbers are substantial compared to what they were trying to achieve before this paper was published.

Elias: Those figures demonstrate the practical impact of their architecture, showing how much parallelism can actually translate into system performance gains on different blockchain environments <ref:2406.05568#pg2>. It's a clear demonstration of the architectural advantage they are presenting.

Priya: From a measurement standpoint, I’m interested in what the simulation results actually tell us about user experience when comparing SAMM to something like Uniswap v3 or v4, which are other AMM architectures <ref:2406.05568#pg2>. What is the actual cost trade-off?

Nadia: The simulation also analyzed costs based on trade size, showing that for small trades, the fee ratio is dominant, but for larger trades, slippage becomes the main factor <ref:2406.05568#pg2>. This suggests a nuanced cost structure depending on how big the transaction is.

Paper summary: Elias: They ultimately conclude that when looking at overall costs across various fee configurations, SAMM's cost structure is either smaller than or only slightly larger than Uniswap across different settings <ref:2406.05568#pg2>. That comparison against established AMMs gives us a clearer picture of its economic viability.

Priya: So, to summarize what we've heard about "SAMM: Sharded Automated Market Maker," it’s an architecture that uses parallel sharding to boost throughput, secures its operation through game-theoretic incentive design, and shows performance gains validated by real trade data <ref:2406.05568#pg2>.

Nadia: That's a solid summary of the core contribution of "SAMM: Sharded Automated Market Maker." Now that we understand the mechanics, we need to think about what this actually means for the future of decentralized finance applications.

Elias: Indeed, and thinking about it in broader terms, this work suggests that scaling AMMs might not be a single solution but rather an architectural approach where multiple independent execution environments work together <ref:2406.05568#pg0>.

Priya: And from a research perspective, the focus on incentive compatibility being the primary security mechanism is something we should pay close attention to when designing future DeFi protocols <ref:2406.05568#pg1>.

Nadia: Exactly. We need to keep asking who can actually exploit this system and at what cost, because that’s where our applied security lens comes in, Elias.

Elias: I agree; the analysis shows that misbehavior is penalized through mechanism design rather than relying on perfect participant honesty <ref:2406.05568#pg1>. That makes the security model much more robust against unknown vulnerabilities.

Priya: And for the data side, it’s important to keep tracking how these performance gains translate into actual user adoption and stability when deployed at scale <ref:2406.05568#pg2>. The real-world metrics will tell us a lot about its practical utility beyond the testnet results.

Nadia: Right, so we've covered the high level of what "SAMM: Sharded Automated Market Maker" is proposing and its initial implications for scaling DeFi, setting us up perfectly to discuss what the authors suggest next.

Elias: We should also consider that the paper hints at an upcoming challenge in smart contract platform design related to minimizing serial transaction processing elements <ref:2406.05568#pg2>. That's where future innovation is likely headed for this type of system.

Priya: I'm looking forward to seeing how the community responds when they start testing these concepts with real-world data, as that will be the next big piece of evidence <ref:2406.05568#pg2>.

Nadia: That’s what we'll be watching closely. We'll keep digging into the details of this paper to understand how this architecture might actually be implemented in production environments <ref:2406.05568#pg1>.

Conclusion: Nadia: So, we've seen how SAMM uses parallel shards to boost trading capacity and game theory to ensure stability, now let's talk about what that title actually means for the wider world and who wrote this paper.

Elias: I agree, Nadia; looking at the authors’ backgrounds helps us understand the assumptions behind the security proofs they present in "SAMM: Sharded Automated Market Maker."

Priya: From a measurement standpoint, I want to focus on how these theoretical concepts translate into actual measurable behavior once you deploy this architecture.

Nadia: That makes sense, Priya; we need to know if these complex models hold up when we look at real-world data and what those numbers actually tell us about scaling DeFi.

Elias: Indeed, Nadia; the cryptographic assumptions underpinning the paper's framework dictate exactly which parameters might cause those theoretical guarantees to break down in practice.

Priya: I think that's crucial; understanding the boundaries of the method helps us predict where future research needs to focus for real-world deployment.

Nadia: Exactly, Elias; we have to keep asking who can actually exploit this system and how cheaply they can do it, because that dictates its practical utility.

Elias: Well put, Nadia; the paper's title hints at a fundamental shift in how we think about building decentralized execution environments on-chain.

Priya: I think the authors are really aiming to show that scaling isn't just about making one pool bigger, but designing an entire system around multiple independent execution environments working together.

Nadia: That suggests a future where DeFi applications might be structured specifically for this sharded setup rather than shoehorning them into existing single-pool models.

Elias: And if the authors' mathematical tools prove robust, it opens up new avenues for designing complex financial instruments that rely on this parallel execution structure.

Priya: I'm excited to see what comes next in the research, especially how they address minimizing serial transaction processing elements as they move toward production environments.

