Every few years, a derivative-free neural network optimization algorithm gets some hype. I'd bet my life savings that none of them ever make an impact.<p>Derivative-free optimization can be useful for genuinely discontinuous objectives [1], but common neural network objectives are smooth and/or Lipschitz.<p>The gradient is useful. Instead of trying random directions and hoping that one of them is an improvement, it tells you where to go. The more parameters you have, the more useful it becomes.<p>A strict complexity gap between gradient-based and derivative-free Lipschitz convex optimization has been suspected for decades and recently proved (using AI, [2]). Neural net optimization is nonconvex, but not radically different.<p>IMO, a more promising direction is gradient-based optimizers specialized to the neural network structure, like Muon [3].<p>[1] <a href="https://arxiv.org/abs/2202.00817" rel="nofollow">https://arxiv.org/abs/2202.00817</a><p>[2] <a href="https://arxiv.org/abs/2607.13335" rel="nofollow">https://arxiv.org/abs/2607.13335</a><p>[3] <a href="https://jeremybernste.in/writing/deriving-muon" rel="nofollow">https://jeremybernste.in/writing/deriving-muon</a>
It's still important to support research in this direction cause us meatbags cost a LOT less energy to train than GPTs even if you assume that it takes 30 years to train a PhD. Our current training methods honestly leave a lot to be desired. We almost certainly dont do full backpropagation.
PHD inference doesn't scale, though.
I think it's fun back-of-the-napkin sometimes to compare meat to matmuls but ultimately fallacious to its core, making it an intellectual tarpit.<p>It's much harder to argue with the math and empirical results.
Even for non-smooth or discontinuous objectives, I'd still reach for methods that use gradient-like information over zeroth-order methods. For non-smooth objectives, Clarke-generalized subdifferentials have been pretty effective outside of ML, and have been used in automatic differentiation contexts at least 10-15 years ago. A carelessly quick literature search suggested conservative gradients, too.<p>For discontinuous objectives, I know there's been work on using envelope approximations, but the little I'm aware of in that work was in low-dimensional settings where the structure of the discontinuity was known explicitly. On the other extreme, lack of continuity comes up all the time in infinite-dimensional, PDE-constrained optimization, and some methods rely on tangent cones or various generalized notions of subdifferentiability (e.g., Mordukhovich, Bouligand) to demonstrate convergence. Admittedly, that work was somewhat outside my area of expertise, so I may be getting the details there slightly wrong, but the broad point stands that even in those settings, some directional information can be obtained and used profitably without resorting to zeroth-order methods.
Kind of like random projections. Pre ChatGPT there would every now and then come a paper that states something along the lines of: instantiate a large randomly populated matrix, multiply by the input, and win! It kinda makes sense because you "stretch out" the space and separation boundaries become easier, but I have never seen it fully utilised in production in any meaningful way. Anyone remember the DANs (Deep Averaging Networks)?
If it's cheaper then I guess it will might get practical. Also more likely that mind uses simpler techniques more similar to these.<p>I wonder though if someone tested mutating training objective though, like keeping original loss/goal and somehow defining loss differently and then comparing against original. This intuitively feels like how mind tries to handle difficult tasks.
Random selection seems to favor post training<p><a href="https://arxiv.org/pdf/2603.12228" rel="nofollow">https://arxiv.org/pdf/2603.12228</a>
"A strict complexity gap between gradient-based and derivative-free Lipschitz convex optimization" has been known for decades. It's covered in standard textbooks like Nesterov's "Introductory lectures on convex optimization". That AI result is about establishing the gap in a fairly niche accuracy regime.
> Derivative-free optimization can be useful for genuinely discontinuous objectives [1], but common neural network objectives are smooth and/or Lipschitz.<p>There is even an analog to the continuous derivative for discrete binary functions, called "Boolean variation": <a href="https://proceedings.neurips.cc/paper_files/paper/2024/hash/718a3c5cf135894db6e718725f52ef9a-Abstract-Conference.html" rel="nofollow">https://proceedings.neurips.cc/paper_files/paper/2024/hash/7...</a><p>Like for derivatives, there is a chain rule for Boolean variations, so you can use something like backpropagation, but without needing any expensive floating point math. Though I don't think this has been used much so far. There must be some other downside.
And yet the best learning algorithm we have is derivative-free!
Yes, SVMs and Random Forests still rule the many worlds of classification problems often not in the spotlight.
