There is a lot of interesting research into predictive coding as an alternative means to solve the credit assignment problem that might be a more plausible model of what happens in the brain.
I really liked this paper that showed using a predictive coding learning rule leads to the exact same gradients as backprop in arbitrary networks:
This paper uses the "fixed prediction assumption" so I think has caused some confusion (i.e. it's not PC, but PC with a small bandaid). It's a great paper though just the title is misleading somewhat. But all of Beren Millidge's papers are quite good and he was so prolific in the space. Cool to have seen him on the Dwarkesh podcast recently as well.
Nice introduction to a simple but useful idea! The Lagrangian works like a time-smoothed optimizing direction state, but it can be placed on any wire, even at non-differentiable boundary! Can it be better than existing training methods for discrete components like argmax, MoE or VQ-VAE? Maybe networks can be composed by a lot of learnable discrete components, or even bits and gates finally.
- can it be used to relax timing order requirement in pipeline parallelism? Each node update lambda on communication, and optimize weights at other time.
- given that BP is using SGD, can batches and T share the same timeline in optimization, while keeping the descent direction?
You can do that with backprop too. Nothing says you can't inference on a set of weights at the same time as you produce an updated copy from them.
They say in the paper what it's about: mostly just scientific curiousity but such approaches might be useful for making DNNs more energy efficient via neuromorphic hardware in future.
For continual learning at the weight level there's the business model issue. The labs are already deep in the red, the last thing they want is to give up shared weights. The I/O and storage costs of that would make it infeasible. Already KV caches are a sort of dynamic 'fast weights' and those are expensive!
Nothing prevents interleaving inference and gradient descent / RMAD / backpropagation from being interleaved.
Is a man a father or a son? It's a false dilemma, it can be both.
Is a training step pretraining or finetuning? It's the same mathematical operation, with the only difference the intention or reason of applying the training step.
Maybe it has some interesting properties that could prevent catastrophic forgetting, but so far it looks like a biologically plausible approximation of backpropagation and it might be useful to decrease the training compute requirements.
I wonder if you could take a traditional backprop trained LLM and apply this approach to finetuning it (presumably needs less memory and compute?). It could be another entry in the spectrum between LORA and full fine tuning.
Oh wow the theoretical implications in neuroscience exite me here - is this a potential model of Fristons Markov Blanket concept
“ Probably the most ambitious and all-encompassing version of the ‘Bayesian turn’ in cognitive science is
the free energy principle (FEP). The FEP is a mathematical framework, developed by Karl Friston and
colleagues (Friston, Kilner, and Harrison 2006; Friston et al. 2010; Friston 2010; Friston et al. 2017a;
Friston 2019), which specifies an objective function that any self-organizing system needs to minimize in
order to ensure adaptive exchanges with its environment. One major appeal of the FEP is that it aims for
(and seems to deliver) an unprecedented integration of the life sciences (including psychology,
neuroscience, and theoretical biology). The difference between the FEP and earlier inferential theories
(e.g., Gregory 1980, Grossberg 1980, Rao and Ballard 1999, Lee and Mumford 2003) is that not only
perceptual processes, but also other cognitive functions such as learning, attention, and action planning
can be subsumed under one single principle: the minimization of free energy through the process of active
inference (Friston 2010; Friston et al. 2017). ”
Isn't the FEP basically just loss minimization over KL-divergence? In other words, it's the same thing we already do with ML and already have been doing for years? I've never understood where this differs to the status quo, or why this isn't just a relabelling of techniques/concepts. Although I didn't look too deeply.
It might be beneficial while not being optimal on its own.
The obvious example is if it has different behaviour around local minima, it could be an altenate pathway out.
I have often wondered if doing training with radically different aproaches for the first few iterarions would avoid any method specific artifacts before the weights had time to denoise.
There is a lot of interesting research into predictive coding as an alternative means to solve the credit assignment problem that might be a more plausible model of what happens in the brain.
I really liked this paper that showed using a predictive coding learning rule leads to the exact same gradients as backprop in arbitrary networks:
Predictive Coding Approximates Backprop Along Arbitrary Computation Graphs https://direct.mit.edu/neco/article/34/6/1329/110646/Predict...
