Lambda Calculus Benchmark for AI

mmarvinborner about 5 hours ago 25 commentsRead Article on victortaelin.github.io

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NitpickLawyer•about 4 hours ago

New, unbenched problems are really the only way to differentiate the models, and every time I see one it's along the same lines. Models from top labs are neck and neck, and the rest of the bunch are nowhere near. Should kinda calm down the "opus killer" marketing that we've seen these past few months, every time a new model releases, esp the small ones from china.

It's funny that even one the strongest research labs in china (deepseek) has said there's still a gap to opus, after releasing a humongous 1.6T model, yet the internet goes crazy and we now have people claiming [1] a 27b dense model is "as good as opus"...

I'm a huge fan of local models, have been using them regularly ever since devstral1 released, but you really have to adapt to their limitations if you want to do anything productive. Same as with other "cheap", "opus killers" from china. Some work, some look like they work, but they go haywire at the first contact with a real, non benchmarked task.

[1] - https://x.com/julien_c/status/2047647522173104145

adrian_b•about 3 hours ago

Benchmarks for LLMs without complete information about the tested models are hard to interpret.

For the OpenAI and Anthropic models, it is clear that they have been run by their owners, but for the other models there are a great number of options for running them, which may run the full models or only quantized variants, with very different performances.

For instance, in the model list there are both "moonshotai/kimi-k2.6" and "kimi-k2.6", with very different results, but there is no information about which is the difference between these 2 labels, which refer to the same LLM.

Moreover, as others have said, such a benchmark does not prove that a certain cheaper model cannot solve a problem. It happened to not solve it within the benchmark, but running it multiple times, possibly with adjusted prompts, may still solve the problem.

While for commercial models running them many times can be too expensive, when you run a LLM locally you can afford to run it much more times than when you are afraid of the token price or of reaching the subscription limits.

NitpickLawyer•about 3 hours ago

Agreed. But, at least as of yesterday, dsv4 was only served by deepseek. And, more importantly, that's what the "average" experience would be if you'd setup something easy like openrouter. Sure, with proper tuning and so on you can be sure you're getting the model at its best. But are you, if you just setup openrouter and go brrr? Maybe. Maybe not.

cmrdporcupine•about 2 hours ago

I think it's important to point out that DeepSeek was basically soft-launching their v4 model, and they weren't emphasizing it as some sort of SOTA-killer but more as proof of a potentially non-NVIDIA serving world, and as a venue for their current research approaches.

I think/hope we'll see a 4.2 that looks a lot better, same as 3.2 was quite competitive at the time it launched.

cmrdporcupine•about 3 hours ago

The question isn't whether it's "as good as Opus" but that there exists something that costs 1/10th the cost to use but can still competently write code.

Honestly, I was "happy" with December 2025 time frame AI or even earlier. Yes, what's come after has been smarter faster cleverer, but the biggest boost in productivity was just the release of Opus 4.5 and GPT 5.2/5.3.

And yes it might be a competitive disadvantage for an engineer not to have access to the SOTA models from Anthropic/OpenAI, but at the same time I feel like the missing piece at this point is improvements in the tooling/harness/review tools, not better-yet models.

They already write more than we can keep up with.

NitpickLawyer•about 3 hours ago

Oh, I agree. Last year I tried making each model a "daily driver", including small ones like gpt5-mini / haiku, and open ones, like glm, minimax and even local ones like devstral. They can all do some tasks reliably, while struggling at other tasks. But yeah, there comes a point where, depending on your workflows, some smaller / cheaper models become good enough.

The problem is with overhypers, that they overhype small / open models and make it sound like they are close to the SotA. They really aren't. It's one thing to say "this small model is good enough to handle some tasks in production code", and it's a different thing to say "close to opus". One makes sense, the other just sets the wrong expectations, and is obviously false.

adrian_b•about 2 hours ago

There is no doubt that for many tasks the SotA models of OpenAI and Anthropic are better than the available open weights models.

Nevertheless, I do not believe that either OpenAI or Anthropic or Google know any secret sauce for better training LLMs. I believe that their current superiority is just due to brute force. This means that their LLMs are bigger and they have been trained on much more data than the other LLM producers have been able to access.

Moreover, for myself, I can extract much more value from an LLM that is not constrained by being metered by token cost and where I have full control on the harness used to run the model. Even if the OpenAI or Anthropic models had been much better in comparison with the competing models, I would have still been able to accomplish more useful work with an open-weights model.

I have already passed once through the transition from fast mainframes and minicomputers that I was accessing remotely by sharing them with other users, to slow personal computers over which I had absolute control. Despite the differences in theoretical performance, I could do much more with a PC and the same is true when I have absolute control over an LLM.

cmrdporcupine•about 3 hours ago

I am desperate for the tooling that puts me back in charge. And just has the models as advisor. In which case the "smart level" is just a dial.

I'm probably going to have to make it myself.

tromp•about 5 hours ago

The corresponding repo https://github.com/VictorTaelin/LamBench describes this as:

    λ-bench
    A benchmark of 120 pure lambda calculus programming problems for AI models.
    → Live results
    What is this?
    λ-bench evaluates how well AI models can implement algorithms using pure lambda calculus. Each problem asks the model to write a program in Lamb, a minimal lambda calculus language, using λ-encodings of data structures to implement a specific algorithm.
    The model receives a problem description, data encoding specification, and test cases. It must return a single .lam program that defines @main. The program is then tested against all input/output pairs — if every test passes, the problem is solved.

