This is very neat work! Will be interested in how they make this sort of thing available to the public but it is clear from some of the results they mention that search + LLM is one path to the production of net-new knowledge from AI systems.
Software engineering will be completely solved. Even systems like v0 are astounding in their ability to generate code, and are very primitive to whats coming. I get downvoted on HN for this opinion, but its truly going to happen. Any system that can produce code, test the code, and iterate if needed will eventually outperform humans. Add in the reinforcement learning, where they can run the code, and train the model when it gets code generation right, and we are on our way to a whole different world.
It is not that you get downvoted because they don’t understand you, it is because you sell your opinion as fact, like an apostle. For example what does it mean that software engineering is solved?
Prophets are always beaten by average citizens, because prophecy is always unpleasant. It can't be otherwise. At the same time, you can't tell right away whether a person is really a prophet, because it becomes known much later. That's probably why beating them (the simplest solution) turns out to be the most observed.
What about brownfield development though? What about vague requirements or cases with multiple potential paths or cases where some technical choices might have important business consequences that shareholders might need to know about? Can we please stop pretending that software engineering happens in a vacuum?
The thing with vague requirements is that the real problem is that making decisions is hard. There are always tradeoffs and consequences. Rarely is there a truly clear and objective decision. In the end either you or the LLM are guessing what the best option is.
Yes, decisions are but they need to be made. Ideally shareholders will be given as much context so they can decide. This communication is as vital as having good programming skills imo. Your beautiful code means nothing if it does not adequately solve the business problem
> What about vague requirements or cases with multiple potential paths or cases where some technical choices might have important business consequences that shareholders might need to know about?
If the cost of developing the software is 0, you can just build both.
or you can build 20 different versions. Your non technical person won't be happy about this though. They wanted 1 software system not 20 nor 2. Just one
"Coding" might be solved, but there is more to software engineering than just churning out code - i.e. what should we build? What are the requirements? Are they right? Whats the other dependencies we want to use - AWS or GCP for example? Why those and not others - whats the reason? How does this impact our users and how they use the system? What level of backwards/forwards compatibility do we want? How do we handle reliability? Failover? Backups? and so on and so on.
Some of these questions change slightly, since we might end up with "unlimited resources" (i.e. instead of having e.g. 5 engineers on a team who can only get X done per sprint, we effectively have near-limitless compute to use instead) so maybe the answer is "build everything on the wish-list in 1 day" to the "what should we prioritize" type questions?
Interesting times.
My gut is that software engineers will end up as glorified test engineers, coming up with test cases (even if not actually writing the code) and asking the AI to write code until it passes.
Testing in general is quickly being outmoded by formal verification. From my own gut, I see software engineering pivoting into consulting—wherein the deliverables are something akin to domain-specific languages that are tailored to a client's business needs.
Generally the product decisions are not given to the engineers. But yeah, engineers will be tuning, prodding, and poking ai systems to generate the code to match the business requirements.
There's cope in the comments about possibility of some software adjacent jobs remaining, which is possible, but the idea of a large number of high paying software jobs remaining by 2030 is a fantasy. Time to learn to be a plumber.
Calling it now - RL finally "just works" for any domain where answers are easily verifiable. Verifiability was always a prerequisite, but the difference from prior generations (not just AlphaGo, but any nontrivial RL process prior to roughly mid-2024) is that the reasoning traces and/or intermediate steps can be open-ended with potentially infinite branching, no clear notion of "steps" or nodes and edges in the game tree, and a wide range of equally valid solutions. As long as the quality of the end result can be evaluated cleanly, LLM-based RL is good to go.
As a corollary, once you add in self-play with random variation, the synthetic data problem is solved for coding, math, and some classes of scientific reasoning. No more modal collapse, no more massive teams of PhDs needed for human labeling, as long as you have a reliable metric for answer quality.
This isn't just neat, it's important - as we run out of useful human-generated data, RL scaling is the best candidate to take over where pretraining left off.
Most things are verifiable, just not with code. I'm not particularly excited for a world where everything is predictable. This is coming from a guy who loves forecasting/prediction modeling too, but one thing I hate about prediction modeling, especially from a hobbyist standpoint is data. Its very hard to get useful data. Investors will literally buy into hospital groups to get medical data for example.
There are monopolies on the coolest sets of data in almost all industries, all the RL in the world won't do us any good if those companies doing the data hoarding are only using it to forecast outcomes that will make them more money, not what can be done to better society.
Are there platforms that make such training more streamlined? Say I have some definition of success for a given problem and it’s data how do I go about generating said RL model as fast and easily as possible?
We're working on an OSS industrial-grade version of this at TensorZero but there's a long way to go. I think the easiest out of the box solution today is probably OpenAI RFT but that's a partial solve with substantial vendor lock-in.
IMO RL can only solve "easy" problems. The reason RL works now is that unsupervised learning is a general recipe for transforming hard problems into easy ones. But it can't go all the way to solutions, you need RL on top for that. Yann LeCun's "cherry on top" analogy was right.
Skimmed quickly the paper. This does not look like RL. It's a genetic algorithm. In a previous life I was working on compbio (protein structure prediction), we built 100s of such heuristic based algorithm (monte carlo simulated annealing, ga..). The moment you have a good energy function (one that provide some sort of gradient), and a fast enough sampling function (llms), you can do looots of cool optmization with sufficient compute.
This depends quite a bit of what you’re trying to optimize.
Gradient descent is literally following the negative of the gradient to minimize a function. It requires a continuous domain, either analytical or numerical derivatives of the cost function, and has well-known issues in narrow valleys and other complex landscapes.
It’s also a local minimization technique and cannot escape local minima by itself.
_Stochastic_ gradient descent and related techniques can overcome some of these difficulties, but are still more or less local minimization techniques and require differentiable and continuous scoring functions.
In contrast, genetic algorithms try to find global minima, do not require differentiable scoring functions, and can operate on both continuous and discrete domains. They have their own disadvantages.
Different techniques for different problems. The field of numerical optimization is vast and ancient for a reason.
> This does not look like RL. It's a genetic algorithm.
couldn't you say that if you squint hard enough, GA looks like a category of RL? There are certainly a lot of similarities, the main difference being how each new population of solutions is generated. Would not at all be surprised that they're using a GA/RL hybrid.
You also need a base model that can satisfy the verifier at least some of the time. If all attempts fail, there's nothing there to reinforce. The reinforcement-learning algorithms themselves haven't changed much, but LLMs got good enough on many problems that RL could be applied. So for any given class of problem you still need enough human data to get initial performance better than random.
This technique doesn't actually use RL at all! There’s no policy-gradient training, value function, or self-play RL loop like in AlphaZero/AlphaTensor/AlphaDev.
As far as I can read, the weights of the LLM are not modified. They do some kind of candidate selection via evolutionary algorithms for the LLM prompt, which the LLM then remixes. This process then iterates like a typical evolutionary algorithm.
This isn't quite RL, right...?
It's an evolutionary approach on specifically labeled sections of code optimizing towards a set of metrics defined by evaluation functions written by a human.
I suppose you could consider that last part (optimizing some metric) "RL".
However, it's missing a key concept of RL which is the exploration/exploitation tradeoff.
Maybe this one can stop writing a fucking essay in code comments.
I'm now no longer surprised just how consistently all the gemini models overcomplicate coding challenges or just plain get them wrong.