This paper uses the "fixed prediction assumption" so I think has caused some confusion (i.e. it's not PC, but PC with a small bandaid). It's a great paper though just the title is misleading somewhat. But all of Beren Millidge's papers are quite good and he was so prolific in the space. Cool to have seen him on the Dwarkesh podcast recently as well.
Nice introduction to a simple but useful idea! The Lagrangian works like a time-smoothed optimizing direction state, but it can be placed on any wire, even at non-differentiable boundary! Can it be better than existing training methods for discrete components like argmax, MoE or VQ-VAE? Maybe networks can be composed by a lot of learnable discrete components, or even bits and gates finally.
other questions:
- can it be used to relax timing order requirement in pipeline parallelism? Each node update lambda on communication, and optimize weights at other time. - given that BP is using SGD, can batches and T share the same timeline in optimization, while keeping the descent direction?
Could this relate to continual learning? It lets you update without pausing the entire system.
You can do that with backprop too. Nothing says you can't inference on a set of weights at the same time as you produce an updated copy from them.
They say in the paper what it's about: mostly just scientific curiousity but such approaches might be useful for making DNNs more energy efficient via neuromorphic hardware in future.
For continual learning at the weight level there's the business model issue. The labs are already deep in the red, the last thing they want is to give up shared weights. The I/O and storage costs of that would make it infeasible. Already KV caches are a sort of dynamic 'fast weights' and those are expensive!
Nothing prevents interleaving inference and gradient descent / RMAD / backpropagation from being interleaved.
Is a man a father or a son? It's a false dilemma, it can be both.
Is a training step pretraining or finetuning? It's the same mathematical operation, with the only difference the intention or reason of applying the training step.
Maybe it has some interesting properties that could prevent catastrophic forgetting, but so far it looks like a biologically plausible approximation of backpropagation and it might be useful to decrease the training compute requirements.
I wonder if you could take a traditional backprop trained LLM and apply this approach to finetuning it (presumably needs less memory and compute?). It could be another entry in the spectrum between LORA and full fine tuning.
Oh wow the theoretical implications in neuroscience exite me here - is this a potential model of Fristons Markov Blanket concept
“ Probably the most ambitious and all-encompassing version of the ‘Bayesian turn’ in cognitive science is the free energy principle (FEP). The FEP is a mathematical framework, developed by Karl Friston and colleagues (Friston, Kilner, and Harrison 2006; Friston et al. 2010; Friston 2010; Friston et al. 2017a; Friston 2019), which specifies an objective function that any self-organizing system needs to minimize in order to ensure adaptive exchanges with its environment. One major appeal of the FEP is that it aims for (and seems to deliver) an unprecedented integration of the life sciences (including psychology, neuroscience, and theoretical biology). The difference between the FEP and earlier inferential theories (e.g., Gregory 1980, Grossberg 1980, Rao and Ballard 1999, Lee and Mumford 2003) is that not only perceptual processes, but also other cognitive functions such as learning, attention, and action planning can be subsumed under one single principle: the minimization of free energy through the process of active inference (Friston 2010; Friston et al. 2017). ”
Isn't the FEP basically just loss minimization over KL-divergence? In other words, it's the same thing we already do with ML and already have been doing for years? I've never understood where this differs to the status quo, or why this isn't just a relabelling of techniques/concepts. Although I didn't look too deeply.
New paper by Sakana.ai [1]
[1]: https://arxiv.org/abs/2605.31022
~85% accuracy on MNIST. Sigh.
How does it do on CIFAR-10, or even better, ImageNet?
Interesting research, not sure it's a backprop alternative.
===
EDIT: accuracy on MNIST is not ~90%. It's ~85%.
It might be beneficial while not being optimal on its own.
The obvious example is if it has different behaviour around local minima, it could be an altenate pathway out.
I have often wondered if doing training with radically different aproaches for the first few iterarions would avoid any method specific artifacts before the weights had time to denoise.
They state replacing backprop is not their goal.
Their goal is to understand how distributed systems which cannot do backprop (the brain) can still do learning.
Their image classification benchmarks include both: https://pub.sakana.ai/pc-alm/assets/figures/benchmark_accura...
It's really sad that they are only a few years away from making backpropagation completely obsolete.
Rolls right off the tongue