"Live results" wrongly links to https://victortaelin.github.io/LamBench/ rather than the correct https://victortaelin.github.io/lambench/

An example task (writing a lambda calculus evaluator) can be seen at https://github.com/VictorTaelin/lambench/blob/main/tsk/algo_...

Curiously, gpt-5.5 is noticeably worse than gpt-5.4, and opus-4.7 is slightly worse than opus-4.6.

lioeters•about 2 hours ago

As an admirer of your work with binary lambda calculus, etc., I'm curious to hear your thoughts on the author's company with HVM and interaction combinators. https://higherorderco.com/ I've always felt there was untapped potential in this area, and their work seems like a way toward a practical application for parallel computing and maybe leveraging LLMs using a minimal language specification.

dataviz1000•about 4 hours ago

lambench is single-attempt one shot per problem.

I don't think they understand how the LLM models work. To truly benchmark a non-deterministic probabilistic model, they are going to need to run each about 45 times. LLM models are distributions and behave accordingly.

The better story is how do the models behave on the same problem after 5 samples, 15 samples, and 45 samples.

That said, using lambda calculus is a brilliant subject for benchmarking.

The models are reliably incorrect. [0]

[0] https://adamsohn.com/reliably-incorrect/

yorwba•about 1 hour ago

Why 45 times in particular? If you want 80% power to distinguish a model at 50% from a model at 51%, you need 39,440 samples per model, or 329 samples per question per model. But that would just give you a more precise estimate of how well the model does on those 120 questions in particular. If you want a more precise estimate of how well the model might do on future questions you come up with, you'll need to test more questions, not just test the same question more times.

UltraSane•about 1 hour ago

Even people benefit from multiple tries over time.

chris_st•about 1 hour ago

Well, to be fair, people cheat by remembering what they did last time. I think the idea here is to run the models from a "clean slate" and see how often they succeed/fail.

They are, like people, non-deterministic, so giving them several "fair" trials makes sense to me.

the_data_nerd•about 1 hour ago

FFT failure makes sense if you think about what cooley-tukey actually needs. integer indexing into an array, log-N recursion depth with shared state across the butterfly. in pure lambda calc you're working with church numerals and church-encoded lists, where every index lookup is O(N) by itself. the algorithm goes from N log N to N^2 log N or worse depending on encoding. the bigger issue: most internet FFT implementations assume mutable arrays, so the model has nothing structurally similar to copy from. it has to derive the encoding-aware version itself. that's a different skill than reproducing C with let-bindings, which is what most coding evals actually measure.

internet_points•about 3 hours ago

Would love to see where the mistral stuff lands.

Also, being from Victor Taelin, shouldn't this be benching Interaction Combinators? :)

maciejzj•about 2 hours ago

Can anyone more familiar with lambda calculus speculate why all models fail to implement fft? There are gazzilion fft implementations in various languages over the web and the actual cooley-tukey algorithm is rather short.

amluto•about 2 hours ago

I can guess:

Pure lambda calculus doesn’t have numbers, and FFT, as traditionally specified, needs real numbers or a decent approximation of them. There are also Fourier transforms over a ring. So the task needs to specify what kind of numbers are being Fourier transformed.

But the prompt is written very tersely written. It’s not immediately obvious to me what it’s asking. I even asked ChatGPT what number system was described by the relevant part of the prompt and it thought it was ambiguous. I certainly don’t really know what the prompt is asking.

Adding insult to injury, I think the author is trying to get LLMs to solve these in one shot with no tools. Perhaps the big US models are tuned a little bit for writing working code in their extremely poor web chat environments (because the companies are already too unwieldy to get their web sites in sync with the rest of their code), but I can’t imagine why a company like DeepSeek would use their limited resources to RL their model for its coding performance in a poor environment when their users won’t actually do this.

fallat•about 2 hours ago

You can express any number type in pure lambda calculus.

amluto•about 2 hours ago

I can also implement compliant IEEE 754 floating point arithmetic, with all rounding modes and exceptions, in Conway’s Game of Life, and I can implement that on a Turing machine and emulate that Turing machine in Brainfuck. This does not mean it’s sensible — it would be a serious engineering project that should be decomposed, built in pieces, and tested or verified in pieces. Which even a Chinese LLM ought to be able to do in an appropriate environment with appropriate resources and an appropriate prompt.

But that is not what this is testing. And I’m not even sure which number system the mentioned roots of unity are in. Maybe it’s supposed to be generic over number systems in a delightfully untyped lambda calculus sort of way?

edit: after pasting the entire problem including the solution, ChatGPT is able to explain “GN numbers”. I suspect its explanation is sort of correct. But I get no web search results for GN numbers and I can’t really tell whether ChatGPT is giving a semi-hallucinated description or figuring it out from the problem and its solution or what.

bediger4000•about 2 hours ago

Lambda calculus people have the phrase "adequate numeral system" because they've discovered many different numeral systems.

cmrdporcupine•about 3 hours ago

Odd to see GPT 5.5 behind 5.4?

no_op•about 3 hours ago

The author posted new results using the API (apparently the original run was through Codex), and 5.5 moves to the top: https://x.com/VictorTaelin/status/2047818978664268071

auggierose•about 1 hour ago

Still doesn't explain why Codex 5.4 is better than Codex 5.5.