Claude is just consistently spot on. A few salient comments for tricky code instead of incessantly telling me what it's changed and what I might want to do, incorrect assumptions when it has the code or is something we've discussed, changing large amounts of unrelated code (eg styles). I could go on.
Shame I'm too tight to pay for Claude RN though...
The paper does not give that many details about the evolution part. Normally, evolutionary algorithms contain some cross-over component where solutions can breed with each other. Otherwise it's better classified as hill climbing / beam search.
There's also 'evolutionary strategy' algorithms that do not use the typical mutation and crossover, but instead use a population of candidates (search samples) to basically approximate the gradient landscape.
The model is fed a few samplings of previous attempts and their evaluations during the optimization of the current algorithm. Using that information, the model is able to combine components of previous attempts into the current attempt at will. That is because all of this is fed into a single prompt, which the LLM can reference arbitrarily. So recombination is well represented here, bringing it closer to a genetic algorithm. In essence, it combines elements from hill climbing, beam search, and genetic algorithms by virtue of its unbounded nature as an LLM.
Remember that GPUs have cache hierarchies and matching block sizes to optimally hit those caches is a big win that you often don't get by default, just because the number of important kernels times important GPUs times effort to properly tune one is greater than what people are willing to do for others for free in open source. Not to mention kernel fusion and API boundaries that socially force suboptimal choices for the sake of clarity and simplicity.
It's a very impressive result, but not magic, but also not cheating!
What it essentially does is a debugging/optimization loop where you change one thing, eval, repeat it again and compare results.
Previously we needed to have a human in the loop to do the change. Of course we have automated hyperparameter tuning (and similar things), but that only works only in a rigidly defined search space.
Will we see LLMs generating new improved LLM architectures, now fully incomprehensible to humans?
If I understood, isn't this software only as useful as the llm powering it is? It sounds like something very useful, but either I'm missing something or it put into a loop and a validator a "please optimize this code". Useful, but maybe not as revolutionary as the underlying llm tech itself
Edit the white paper says this: AlphaEvolve employs an ensemble of large language models. Specifically, we
utilize a combination of Gemini 2.0 Flash and Gemini 2.0 Pro. This ensemble approach allows
us to balance computational throughput with the quality of generated solutions. Gemini 2.0
Flash, with its lower latency, enables a higher rate of candidate generation, increasing the
number of ideas explored per unit of time. Concurrently, Gemini 2.0 Pro, possessing greater
capabilities, provides occasional, higher-quality suggestions that can significantly advance
the evolutionary search and potentially lead to breakthroughs. This strategic mix optimizes
the overall discovery process by maximizing the volume of evaluated ideas while retaining
the potential for substantial improvements driven by the more powerful model.
So, I remain of my opinion before. Furthermore, in the paper they don't present it as something extraordinary as some people here say it is, but as an evolution of another existing software, funsearch
"Make this better in a loop" is less powerful than using evolution on a population. While it may seem like evolution is just single steps in a loop, something qualitatively different occurs due to the population dynamics - since you get the opportunity for multiple restarts / interpolation (according to an LLM) between examples / and 'novelty' not being instantly rejected.
The “fully incomprehensible to humans” aspect of this potential future state interests me as a software person.
The last 50 years of software evolution have been driven by a need to scale human comprehension for larger and more integrated codebases. If we decreasingly need/rely on humans to understand our code, source code’s forward-progress flywheel is going to slow down and will bring us closer to (as you suggest) incomprehensibility.
Not only did we scale the breadth of codebases - the flywheel built layers and layers of abstraction over time (have you seen the code sample in this article??), fostering a growing market of professional developers and their career progressions; if most code becomes incomprehensible, itll be the code closer to “the bottom”, a thin wrapper of API on top of an expanding mass of throwaway whatever-language AlphaAlgo creates.
If we don’t wrangle this, it will destroy a profession and leave us with trillions of LoC that only people with GPUs can understand. Which may be another profession I suppose.
Very few people already understand highly optimized numerical kernels. Many are already machine optimized. This takes it just a bit further. Most programmers do not do high performance algorithm development.
Strange that AlphaEvolve authors do not compare their work to what is achievable by equality saturation. An implementation of equality saturation can take interesting integrals with very simple rules [2].
Absolutely - not arguing that the results are unreasonable to the point of illegitimacy - just curious to see when they perform as well as reported and how well the presented solutions generalize to different test cases - or if it's routing to different solutions based on certain criteria etc.
https://ppc.cs.aalto.fi/ covers some of this (overlapping with the topics the person you responded to mentioned, but not covering all, and including some others)
> AlphaEvolve is accelerating AI performance and research velocity. By finding smarter ways to divide a large matrix multiplication operation into more manageable subproblems, it sped up this vital kernel in Gemini’s architecture by 23%, leading to a 1% reduction in Gemini's training time.
I have not read this linked article, but your comment made me recall a discussion about a speed up of CUDA kernels presented by Sakana AI Labs. The researcher Ravid Shwartz Ziv at NYU posted about it on LinkedIn [1], and here is the Twitter post of interest [2]
"""
Yesterday's news about Sakana AI Labs provided an important lesson for all of us working with AI agents. Their announcement of an AI system that could supposedly optimize CUDA kernels to run 100x faster initially seemed like exactly the kind of use cases we've been hoping for in AI-assisted development.
Like many others, I was excited about it. After all, isn't this exactly what we want AI to do - help us optimize and improve our technical systems?
However, careful investigation by the community (on Twitter) revealed a different story. What really happened? The AI-generated CUDA kernel appeared to achieve incredible speedups, but the code was inadvertently reusing memory buffers containing previous results, essentially bypassing the actual computation. When properly evaluated, the kernel actually runs about 3x slower than the baseline.
"""
lmao this is exactly the kind of stuff I always see from Claude. It’s like adding a Skip() to a test and declaring it works now. “Well it’s a lot faster, I met the criteria of my TODOs cya”
I’ve seen it so much I kinda doubt it was “inadvertent” because they’re like seemingly intentional about their laziness, and will gaslight you about it too.
From the paper it was a speedup on the XLA GPU kernel they wrote using Jax, which is probably not SOTA. I don't think Jax even has a official flash attention implementation.
Not sure what “official” means but would direct you to the GCP MaxText [0] framework which is not what this GDM paper is referring to but rather this repo contains various attention implementations in MaxText/layers/attentions.py
Are you sure? From my experience, no AI assistant is fast enough to handle fast-paced questions on the code the candidate just wrote. Also, frequent requests to adjust variable names and deactivating pasting on the page make it extremely laborious for the candidate to get AI to modify the code on the screen.
AI will indeed kill the leetcode interview - because once it replaces human SWEs you don't really need to give leetcode-style brainteasers to any human anymore.
Not defending it but I think it was more of a test if you have the dedication (and general smarts) to grind them for a few months than software engineering skills.
Similar to hiring good students from famous universities even if most of CS isn't that applicable to day to day programming work, just because it's a signal that they're smart and managed to get through a difficult course.
Interestingly, they improved matrix multiplication and there was a paper on Arxiv a few days ago [1] that also improved matrix multiplication and the only case common to both is <4,5,6> (multiplying 4x5 matrix with 5x6 matrix) and they both improved it from 93 to 90.