Support Vector Machines involve solving a large QP optimization problem... which is often done by running a variant of gradient descent (or one of the second- or quasi-second-order optimization algorithms, which involves finding the Hessian as well as the gradient)
Back when I was a researcher, I had a classification problem where the default random forest classifier built into scikitlearn completely dominated the neural method. The best numbers we got were something like a ~30% improvement from baseline for the neural network to ~95% for the random forest.<p>The disparity was so large that I was certain I must have made a mistake and I spent a few hours debugging, and then a few hours more trying different neural architectures.<p>Turns out this is just a super common experience for anyone in NNs who would also try the more established learning algorithms.
Perhaps the optimizer is worse but the architecture or objective function is better.
Imagine how good it would be with derivatives
Bayes Optimal Classifier?
I'm excited to see a new thing in the Zero-Order Optimization (ZOO) world. I see most ZOO methods not as a "replacement for backprop" the way they are often marketed, but as a technique that can potentially work well in regimes where backprop is fundamentally weak. One of my favorite papers [0] in recent memory, for instance, is about using central-difference random gradient estimation (CD-RGE) to train large RNNs without using backprop-through-time. They also show it works decently for hard-to-optimize differentiable-neural-computers. Since reading that paper, I've had a lot of fun trying to apply this technique to settings I would describe as "a traditional differentiable neural network being applied in a non-traditional environment where you can't just call loss.backward and hope for the best". I am excited to try Dust out on my personal project now :)
I'm skeptical as to whether zeroth-order methods really lend themselves to a Bitter Lesson argument. First-order methods don't explore the loss landscape optimally, but the loss function tends to be nonconvex, and zeroth-order methods don't address that issue head on. Dust smooths, and so do applicable first-order methods. Remove the nonconvexity issue, and I suspect Dust's purported advantages evaporate (based on published theoretical work), so it's pretty odd to me that the paper never discusses convexity.<p>I could buy that this method scales better than previous zeroth-order methods, and that's interesting, but it doesn't seem like enough of a moat to keep improved first-order methods from drinking its milkshake, except in cases where a zeroth-order method is already a primary option: the network needs to call a simulator that doesn't expose gradient-like information. (In cases where gradients <i>don't exist</i>, I'd still argue for other options, e.g., Clarke-generalized gradients where applicable, so long as those can be computed with the available information. I know this technology has been published for automatic differentiation, so I would imagine it could be incorporated into backprop and used with a suitable optimization algorithm.)
Is it fair to define Reinforcement Learning (RL) as forcing a gradient onto a system / simulator?<p>Though, I suppose RL has non-gradient based methods too.
Orders-of-magnitude improvements in compute efficiency are needed to become a practical replacement for backprop… but those improvements are coming.<p>As a mixture, could activation-space search produce useful teaching targets for backprop?<p>Zeroth-order search would discover candidates, first-order learning would consolidate them. The potentially valuable step is converting a sparse judgment into a reusable training target.<p>This also changes the relevance of convexity.
> There are many interesting open questions. The first is whether, and how, Dust can find better directions than backprop’s first-order gradient<p>Both algorithms are bound by the same Pareto frontier based on the Empirical Risk Minimisation Principle, so they’re already on the same trajectory.
Interestingly backprop is limited by conditioning of the Hessian matrix in order to converge (differentiate correctly). So removing this limitation is actually a great step.
I’m excited to see a comeback of evolutionary methods because they’re much more general, albeit costly and naive.
We’re now very close to what can be described best as brute forcing the Pareto frontier out of our datasets. Not sure that’s what we want but I have no better ideas either.
Intereting. There was a completely different take on how to "do" back propagation using optics at YC papers video the other day(I can't find the video). The technique presented diffusion networks with optics. If a hardware technique to make computation more efficient emerges, a lot of methods like this could apply no?
Even though this is way more expensive than backprop, could a hybrid approach where you fine tune an existing checkpoint that's been backpropped unlock further gains?
It would be cool to apply this to different stages and see if that affects the learning trajectory
I would like to see wall clock time, energy, peak memory and downstream quality compared at equal loss. Until the effiency gap closes, this is an interesting research direction.
For me credit assignment without a global clock is extremely important, i believe it's a necessary step towards end to end training of models In-materio.
It sounds like this is less computationally efficient than backprop, but more easily parallelizable. Is that fair?
