Positive users express excitement over Lanyon Neurosymbolic AI outperforming frontier models on linear PDE benchmarks, while negative users question the trustworthiness due to missing formal verification in its C implementations.
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Lanyon's neurosymbolic approach is consistently 20-250x faster and 50-250x more token-efficient than all existing frontier models (Fable 5, Opus 4.8, GPT-5.6 Sol, GPT-5.5, and Kimi K3), and doesn't commit any of the same mathematical, algorithmic, or implementational errors. That's the main takeaway of the initial benchmarking work for simple linear PDE solvers by @JunoRavin. And there's a lot more still to come.
Our internal (non-Lean-based) symbolic theorem-proving framework, based on prior research by me and @minmodammar on the axiomatization of IEEE-754 floating point arithmetic, also gives Lanyon a significant edge in the automated verification of numerical solvers that the frontier models cannot (yet) match.
Our first official benchmarking post from our Chief Scientist Jimmy Juno (@JunoRavin), comparing the performance of Lanyon's neurosymbolic architecture against frontier models Fable 5, Opus 4.8, GPT-5.6 Sol, GPT-5.5, and Kimi K3, for simple linear PDE problems (linear advection, Maxwell's equations).
The headline is that, across multiple trials, Lanyon is consistently 20-250x faster and exhibits 50-250x lower token consumption. Several frontier models consistently commit mathematical, algorithmic, and computational errors (such as implementing numerical schemes with the wrong order of accuracy, or not correctly limiting discontinuous solutions), *even* when given highly detailed prompting regarding what exactly to implement. For terser prompting (equivalent to what Lanyon typically receives), performance is worse still.
We have tried throughout to give the frontier models every possible advantage (more detailed prompts, maximum reasoning and effort where necessary, more tools where necessary).
The post also contains a brief discussion of how Lanyon's internal (non-Lean-based) symbolic theorem-prover handles floating point precision issues, based on our previous academic research, which gives it an inherent advantage over the formalization approaches used by frontier models, though we intend to write a more complete post on this soon. We hope to make this benchmark public in the near future. Post below 👇
Lanyon's neurosymbolic approach is consistently 20-250x faster and 50-250x more token-efficient than all existing frontier models (Fable 5, Opus 4.8, GPT-5.6 Sol, GPT-5.5, and Kimi K3), and doesn't commit any of the same mathematical, algorithmic, or implementational errors. That's the main takeaway of the initial benchmarking work for simple linear PDE solvers by @JunoRavin. And there's a lot more still to come.
Our internal (non-Lean-based) symbolic theorem-proving framework, based on prior research by me and @minmodammar on the axiomatization of IEEE-754 floating point arithmetic, also gives Lanyon a significant edge in the automated verification of numerical solvers that the frontier models cannot (yet) match.
@getjonwithit Lanyon's C implementations aren't formally verified, though. You can claim that it was generated in such a way that it corresponds to the Lean proofs, but the whole point of formal verification is for there to be no need to trust claims like that. That's the theorem prover's job.
@getjonwithit Pure LLM solvers keep failing basic numerical order and discontinuity handling even with detailed prompts. Hybrid symbolic layers are the only path that actually reduces verification cost.
@getjonwithit Obviously speed and token efficiency don't translate immediately into theorems but I expect there are a bunch of thresholds at current capacity edge given the recent whirl of results
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God judges even our thoughts and intentions. It is written: “…everyone who looks at a woman with lustful intent has already committed adultery with her in his heart” (Matthew 5:28). And also: “Everyone who hates his brother is a murderer…” (1 John 3:15). Since we have all sinned (lied, harbored lustful thoughts, and stolen) so many times in our lives, we are all destined to end up in hell.
Is there any hope?
Yes, there is!
God, in His mercy, sent His only Son, Jesus Christ, to rescue us by taking our punishment on the cross. Jesus Christ lived a life of perfect righteousness in our place, died on the cross to pay the penalty for our sin, and resurrected on the third day. “For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God” (2 Corinthians 5:21). This Bible verse describes the great exchange: Jesus Christ took the sins of all believers upon Himself and accepted the punishment—the curse—that believers deserved for their sin; in exchange, God imputes, or credits, the righteousness of Jesus Christ to all believers so that they might possess the eternal life that Jesus Christ deserves.
Repent of your sins and believe in Jesus Christ as LORD (God) and Savior, then you will be saved from hell and death and will receive the gift of eternal life. God is one, yet He exists in three distinct persons: the Father, the Son, and the Holy Spirit. The Son of God became man 2,000 years ago—taking on flesh to save us—by living a life of perfect righteousness on our behalf and dying on the cross. Only One who was truly God and truly man could pay the price for our sin. Only He could bear the eternal punishment we deserved. Only He could drink the infinite cup of God’s wrath. Jesus Christ, as God-man, took upon Himself the infinite punishment that believers deserved in hell.
“For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast” (Ephesians 2:8–9). This verse tells us that salvation is not earned by works but is a free gift. Good works of unbelievers are like filthy rags in God’s eyes; they are sin because when they do their good works they do not do them out of perfect love toward the true triune God. "as it is written: “None is righteous, no, not one; no one understands; no one seeks for God. All have turned aside; together they have become worthless; no one does good, not even one.”" (Romans 3:10-12). But when you believe in Jesus Christ, His righteousness is credited to you. Faith is like a hand that receives Jesus Christ. Yet even faith itself comes from God. Therefore, salvation is God’s work from beginning to end. However, Roman Catholic churches (which are false churches because they teach the false Gospel) teach that salvation is by faith and our own good works, which contradicts this verse. Therefore, trust only in Jesus Christ for salvation, not in your own good works.
“For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.”
John 3:16
I recommend you read the word of the Lord Jesus Christ in the ESV translation: https://www.esv.org/
The Second London Baptist Confession of Faith: https://founders.org/library-book/1689-confession/
Sermons: https://www.youtube.com/@GraceChurchSunValley
• • Ministries: https://www.ligonier.org/, https://www.desiringgod.org/, https://www.gotquestions.org/, https://www.gty.org/
@getjonwithit Have you guys solved anything interesting yet