There’s been a ton of work on multiplying very large matrices. But actually, I have no idea—how well explored is the space of multiplying small matrices? I guess I assume that, like, 4x4 is done very well, and everything else is kind of… roll the dice.
For the people awaiting the singularity, lines like this written almost straight from science fiction:
> By suggesting modifications in the standard language of chip designers, AlphaEvolve promotes a collaborative approach between AI and hardware engineers to accelerate the design of future specialized chips."
Not necessarily. Theorem provers provide goals that can serve the same function as "debug text." Instead of interpreting the natural language chosen by the dev who wrote the compiler, these goals provide concrete, type-accurate statements that indicate the progress of an ongoing proof.
> AlphaEvolve enhanced the efficiency of Google's data centers, chip design and AI training processes — *including training the large language models underlying AlphaEvolve itself*.
Singularity people have been talking for decades about AI improving itself better than humans could, and how that results in runaway compounding growth of superintelligence, and now it's here.
Most code optimizations end up looking somewhat asymptotic towards a non-zero minimum.
If it takes you a week to find a 1% speedup, and the next 0.7% speedup takes you 2 weeks to find ... well, by using the 1% speedup the next one only takes you 13.86 days. This kind of small optimization doesn't lead to exponential gains.
That doesn't mean it's not worthwhile - it's great to save power & money and reduce iteration time by a small amount. And it combines with other optimizations over time. But this is in no way an example of the kind of thing that the singularity folks envisioned, regardless of the realism of their vision or not.
Exactly - the possible improvements may compound, but they converge logarithmically towards an upper limit absent new insight that establishes a new upper limit.
Long way to go Singularity. We don't even know if its possible.
Basically, singularity assumes that you can take the information about the real world "state", and compress it into some form, and predict the state change faster than reality happens. For a subset of the world, this is definitely possible. But for entire reality, it seems that there is a whole bunch of processes that are computationally irreducible, so an AI would never be able to "stay ahead" or so to to speak. There is also the thing about computational ir-reversibility - for example observing a human behavior is seeing the output of a one way hashing function of neural process in our brain that hides a lot of detail and doesn't let you predict it accurately in all cases.
Also, optimization algorithms are nothing new. Even before AI, you could run genetic algorithm or PSO on code, and given enough compute it would optimize the algorithm, including itself. The hard part that nobody has solved this is abstracting this to a low enough level to where its applicable across multiple layers that correspond to any task.
For example, let say you have a model (or rather an algorithm) that has only a single interface, and that is the ability to send ethernet packets, and it hasn't been trained on any real world data at all. If you task it with building you a website that makes money, the same algorithm that iterates over figuring out how to send IP packets then TCP packets then HTTP packets should also be able to figure out what the modern world wide web looks like and what concepts like website and money is, building its knowledge graph and searching on it and interpolating on it to figure out how to solve the problem.
The singularity has always existed. It is located at the summit of Mount Stupid, where the Darwin Awards are kept. AI is really just psuedo-intelligence; an automated chairlift to peak overconfidence.
I love these confident claims! It sounds like you really know what you are talking about. It's either that or you are projecting. Could you elaborate? I for one find the level of intelligence quite real, I use AIs to do a lot of quite complex stuff for me nowadays. I have an agent that keeps my calendar, schedules appointments with people that want meetings with me, summarizes emails and add these summaries to notion and breaks them up in todo-lists, answers questions about libraries and APIs, writes most of my code (although I do need to hold it's hand and it cannot improve by learning from me).
> AlphaEvolve was able to find a simple code rewrite (within an arithmetic unit within the matmul unit) that removed unnecessary bits, a change validated by TPU designers for correctness.
I speculate this could refer to the upper bits in the output of a MAC circuit being unused in a downstream connection (perhaps to an accumulation register). It could also involve unused bits in a specialized MAC circuit for a non-standard datatype.
> While this specific improvement was also independently caught by downstream synthesis tools, AlphaEvolve’s contribution at the RTL stage demonstrates its capability to refine source RTL and provide optimizations early in the design flow.
As the authors admit, this bit-level optimization was automatically performed by the synthesis tool (the equivalent to this in the software-world is dead code elimination being performed by a compiler). They seem to claim it is better to perform this bit-truncation explicitly in the source RTL rather than letting synthesis handle it. I find this dubious since synthesis guarantees that the optimizations it performs do not change the semantics of the circuit, while making a change in the source RTL could change the semantics (vs the original source RTL) and requires human intervention to check semantic equivalence. The exception to this is when certain optimizations rely on assumptions of the values that are seen within the circuit at runtime: synthesis will assume the most conservative situation where all circuit inputs are arbitrary.
I do agree that this reveals a deficiency in existing synthesis flows being unable to backannotate the source RTL with the specific lines/bits that were stripped out in the final netlist so humans can check whether synthesis did indeed perform an expected optimization.
> This early exploration demonstrates a novel approach where LLM-powered code evolution assists in hardware design, potentially reducing time to market.
I think they are vastly overselling what AlphaEvolve was able to achieve. That isn't to say anything about the potential utility of LLMs for RTL design or optimization.
We are further getting to the point where no one on the planet understand how any of this stuff really works. This will last us until a collapse. Then we are done for.
Interesting that this wasn't tested on ARC-AGI. Francois has always said he believed program search of this type was the key to solving it. It seems like potentially this approach could do very well.
> Most of these discoveries are on open problems suggested to us by external mathematicians Javier Gomez Serrano and Terence Tao, who also advised on how to best formulate them as inputs to AlphaEvolve. This highlights the potential for synergistic partnerships between AI-driven discovery engines like AlphaEvolve and human mathematical expertise.
That’s a really cool idea. I often used https://dannymator.itch.io/randomicon to come up with novel ideas, never thought of feeding random words to llm as a way of doing it.
Maybe the actual solution to the interpretability/blackbox problem is to not ask the llm to execute a given task, but rather to write deterministic programs that can execute the task.
Cool, but don't get me wrong, isn't this essentially similar to Google's Co-Scientist, where multiple models are in a loop, passing context back and forth validating things? At its core, it's still a system of LLMs, which is impressive in execution but not fundamentally new.
LLMs are undoubtedly useful at tasks like code "optimisation" and detecting patterns or redundancies that humans might overlook, but this announcement feels like another polished, hypey blog post from Google.
What's also becoming increasingly confusing is their use of the "Alpha" branding. Originally, it was for breakthroughs like AlphaGo or AlphaFold, where there was a clear leap in performance and methodology. Now it's being applied to systems that, while sophisticated, don't really rise to the same level of impact.
edit: I missed the evaluator in my description, but an evaluation method is applied also in Co-Scientist:
"The AI co-scientist leverages test-time compute scaling to iteratively reason, evolve, and improve outputs. Key reasoning steps include self-play–based scientific debate for novel hypothesis generation, ranking tournaments for hypothesis comparison, and an "evolution" process for quality improvement."[0]
No, you're extending the domain to which it is applicable. It's like noting that vaccines are useful for smallpox -- and the flu! Same idea, but different recipes.
"While AI Co-Scientist represents scientific hypotheses and their evaluation criteria in natural language, AlphaEvolve focuses on evolving code, and directs evolution using programmatic evaluation functions. This choice enables us to substantially sidestep LLM hallucinations, which allows AlphaEvolve to carry on the evolution process for a large number of time steps."