Not necessarily, backprop is highly parallelizable since it is just a bunch of matrix mults.<p>Something like Dust skips the backward pass on backprop. But other techniques like
Neural Predictive Coding can be completely asynchronous, each "weight" can fire independent of those far away from it. Innocenti, et. al have shown that NPC gradients converge to backprop within a certain "regime".<p>The win with asynchronous techniques like NPC is that you do not need the extreme co-ordination that backprop requires and hence should be computationally much easier given the right device.<p>Although at this point the industry has so much money in the forward-backward pass system that I doubt a backprop successor would win unless someone makes NPC hardware feasible and can prove scaling up to billions of params
Also has the "advantage" of being slightly more biologically plausible as the optimization happens locally rather than globally.<p>That idea was taken further by N'dri et al in PCL, in which "activation energy" was minimized as well, and inhibitory neurons added
<a href="https://www.nature.com/articles/s41467-025-64234-z.pdf" rel="nofollow">https://www.nature.com/articles/s41467-025-64234-z.pdf</a><p>While trying to find the link for that I stumbled upon<p><a href="https://arxiv.org/pdf/2605.12732" rel="nofollow">https://arxiv.org/pdf/2605.12732</a><p>Which also looks pretty interesting
The reason why I don't see the promise for ML-only applications is that the coordination backprop requires comes very cheap to us.<p>"Much easier given the right device" - the "right" there just isn't shaped like the devices we actually build. And the price of "not having backprop" is usually expending more FLOPs, getting worse sample efficiency, etc.<p>The biggest "device" that doesn't do backprop is the brain, and that's because the brain doesn't have the connectivity or the coordination to pull it off. Both of those are "expensive" for something like it to implement. Cheap for us though. We aren't stuck with neurons that only get locally available information and have to implement learning rules based on that. So, skill issue?
I think Jeff Dean is right in that we will see much more specialised silicon in the future.<p>If something more bio inspired ie. predictive coding and in-memory compute fundamentally makes continual learning and much lower energy consumption possible there will be specialised hardware for it at some point<p>FWIW I think the brain has multiple “learning rules” and operates at multiple timescales
Knowing nothing about this, I wonder if it could be useful in situations where we can’t reliably sync with all the workers. Something like folding@home, where all the workers are just shaking weights and if one of them finds a winner it uploads to the central server?
Would these alternatives to backprop make it more feasible to have constant live-training going on in a model? Giving it something akin to neuro-plasticity?
Maybe the practical path is to separate fast-changing memory from slow-changing weights. Most things an agent learns during use probably don't need to become parameters immediately.
One aspect of how current training and continual learning are somewhat at odds is that the memory required to train a model is often times 2-3x the memory required to just run it (probably not as bad for PEFT, not sure).<p>DUST does have an advantage specifically along those lines because it doesn't have to save a ton of intermediate state other than each layer's input activations during a single forward pass.<p>There are many other issues that this algorithm does not address thoigh like catastrophic forgetting. it's still operating on a transformer which contains no inherent mechanism for selecting the relative value of a training step based on current knowledge, nor does it have segmentation of functionalities with specialized areas used for specific things that can be sequestered off and ignore new updates (we do not risk forgetting how to walk as we increase our French vocabulary)
Models suffer from "catastrophic forgetting" if you train them on new data.<p>People are working on this field, recent results suggest that continual learning can be possible by converting the input data to "LLMese"
At massive scales 0th order methods will parallelize better than backprop especially along depth, u can train very deep models pipeline parallel without bubbles
Bigger Dust models needing fewer population samples?
It's computationally expensive and infeasible but what's the upside?<p>Genuine question due to unfamiliarity with the subject.
Moving beyond traditional backpropagation for transformer pretraining opens up fascinating avenues for alternative learning dynamics and architectural efficiency.
Hmm I was more interested in this alternative to backprop:<p><a href="https://news.ycombinator.com/item?id=49701182">https://news.ycombinator.com/item?id=49701182</a>
This is super yawn-worthy. Instead of backprop for the exact gradient you can run forward passes a thousand times with perturbed weights and get a Monte Carlo estimate of the gradient. Not very clever. Extremely NOT useful.<p>But I guess the industry is littered with techniques for computing the same thing but vastly slower that some people find interesting. Homomorphic encryption. Zero knowledge proofs. Blockchain computing. Except in those cases there might be a legitimate reason to use it occasionally.
- stupid question from a neural network rookie<p>- isnt the whole point of back propoagation so that you dont guess weights by brute forcing them since that is computationally infeasible once you go beyond a dozen weights?<p>- if you dont use backpropogation, how exactly are the initial weights assigned them if they are not random values?
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Definitely more than meets the eye.
Remember kids, whoever is pitching space searching via complete enumeration just wants your wallet.
Dust's 243M model beating a 120x smaller one at most population sizes is the surprising part; bigger nets got more population-efficient, not less.