Technion

cs.DC, cs.CR

Submitted: 2024-06-08

Updated: 2026-10-03

Comments: Full version of the paper published at the 8th Conference on Advances in Financial Technologies (AFT 2026)

Journal ref: 8th Conference on Advances in Financial Technologies (AFT 2026), LIPIcs vol. 395, pp. 11:1--11:27

DOI: 10.4230/LIPIcs.AFT.2026.11

Code: https://github.com/MountainGold/SAMM-Sui-Evaluation

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 92/100

The gist: As a diligent researcher, I have thoroughly analyzed both provided texts concerning the "SAMM: Sharded Automated Market Maker" paper.

Key concepts

Sharding: SAMM splits the market into several independent 'shards' that operate in parallel on the same blockchain. This allows many trades to happen simultaneously instead of sequentially, which directly solves the speed limits faced by single-pool AMMs under high demand.
Subgame-Perfect Nash Equilibrium (SPNE): This is a mathematical tool used to determine the best possible strategies for all participants—liquidity providers and traders—in a game. SAMM uses SPNE to prove that the system's design ensures everyone acts optimally to keep the market stable and balanced.
Fillup Strategy ($ au_{ ext{fillup}}$): This is the specific rule liquidity providers follow in SAMM. It dictates how often and where LPs should rebalance their deposited tokens across different shards. This strategy prevents imbalances between shards, ensuring that all parts of the market remain equally populated.
tfBRP Function: This is a novel mathematical fee design used in SAMM trading. It's a complex function designed to control how transaction fees are calculated, ensuring trades execute correctly within the sharded structure and contributing to overall scaling efficiency.

Terminology

Nadia — 18× in this paper · explained in 2 episodes
Elias — 17× in this paper · explained in 2 episodes
Sharded Automated Market Maker — 11× in this paper
Core — 9× in this paper · explained in 2 episodes
Constant Product Market Maker — 5× in this paper
Robustness — 5× in this paper · explained in 5 episodes
Adam — 4× in this paper · explained in 2 episodes
Theoretical Guarantees — 4× in this paper · explained in 2 episodes
Generalization — 3× in this paper · explained in 13 episodes
Nash Equilibrium — 3× in this paper · explained in 2 episodes
Subgame-Perfect Nash Equilibria — 3× in this paper
Action Space — 2× in this paper · explained in 1 episode
IEEE Symposium on Security and Privacy — 2× in this paper
Trace — 2× in this paper · explained in 2 episodes
Alignment — 1× in this paper · explained in 1 episode
Axioms — 1× in this paper · explained in 2 episodes
Benchmark — 1× in this paper · explained in 2 episodes
Clustering — 1× in this paper · explained in 2 episodes
Deep Reinforcement Learning — 1× in this paper · explained in 2 episodes
Differential Privacy — 1× in this paper · explained in 4 episodes
Fine-Tuning — 1× in this paper · explained in 5 episodes
Metastability — 1× in this paper · explained in 2 episodes
Reinforcement Learning — 1× in this paper · explained in 4 episodes
Scaffolding — 1× in this paper · explained in 3 episodes

Summary

As a diligent researcher, I have thoroughly analyzed both provided texts concerning the SAMM: Sharded Automated Market Maker paper. The information is rich, detailing both the technical architecture, theoretical guarantees (game-theoretic analysis), empirical performance metrics, and security proofs.

Here is a comprehensive and detailed summary combining the key findings from both sources:

The paper introduces SAMM (Sharded Automated Market Maker) as a novel architecture designed to overcome the scaling bottlenecks inherent in existing Automated Market Makers (AMMs) when faced with rapidly growing demand. Traditional AMMs suffer from non-parallelizable execution, which limits throughput. SAMM addresses this by implementing an AMM comprising multiple independent shards running concurrently on the same blockchain, thereby enabling true parallel execution and significant performance gains.

Architecture: SAMM consists of multiple AMM shards operating in parallel on the same underlying chain (e.g., Sui or Solana testnets). This sharding structure fundamentally allows trades to occur simultaneously across different shards, directly mitigating scaling limitations.

Throughput Improvement: Empirical evaluation on local testnets demonstrates substantial performance enhancements:

Sui: Up to a 5x throughput increase.
Solana: Up to a 16x throughput increase.

This parallelization is the primary mechanism by which SAMM tackles the bottleneck caused by high-demand contracts.

The security and stability of SAMM are rigorously established through a sophisticated game-theoretic analysis based on Subgame-Perfect Nash Equilibria (SPNE). The system's incentive design is crucial for ensuring that liquidity providers (LPs) behave optimally to maintain system health.

Liquidity Provider Strategy:

The analysis proves that the SPNE dictates the fillup strategy (tau fillup) as the optimal response for liquidity providers. This strategy ensures that LPs actively rebalance their liquidity across all shards, preventing imbalances and overcoming potential destabilization attacks.
The system is proven to always converge to a state where all shards have an equal amount of deposited tokens, ensuring perfect balance.

Trader Strategy:

The analysis identifies a dominant strategy for traders: they should randomly select one of the smallest shards to execute their trade without splitting the order. This strategy, denoted as tau BA, is shown to be part of the stable SPNE when paired with the LP's fillup strategy.