It is interesting how google turned the tide on GenAI race, and seems to be leading the pack, with not only great fundamental research, but also interesting model and products. To what extent these remain a niche/nice to have or become a sensation remains to be seen, but I hope if they don't reach hype status, they might be released to the open weights world.
People often forget that Google was behind Mu Zero, which IMO is the most important AI paper of the decade, not the Transformer one, because they effectively showed how models can learn how to search.
For example, for self driving, it makes much more sense to treat it like a game, where the model learns the evolution of the surrounding environment, and learns how its own actions affect it, and can MCTS its way into correct behavior - specifically because once it learns the environment dynamics, it can internally simulate crashes and retrain itself.
If this process is refined (namely the functions that control direction of training) , you can pretty much start training a model on the dataset of real world (sights, sounds, physical interactions, as well as digital ones), and as it learns the environment, it can be further and further refined, and then we get to the point where it can self evolve its decision making to be truly considered "intelligent".
> It is interesting how google turned the tide on GenAI race, and seems to be leading the pack
I think this is perhaps due to Google combining Google Brain and DeepMind, and putting Demis Hassabis at the helm?
I agree, Google is very much leading the pack in AI now. My worry is that they have mentioned recently that they are less inclined to release research into the open if they think it will give their competition a step-up. Demis is more scientist than business-man, so perhaps there's hope that he will be willing to continue to release research.
From the paper, "Notably, for multiplying two 4 × 4 matrices, applying the algorithm of Strassen recursively results in an algorithm with 49 multiplications, which works over any field...AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications."
If you do naive matrix multiplication, you get a sense that you're doing similar work multiple times, but it's hard to quantify just what that duplicated work entails. Compare it to, for example, calculating the size of the union of two sets:
Total size = size(A) + size(B) - size(intersection(A, B))
You have to take out that extra intersection amount because you've counted it twice. What if you could avoid counting it twice in the first place? That's easy, you just iterate over each set once, keeping track of the elements you've already seen.
Strassen's algorithm keeps track of calculations that are needed later on. It's all reminiscent of dynamic programming.
What I find interesting is that it seems the extra savings requires complex values. There must be something going on in the complex plane that is again over-counting with the naive approach.
It seems like you have some misconceptions about Strassen's alg:
1. It is a standard example of the divide and conquer approach to algorithm design, not the dynamic programming approach. (I'm not even sure how you'd squint at it to convert it into a dynamic programming problem.)
2. Strassen's does not require complex valued matrices. Everything can be done in the real numbers.
I think the OP was pointing out that the reason Strasssen's algorithm works is that it somehow uncovered a kind of repeated work that's not evident in a simple divide and conquer approach. It's by the clever definition of the various submatrices that this "overlapping" work can be avoided.
In other words, the power of Strasssens algorithm comes from a strategy that's similar to / reminiscent of dynamic programming.
By googling "4x4 matrices multiplication 48" I ended up on this discussion on math.stackexchange https://math.stackexchange.com/questions/578342/number-of-el... , where in 2019 someone stated "It is possible to multiply two 4×4 matrix A,B with only 48 multiplications.", with a link to a PhD thesis. This might mean that the result was already known (I still have to check the outline of the algorithm).
From some conversations on Twitter, it seems plausible that the rank-48 decomposition of the 4×4 matrix multiplication tensor really is new; and that perhaps where things have gone awry is attempting to summarise this result in a more lay-friendly manner: the algorithm in that post apparently doesn't constitute or imply a rank-48 tensor decomposition.
As already noted in a post by fdej further down, Waksman's algorithm from 1970, which works over the complex numbers, requires only 46 multiplications (and I guess, divisions by 2, which may or may not be relevant depending on your actual ring).
The answer says "For rings in which division by 2 is permitted". Is there the same constraint for AlphaEvolve's algorithm?
Edit2: Z_2 has characteristics 2.
Edit: AlphaEvolve claims it works over any field with characteristic 0. It appears Waksman's could be an existing work. From the AlphaEvolve paper: "For 56 years, designing an algorithm with fewer than 49 multiplications over any field with characteristic 0 was an open problem. AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications."
If you don't want to allow division by 2 then there is Winograd's algorithm from 1967 which works over any commutative ring and uses 48 multiplications for 4 x 4.
One of the authors here. We are aware of the Winograd scheme, but note that it only works over commutative rings, which means that it's not applicable recursively to larger matrices (and doesn't correspond to a rank 48 factorization of the <4,4,4> matrix multiplication tensor). The MathOverflow answer had a mistake corrected in the comments by Benoit Jacob.
More details: the Winograd scheme computes (x1+ y2 )(x2+ y1 ) + (x3+y4)(x4+y3)-Ai-Bj, and relies on y2y1 (that comes from expanding the first brackets) cancelling with y1y2 in Bj=y1y2 + y3y4. This is fine when working with numbers, but if you want to apply the algorithm recursively to large matrices, on the highest level of recursion you're going to work with 4x4 block matrices (where each block is a big matrix itself), and for matrices Y2Y1 != Y1Y2 (for general matrices).
Here is a website that tracks fastest (recursively applicable) matrix multiplication algorithms for different matrix sizes, and it stands at 49: https://fmm.univ-lille.fr/4x4x4.html
So, did LLM (namely Gemini-Flash) helepd with the combinatorial optimization process? I'm sure not all of their discoveries (one on kissing numbers, etc.) have previous solutions in some other form, but yeah these findings looks more like very large combinatorial optimization tasks.
Are you sure the saving needs complex values? I think their algorithm works over any char 0 field. Probably needs to just divide by some divisor of 4!=24 if I had to guess.
Fair point! A single complex multiplication `(a+bi)(c+di)` indeed requires at least 3 real multiplications to be implemented.
However, when researchers (and systems like AlphaEvolve in this context) analyze fast matrix multiplication algorithms like Strassen's, the primary goal is usually to improve the asymptotic complexity (and understand the space of these algorithms better). This complexity is determined by the number of multiplications in the field over which the matrices are defined.
* For real matrices, we count real scalar multiplications.
* For complex-valued matrices (as in the 4x4 example where AlphaEvolve found a solution with 48 scalar multiplications), "scalar multiplication" refers to a complex scalar multiplication.
The key is that these are the operations you recurse on. Additions, or the constant factor cost of implementing one field's multiplication, don't change the exponent in the `N^(log_base(multiplications))` complexity. They are constant factors.
Of course, for practical performance on a specific 4x4 matrix, one would absolutely dive into the real operations, additions, memory layout, etc., but making 4x4 matrix multiplication practically faster on some particular hardware was not the focus in this section. (We do improve practical implementation of large matrix multiplications on the target hardware in the “Enhancing AI training and inference” section of the blog post.)
>What I find interesting is that it seems the extra savings requires complex values. There must be something going on in the complex plane that is again over-counting with the naive approach.
"The rank of a tensor depends on the field over which the tensor is decomposed. It is known that some real tensors may admit a complex decomposition whose rank is strictly less than the rank of a real decomposition of the same tensor."
I'm surprised I'm not able to find this out - can some one tell me whether AlphaEvolve involves backprop or not?
I honestly have no idea how AlphaEvolve works - does it work purely on the text level? Meaning I might be able to come up with something like AlphaEvolve with some EC2's and a Gemini API access?
I picked one at random (B.2 -- the second autocorrelation inequality). Then, I looked up the paper that produced the previous state of the art (https://arxiv.org/pdf/0907.1379). It turns out that the authors had themselves found the upper bound by performing a numerical search using "Mathematica 6" (p.4). Not only did the authors consider this as a secondary contribution (p.2), but they also argued that finding something better was very doable, but not worth the pain:
"We remark that all this could be done rigorously, but one needs to control
the error arising from the discretization, and the sheer documentation
of it is simply not worth the effort, in view of the minimal gain." (p.5)
So at least in this case it looks like the advancement produced by AlphaEvolve was quite incremental (still cool!).
That right and In fact it’s the core purpose of the tool.
This is complex automation which by definition compresses the solution into a computable process that works more efficiently than the non-automated process
That, in fact, is the revolutionary part - you’re changing how energy is used to solve the problem.
This is exactly why I think the concerns about AI taking people's jobs are overblown. There is not a limited amount of knowledge work to do or things that can be invented or discovered. There's just work that isn't worth the effort, time or money to do right now, it doesn't mean it's not valuable, it's just not cost effective. If you reduce effort, time and money, then suddenly you can do it.
Like even just for programming. I just had an AI instrument my app for tracing, something I wanted to do for a while, but I didn't know how to do and didn't feel like figuring out how to do it. That's not work we were likely to hire someone to do or that would ever get done if the AI wasn't there. It's a small thing, but small things add up.
It is not some very explicit threshold beyond which AI will take job but before it won't. What's already happening is long drawn attrition where tools at different level of code, low code , no code will keep creeping up. And it will start with people are not respected or valued for their work, so they can leave, once left, they will not be replaced or replaced lower skilled folks and at some point that position stop existing altogether.
In a way it is nothing new but natural progression of technology. It is increasing pace of change that is different. Can a person learn some skills by their 20s and apply productively throughout their lifetime? Now at this point it is so thoroughly untrue that I'd be laughed out if I asked for such thing. We are told to up skill few times in career to up-skilling continuously.
As changes are getting faster and faster more people are gonna fall wayside and of course they can blame themselves for their predicament.
> And it will start with people are not respected or valued for their work, so they can leave, once left, they will not be replaced or replaced lower skilled folks and at some point that position stop existing altogether.
Automation changed farming for the worse? Farmers today are not respected / valued for their work? Farmers were replaced with low skilled labor? Do you think the job of a farmer (aka "food grower") will stop existing?
I do not predict future only look at what happened in the past and my answer to each question above about farming is the opposite what your comment would imply if it was applied to farming.
And the invention of AGI will have the same impact as the electricity, i mean, they're both inventions, right ? I can't wait for all these billions of new full time jobs coming to replace the current ones.
Farmers couldn't be replaced by low skill labor because they are low skill.
Farmer didn't stop existing, but we went from 80% of the population farming is to 1-10%. If farming automation had happened in 1800 when 80% of the workforce was working in agriculture, it'd have been a cataclysm.
I'm pretty sure there is a slight widespread lack of respect for software engineers, mainly offset by their high salaries. Wait and see once vibecoding becomes the new norm.
And for software engineers, yeah, automation will wreck their jobs and their paychecks because software engineering's higher speed limit in efficiency is the speed of light, not a tractor's.
Great points. Besides if one look around even today beyond people who somehow still succeeding at software hustle, there are already tons of people fallen off IT gravy train. A lot of manual testers who would make decent living are now eliminated by automation. Software document writers jobs are kind of gone. Developers are supposed to create document themselves on Confluent wiki etc. A lot of prized SAP consultants and such from past are now downgraded to generic mid level project managers / IT managers if they were hold onto IT jobs at all.
I can list lot more jobs e.g exchange admins, app server admins, DBAs, they are either gone or far fewer available. And lot of people were not able to up-skill and fell out of race in just a matter of 15-20 years.
There are two ways to think about your work in IT, one is as a person who really understands how to use a particular technology, and the other is as someone who can figure out how to use technology in general to achieve some particular end. Anybody who picks the first path might have a very well paid career for the few years that that technology is relevant, but will eventually crash out. You need to always be looking at the next thing and keeping your skills and knowledge up to date. Nobody ever guaranteed that Microsoft Outlook admins would have a career for life.
I am talking about aggregate distribution not individual motivation to do better. Of course some can do better, learn new things, update LinkedIn profile regularly, attend local networking events, take paid membership to enhance visibility in job search and so on.
The point is more and more people who survived with average skills or one time learning in past are not able to do so now. And it is not a complain about anything or anyone but observation that few people are seeing marked improvement in their lives with changing technology and many more are seeing degradation due to same changes.
I feel like this begs for a careful analysis, we could probably drop a dozen more reasons as to why demand in devs and perhaps even in # of lines of code might plateau or decline in the near future, without even mentioning AI at any point.
I totally agree that there are whole host of reasons for this. One of them I think is plainly a ton of work which was novel and custom in past is now subsumed in base infrastructure of today's world. Despite big tech and other vendor keep pushing of new things lot of people and companies are finding base level acceptable for many tasks which would need custom work in past. So no growing demand custom software for everything.
We can already see for example as per Ericsson report[1] after exponential demand for mobile data and speed it is now plateauing and next decade will not see huge growth. As users are finding things they do and apps they use with phones are now fast/good enough.
Your point is about as good as saying that "Is my life worse off at home since I can clean whole area in 30 min of mild effort with my cordless vacuum cleaner where as manual broom would've taken me at half day of hard work?"
Of course my life is bit better as I saved few hours on weekend as owner of house and a vacuum cleaner.
But my life as worker is worse in last 10 years as knowledge of developing large complex applications is not valuable because we are in Next Gen Cloud native era where one application will not contain more than 5 functions anyway. Even if I claim I can write better maintainable, performance code , the employer directly or indirectly says "Well we don't care, we need you to complete these 10 JIRAs in this sprint" And only answer they take from me is yes.
> Farmers today are not respected / valued for their work?
Pretty much most of them feel underpaid for the amount of hard work and I hear they're having problem recruiting younger people to the business, so many foreigners take those jobs.
Anyone in computing, especially things related to deep learning, do.
If you prefer to think of human effort, there was also immense human effort building the models, the needed infra, assembling the data to train on, etc. There's usually 1000+ specialists on projects like this (see the last chat gpt paper author list, which took pages and pages as an appendix).
There is no way I can think any of this result was anything more than a massive effort, costing 10s to 100+ millions of dollars.
not worth the time for a human, but if you can throw AI at all of those "opportunities" it adds up substantially because all the chores can be automated.
Yeah for the kissing number stuff people can find slight improvements if they want. It usually isn't worth it because it provides no insight. But maybe when you generate a lot of them one or some family will turn out to be interesting.
> Here, the code between <<<<<<< SEARCH and======= is the exact segment to match in the current program version. The code between======= and >>>>>>> REPLACE is the new segment that will replace the original one. This allows for targeted updates to specific parts of the code.
Anybody knows how they can guarantee uniqueness of searched snipped within code block or is it even possible?
I'm surprised by how little detail is given about the evolution procedure:
>In AlphaEvolve, the evolutionary database implements an algorithm that is inspired by a combination of the MAP elites algorithm [71] and island-based population models [80, 94].
"inspired by" is doing a lot of heavy lifting in this sentence. How do you choose dimensions of variation to do MAP-elites? How do you combine these two algorithms? How loose is the inspiration? It feels like a lot of the secret sauce is in the answers to these questions, and we get a single paragraph on how the evolution procedure works, which is so vague as to tell us almost nothing.