Robustness Against Attacks:

The analysis explicitly addresses potential vulnerabilities, such as sandwich attacks and losses due to price fluctuations. The paper demonstrates that sharding does not exacerbate these issues; rather, the profitability of sandwich attacks decreases as liquidity is distributed across multiple shards.
Furthermore, when neglecting trading fees (as attackers must incur gas costs for two transactions), the reduced liquidity in each shard does not worsen sandwich attack profitability compared to a single pool.

A key technical contribution is the generalization of the AMM trading fee function, specifically introducing the bounded-ratio polynomial function (tfBRP):

tfBRP(R A,R B,O A; beta 1, beta 2, beta 3, beta 4, beta 5):= R B/R A O A times [rmin, []]

This function is mathematically designed to satisfy crucial properties necessary for scaling:

c-Non-Splitting Property: Ensures trades are executed within the intended structure.
c-Smaller-Better Property: Contributes to overall throughput scaling.

The simulation using real trade data validates the theoretical guarantees with concrete economic results:

Revenue Enhancement for LPs: SAMM significantly outperforms standard AMMs like Uniswap in terms of liquidity provider revenue while maintaining comparable costs for traders. For instance, with c=0.01 and 7 shards, SAMM yields over 15 times the revenue compared to Uniswap.
Cost Analysis: The cost structure is analyzed based on trade size:
For small trades, the high fee ratio dominates the cost, while slippage is negligible.
For large trades, the fee ratio decreases, and slippage becomes the dominant factor. This concentration of costs reduces extreme price movements that would otherwise cause transaction failure due to exceeding a cost threshold.
The overall cost of SAMM is shown to be either smaller than or only slightly larger (less than 1%) than Uniswap across various fee configurations.

Improvements for AI systems

As a fastidious researcher, I have analyzed the SAMM (Sharded Automated Market Maker) paper by Chen et al. The core contribution is a novel sharding mechanism for AMMs that uses game-theoretic security (Subgame-Perfect Nash Equilibria) to ensure parallel execution and balanced liquidity distribution.

Here are the specific improvements and capabilities this research enables for AI systems, focusing on decentralized finance (DeFi) infrastructure:

) 1. High-Throughput, Scalable Decentralized Finance (DeFi) Infrastructure

The primary improvement is the transition from sequentially limited AMMs to highly parallelizable sharded AMMs. This directly addresses the throughput bottleneck of existing DeFi protocols like Uniswap V2/V3 on current blockchains (e.g., Sui, Solana).

An improved AI system could design and deploy a DeFi protocol layer that utilizes SAMM architecture.
This system can handle projected high demand (estimated > 200 tps by 2029) without relying solely on inefficient Layer-2 scaling solutions or suffering from front-running vulnerabilities like sandwich attacks, as the protocol is designed to be robust via incentive compatibility.

) 2. Optimized Liquidity Provision Incentives

The paper introduces a novel trading fee function (tfBRP) that is mathematically derived to satisfy key properties:

It enforces the c-Non-Splitting property and c-smaller-better property.
This design ensures that liquidity providers are incentivized to balance liquidity across all shards, preventing destabilization attacks.
An AI system could dynamically adjust the parameters of this fee function (e.g., tuning the parameter set in Theorem 4.4) based on real-time market conditions or perceived attack vectors to optimize the revenue-to-risk ratio for liquidity providers.

) 3. Guaranteed Parallel Execution and Reduced Latency

The mechanism guarantees that traders will randomly select a shard, and liquidity providers will gravitate towards balancing shard sizes (via the fillup strategy).

An improved AI system could function as an autonomous protocol orchestrator for sharded AMMs. It would ensure that trading operations are distributed across shards in a way that maximizes parallelism, leading to significantly improved trade latency compared to single-contract AMMs.
This capability allows for real-time, high-frequency trading applications (e.g., algorithmic trading bots) to execute trades with deterministic, low latency and high reliability.

) 4. Robust Security Against Market Manipulation

The security is rooted in game theory rather than reliance on external consensus mechanisms or simple fee structures:

The system is shown to be robust against destabilization attacks because the equilibrium favors balanced shards.
It demonstrates that smaller liquidity pools do not necessarily exacerbate known vulnerabilities like sandwich attacks or price fluctuation losses (LVR), suggesting a more resilient economic model for DeFi.

) 5. Dynamic Performance Tuning and Platform Adaptability

The research provides a clear roadmap for scaling: throughput scales with the number of shards, but further improvement depends on underlying platform parallelism (Amdahl's Law).

An AI system could act as a performance optimizer, analyzing the specific constraints of different blockchains (Sui vs. Solana) and dynamically recommending optimal sharding configurations and fee function parameters to maximize throughput for a given network environment.

In summary, this research moves DeFi from a single-bottleneck model to a scalable, self-regulating parallel architecture. The resulting AI system can be:

A high-performance, low-latency trading engine capable of processing massive transaction volumes reliably.
A dynamic protocol optimizer that tunes its fee structure and sharding depth in real-time to maximize liquidity provider returns while maintaining system stability against adversarial behavior.