Most straightforward would be to ask the model to generate different evaluation metrics (which they already seem to do) and use each one as one of the dimensions
297 comments
[ 2.9 ms ] story [ 281 ms ] thread> about: I believe in the creation of a machine god
Sounds about right.
Not necessarily. 'Gospel' is translated as good news. The unpleasant news tends towards those within the power structure that the prophet challenges.
The guy's making a prediction. Classifying it as some kind of religious zealotry isn't fair to his point or him.
That isn't every problem in software engineering.
If the cost of developing the software is 0, you can just build both.
Some of these questions change slightly, since we might end up with "unlimited resources" (i.e. instead of having e.g. 5 engineers on a team who can only get X done per sprint, we effectively have near-limitless compute to use instead) so maybe the answer is "build everything on the wish-list in 1 day" to the "what should we prioritize" type questions?
Interesting times.
My gut is that software engineers will end up as glorified test engineers, coming up with test cases (even if not actually writing the code) and asking the AI to write code until it passes.
As a corollary, once you add in self-play with random variation, the synthetic data problem is solved for coding, math, and some classes of scientific reasoning. No more modal collapse, no more massive teams of PhDs needed for human labeling, as long as you have a reliable metric for answer quality.
This isn't just neat, it's important - as we run out of useful human-generated data, RL scaling is the best candidate to take over where pretraining left off.
There are monopolies on the coolest sets of data in almost all industries, all the RL in the world won't do us any good if those companies doing the data hoarding are only using it to forecast outcomes that will make them more money, not what can be done to better society.
They are having some success in making it work internally. Maybe only the team that built it can get it to work? But it does seem promising.
I guess that's now becoming true with LLMs.
Faster LLMs -> More intelligence
If variety is sought, why not beam with nice population statistic.
Gradient descent is literally following the negative of the gradient to minimize a function. It requires a continuous domain, either analytical or numerical derivatives of the cost function, and has well-known issues in narrow valleys and other complex landscapes.
It’s also a local minimization technique and cannot escape local minima by itself.
_Stochastic_ gradient descent and related techniques can overcome some of these difficulties, but are still more or less local minimization techniques and require differentiable and continuous scoring functions.
In contrast, genetic algorithms try to find global minima, do not require differentiable scoring functions, and can operate on both continuous and discrete domains. They have their own disadvantages.
Different techniques for different problems. The field of numerical optimization is vast and ancient for a reason.
couldn't you say that if you squint hard enough, GA looks like a category of RL? There are certainly a lot of similarities, the main difference being how each new population of solutions is generated. Would not at all be surprised that they're using a GA/RL hybrid.
As far as I can read, the weights of the LLM are not modified. They do some kind of candidate selection via evolutionary algorithms for the LLM prompt, which the LLM then remixes. This process then iterates like a typical evolutionary algorithm.
I suppose you could consider that last part (optimizing some metric) "RL".
However, it's missing a key concept of RL which is the exploration/exploitation tradeoff.
I'm now no longer surprised just how consistently all the gemini models overcomplicate coding challenges or just plain get them wrong.
Claude is just consistently spot on. A few salient comments for tricky code instead of incessantly telling me what it's changed and what I might want to do, incorrect assumptions when it has the code or is something we've discussed, changing large amounts of unrelated code (eg styles). I could go on.
Shame I'm too tight to pay for Claude RN though...
You can try asking it to not do that, but I would bet it would slightly degrade code quality.
You can take the code and give it to another LLM instance and ask it to strip all comments.
> In roughly 75% of cases, it rediscovered state-of-the-art solutions, to the best of our knowledge.
> And in 20% of cases, AlphaEvolve improved the previously best known solutions
These sound like incredible results. I'd be curious what kind of improvements were made / what the improvements were.
Like, was that "up to a 32.5% speedup" on some weird edge case and it was negligible speed up otherwise? Would love to see the benchmarks.
It's a very impressive result, but not magic, but also not cheating!
Previously we needed to have a human in the loop to do the change. Of course we have automated hyperparameter tuning (and similar things), but that only works only in a rigidly defined search space.
Will we see LLMs generating new improved LLM architectures, now fully incomprehensible to humans?
Edit the white paper says this: AlphaEvolve employs an ensemble of large language models. Specifically, we utilize a combination of Gemini 2.0 Flash and Gemini 2.0 Pro. This ensemble approach allows us to balance computational throughput with the quality of generated solutions. Gemini 2.0 Flash, with its lower latency, enables a higher rate of candidate generation, increasing the number of ideas explored per unit of time. Concurrently, Gemini 2.0 Pro, possessing greater capabilities, provides occasional, higher-quality suggestions that can significantly advance the evolutionary search and potentially lead to breakthroughs. This strategic mix optimizes the overall discovery process by maximizing the volume of evaluated ideas while retaining the potential for substantial improvements driven by the more powerful model.
So, I remain of my opinion before. Furthermore, in the paper they don't present it as something extraordinary as some people here say it is, but as an evolution of another existing software, funsearch
The last 50 years of software evolution have been driven by a need to scale human comprehension for larger and more integrated codebases. If we decreasingly need/rely on humans to understand our code, source code’s forward-progress flywheel is going to slow down and will bring us closer to (as you suggest) incomprehensibility.
Not only did we scale the breadth of codebases - the flywheel built layers and layers of abstraction over time (have you seen the code sample in this article??), fostering a growing market of professional developers and their career progressions; if most code becomes incomprehensible, itll be the code closer to “the bottom”, a thin wrapper of API on top of an expanding mass of throwaway whatever-language AlphaAlgo creates.
If we don’t wrangle this, it will destroy a profession and leave us with trillions of LoC that only people with GPUs can understand. Which may be another profession I suppose.
[1] https://arxiv.org/abs/1012.1802
Strange that AlphaEvolve authors do not compare their work to what is achievable by equality saturation. An implementation of equality saturation can take interesting integrals with very simple rules [2].
[2] https://github.com/alt-romes/hegg/blob/master/test/Sym.hs#L3...
FA achieving a 32.5% speed up? Cool.
Why not submit it as a PR to the Flash Attention repo then? Can I read about it more in detail?
""" Yesterday's news about Sakana AI Labs provided an important lesson for all of us working with AI agents. Their announcement of an AI system that could supposedly optimize CUDA kernels to run 100x faster initially seemed like exactly the kind of use cases we've been hoping for in AI-assisted development.
Like many others, I was excited about it. After all, isn't this exactly what we want AI to do - help us optimize and improve our technical systems?
However, careful investigation by the community (on Twitter) revealed a different story. What really happened? The AI-generated CUDA kernel appeared to achieve incredible speedups, but the code was inadvertently reusing memory buffers containing previous results, essentially bypassing the actual computation. When properly evaluated, the kernel actually runs about 3x slower than the baseline. """
[1] https://www.linkedin.com/posts/ravid-shwartz-ziv-8bb18761_ye...
[2] https://x.com/main_horse/status/1892473238036631908
I’ve seen it so much I kinda doubt it was “inadvertent” because they’re like seemingly intentional about their laziness, and will gaslight you about it too.
Funny, 5 years ago we had these same complaints, but about (some) people.
[0] https://github.com/AI-Hypercomputer/maxtext
Similar to hiring good students from famous universities even if most of CS isn't that applicable to day to day programming work, just because it's a signal that they're smart and managed to get through a difficult course.
[1]: https://arxiv.org/html/2505.05896v1
> By suggesting modifications in the standard language of chip designers, AlphaEvolve promotes a collaborative approach between AI and hardware engineers to accelerate the design of future specialized chips."
Cf. the second paragraph of 3.3.4 of https://storage.googleapis.com/deepmind-media/DeepMind.com/B...
> AlphaEvolve enhanced the efficiency of Google's data centers, chip design and AI training processes — *including training the large language models underlying AlphaEvolve itself*.
Singularity people have been talking for decades about AI improving itself better than humans could, and how that results in runaway compounding growth of superintelligence, and now it's here.
If it takes you a week to find a 1% speedup, and the next 0.7% speedup takes you 2 weeks to find ... well, by using the 1% speedup the next one only takes you 13.86 days. This kind of small optimization doesn't lead to exponential gains.
That doesn't mean it's not worthwhile - it's great to save power & money and reduce iteration time by a small amount. And it combines with other optimizations over time. But this is in no way an example of the kind of thing that the singularity folks envisioned, regardless of the realism of their vision or not.
Basically, singularity assumes that you can take the information about the real world "state", and compress it into some form, and predict the state change faster than reality happens. For a subset of the world, this is definitely possible. But for entire reality, it seems that there is a whole bunch of processes that are computationally irreducible, so an AI would never be able to "stay ahead" or so to to speak. There is also the thing about computational ir-reversibility - for example observing a human behavior is seeing the output of a one way hashing function of neural process in our brain that hides a lot of detail and doesn't let you predict it accurately in all cases.
Also, optimization algorithms are nothing new. Even before AI, you could run genetic algorithm or PSO on code, and given enough compute it would optimize the algorithm, including itself. The hard part that nobody has solved this is abstracting this to a low enough level to where its applicable across multiple layers that correspond to any task.
For example, let say you have a model (or rather an algorithm) that has only a single interface, and that is the ability to send ethernet packets, and it hasn't been trained on any real world data at all. If you task it with building you a website that makes money, the same algorithm that iterates over figuring out how to send IP packets then TCP packets then HTTP packets should also be able to figure out what the modern world wide web looks like and what concepts like website and money is, building its knowledge graph and searching on it and interpolating on it to figure out how to solve the problem.
You can't write an evaluation function for general "intelligence"...
> AlphaEvolve was able to find a simple code rewrite (within an arithmetic unit within the matmul unit) that removed unnecessary bits, a change validated by TPU designers for correctness.
I speculate this could refer to the upper bits in the output of a MAC circuit being unused in a downstream connection (perhaps to an accumulation register). It could also involve unused bits in a specialized MAC circuit for a non-standard datatype.
> While this specific improvement was also independently caught by downstream synthesis tools, AlphaEvolve’s contribution at the RTL stage demonstrates its capability to refine source RTL and provide optimizations early in the design flow.
As the authors admit, this bit-level optimization was automatically performed by the synthesis tool (the equivalent to this in the software-world is dead code elimination being performed by a compiler). They seem to claim it is better to perform this bit-truncation explicitly in the source RTL rather than letting synthesis handle it. I find this dubious since synthesis guarantees that the optimizations it performs do not change the semantics of the circuit, while making a change in the source RTL could change the semantics (vs the original source RTL) and requires human intervention to check semantic equivalence. The exception to this is when certain optimizations rely on assumptions of the values that are seen within the circuit at runtime: synthesis will assume the most conservative situation where all circuit inputs are arbitrary.
I do agree that this reveals a deficiency in existing synthesis flows being unable to backannotate the source RTL with the specific lines/bits that were stripped out in the final netlist so humans can check whether synthesis did indeed perform an expected optimization.
> This early exploration demonstrates a novel approach where LLM-powered code evolution assists in hardware design, potentially reducing time to market.
I think they are vastly overselling what AlphaEvolve was able to achieve. That isn't to say anything about the potential utility of LLMs for RTL design or optimization.
> Most of these discoveries are on open problems suggested to us by external mathematicians Javier Gomez Serrano and Terence Tao, who also advised on how to best formulate them as inputs to AlphaEvolve. This highlights the potential for synergistic partnerships between AI-driven discovery engines like AlphaEvolve and human mathematical expertise.
LLMs are undoubtedly useful at tasks like code "optimisation" and detecting patterns or redundancies that humans might overlook, but this announcement feels like another polished, hypey blog post from Google.
What's also becoming increasingly confusing is their use of the "Alpha" branding. Originally, it was for breakthroughs like AlphaGo or AlphaFold, where there was a clear leap in performance and methodology. Now it's being applied to systems that, while sophisticated, don't really rise to the same level of impact.
edit: I missed the evaluator in my description, but an evaluation method is applied also in Co-Scientist:
"The AI co-scientist leverages test-time compute scaling to iteratively reason, evolve, and improve outputs. Key reasoning steps include self-play–based scientific debate for novel hypothesis generation, ranking tournaments for hypothesis comparison, and an "evolution" process for quality improvement."[0]
[0]: https://research.google/blog/accelerating-scientific-breakth...
https://research.google/blog/accelerating-scientific-breakth...
"While AI Co-Scientist represents scientific hypotheses and their evaluation criteria in natural language, AlphaEvolve focuses on evolving code, and directs evolution using programmatic evaluation functions. This choice enables us to substantially sidestep LLM hallucinations, which allows AlphaEvolve to carry on the evolution process for a large number of time steps."
For example, for self driving, it makes much more sense to treat it like a game, where the model learns the evolution of the surrounding environment, and learns how its own actions affect it, and can MCTS its way into correct behavior - specifically because once it learns the environment dynamics, it can internally simulate crashes and retrain itself.
If this process is refined (namely the functions that control direction of training) , you can pretty much start training a model on the dataset of real world (sights, sounds, physical interactions, as well as digital ones), and as it learns the environment, it can be further and further refined, and then we get to the point where it can self evolve its decision making to be truly considered "intelligent".
I think this is perhaps due to Google combining Google Brain and DeepMind, and putting Demis Hassabis at the helm?
I agree, Google is very much leading the pack in AI now. My worry is that they have mentioned recently that they are less inclined to release research into the open if they think it will give their competition a step-up. Demis is more scientist than business-man, so perhaps there's hope that he will be willing to continue to release research.
If you do naive matrix multiplication, you get a sense that you're doing similar work multiple times, but it's hard to quantify just what that duplicated work entails. Compare it to, for example, calculating the size of the union of two sets:
Total size = size(A) + size(B) - size(intersection(A, B))
You have to take out that extra intersection amount because you've counted it twice. What if you could avoid counting it twice in the first place? That's easy, you just iterate over each set once, keeping track of the elements you've already seen.
Strassen's algorithm keeps track of calculations that are needed later on. It's all reminiscent of dynamic programming.
What I find interesting is that it seems the extra savings requires complex values. There must be something going on in the complex plane that is again over-counting with the naive approach.
1. It is a standard example of the divide and conquer approach to algorithm design, not the dynamic programming approach. (I'm not even sure how you'd squint at it to convert it into a dynamic programming problem.)
2. Strassen's does not require complex valued matrices. Everything can be done in the real numbers.
In other words, the power of Strasssens algorithm comes from a strategy that's similar to / reminiscent of dynamic programming.
On the other side, it's claimed here that an algorithm that uses only 46 multiplications has been known since 1970: https://mathstodon.xyz/@fredrikj/114508287537669113
Edit2: Z_2 has characteristics 2.
Edit: AlphaEvolve claims it works over any field with characteristic 0. It appears Waksman's could be an existing work. From the AlphaEvolve paper: "For 56 years, designing an algorithm with fewer than 49 multiplications over any field with characteristic 0 was an open problem. AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications."
More details: the Winograd scheme computes (x1+ y2 )(x2+ y1 ) + (x3+y4)(x4+y3)-Ai-Bj, and relies on y2y1 (that comes from expanding the first brackets) cancelling with y1y2 in Bj=y1y2 + y3y4. This is fine when working with numbers, but if you want to apply the algorithm recursively to large matrices, on the highest level of recursion you're going to work with 4x4 block matrices (where each block is a big matrix itself), and for matrices Y2Y1 != Y1Y2 (for general matrices).
Here is a website that tracks fastest (recursively applicable) matrix multiplication algorithms for different matrix sizes, and it stands at 49: https://fmm.univ-lille.fr/4x4x4.html
UPD: s/fields/rings/ and fixed equation rendering
However, when researchers (and systems like AlphaEvolve in this context) analyze fast matrix multiplication algorithms like Strassen's, the primary goal is usually to improve the asymptotic complexity (and understand the space of these algorithms better). This complexity is determined by the number of multiplications in the field over which the matrices are defined. * For real matrices, we count real scalar multiplications. * For complex-valued matrices (as in the 4x4 example where AlphaEvolve found a solution with 48 scalar multiplications), "scalar multiplication" refers to a complex scalar multiplication.
The key is that these are the operations you recurse on. Additions, or the constant factor cost of implementing one field's multiplication, don't change the exponent in the `N^(log_base(multiplications))` complexity. They are constant factors.
Of course, for practical performance on a specific 4x4 matrix, one would absolutely dive into the real operations, additions, memory layout, etc., but making 4x4 matrix multiplication practically faster on some particular hardware was not the focus in this section. (We do improve practical implementation of large matrix multiplications on the target hardware in the “Enhancing AI training and inference” section of the blog post.)
(Disclaimer: one of the authors.)
"The rank of a tensor depends on the field over which the tensor is decomposed. It is known that some real tensors may admit a complex decomposition whose rank is strictly less than the rank of a real decomposition of the same tensor."
https://en.wikipedia.org/wiki/Tensor_rank_decomposition#Fiel...
I honestly have no idea how AlphaEvolve works - does it work purely on the text level? Meaning I might be able to come up with something like AlphaEvolve with some EC2's and a Gemini API access?
But how incremental are these advancements?
I picked one at random (B.2 -- the second autocorrelation inequality). Then, I looked up the paper that produced the previous state of the art (https://arxiv.org/pdf/0907.1379). It turns out that the authors had themselves found the upper bound by performing a numerical search using "Mathematica 6" (p.4). Not only did the authors consider this as a secondary contribution (p.2), but they also argued that finding something better was very doable, but not worth the pain:
"We remark that all this could be done rigorously, but one needs to control the error arising from the discretization, and the sheer documentation of it is simply not worth the effort, in view of the minimal gain." (p.5)
So at least in this case it looks like the advancement produced by AlphaEvolve was quite incremental (still cool!).
This is complex automation which by definition compresses the solution into a computable process that works more efficiently than the non-automated process
That, in fact, is the revolutionary part - you’re changing how energy is used to solve the problem.
Like even just for programming. I just had an AI instrument my app for tracing, something I wanted to do for a while, but I didn't know how to do and didn't feel like figuring out how to do it. That's not work we were likely to hire someone to do or that would ever get done if the AI wasn't there. It's a small thing, but small things add up.
In a way it is nothing new but natural progression of technology. It is increasing pace of change that is different. Can a person learn some skills by their 20s and apply productively throughout their lifetime? Now at this point it is so thoroughly untrue that I'd be laughed out if I asked for such thing. We are told to up skill few times in career to up-skilling continuously.
As changes are getting faster and faster more people are gonna fall wayside and of course they can blame themselves for their predicament.
Automation changed farming for the worse? Farmers today are not respected / valued for their work? Farmers were replaced with low skilled labor? Do you think the job of a farmer (aka "food grower") will stop existing?
I do not predict future only look at what happened in the past and my answer to each question above about farming is the opposite what your comment would imply if it was applied to farming.
Farmers couldn't be replaced by low skill labor because they are low skill.
Farmer didn't stop existing, but we went from 80% of the population farming is to 1-10%. If farming automation had happened in 1800 when 80% of the workforce was working in agriculture, it'd have been a cataclysm.
I'm pretty sure there is a slight widespread lack of respect for software engineers, mainly offset by their high salaries. Wait and see once vibecoding becomes the new norm.
And for software engineers, yeah, automation will wreck their jobs and their paychecks because software engineering's higher speed limit in efficiency is the speed of light, not a tractor's.
I can list lot more jobs e.g exchange admins, app server admins, DBAs, they are either gone or far fewer available. And lot of people were not able to up-skill and fell out of race in just a matter of 15-20 years.
The point is more and more people who survived with average skills or one time learning in past are not able to do so now. And it is not a complain about anything or anyone but observation that few people are seeing marked improvement in their lives with changing technology and many more are seeing degradation due to same changes.
We can already see for example as per Ericsson report[1] after exponential demand for mobile data and speed it is now plateauing and next decade will not see huge growth. As users are finding things they do and apps they use with phones are now fast/good enough.
1. https://www.ericsson.com/en/reports-and-papers/mobility-repo...
I get the opposite impression. If anything software developers get more respect than they deserve.
Of course my life is bit better as I saved few hours on weekend as owner of house and a vacuum cleaner.
But my life as worker is worse in last 10 years as knowledge of developing large complex applications is not valuable because we are in Next Gen Cloud native era where one application will not contain more than 5 functions anyway. Even if I claim I can write better maintainable, performance code , the employer directly or indirectly says "Well we don't care, we need you to complete these 10 JIRAs in this sprint" And only answer they take from me is yes.
Pretty much most of them feel underpaid for the amount of hard work and I hear they're having problem recruiting younger people to the business, so many foreigners take those jobs.
If you prefer to think of human effort, there was also immense human effort building the models, the needed infra, assembling the data to train on, etc. There's usually 1000+ specialists on projects like this (see the last chat gpt paper author list, which took pages and pages as an appendix).
There is no way I can think any of this result was anything more than a massive effort, costing 10s to 100+ millions of dollars.
Go ahead and explain how this was low effort.
Anybody knows how they can guarantee uniqueness of searched snipped within code block or is it even possible?
>In AlphaEvolve, the evolutionary database implements an algorithm that is inspired by a combination of the MAP elites algorithm [71] and island-based population models [80, 94].
"inspired by" is doing a lot of heavy lifting in this sentence. How do you choose dimensions of variation to do MAP-elites? How do you combine these two algorithms? How loose is the inspiration? It feels like a lot of the secret sauce is in the answers to these questions, and we get a single paragraph on how the evolution procedure works, which is so vague as to tell us almost nothing.
Agreed the dimensions/features are key. These white papers are an insult to science...