5 ms·

Thermodynamic Natural Gradient Descent

200 points by jasondavies 2y ago

stefanpie 2y ago
I know they mainly present results on deep learning/neural network training and optimization, but I wonder how easy it would be to use the same optimization framework for other classes of hard or large optimization problems. I was also curious about this when I saw posts about Extropic (https://www.extropic.ai/ https://www.extropic.ai/) stuff for the first time. I tried looking into any public info on their website about APIs or software stack to see what's possible beyond NN stuff to model other optimization problems. It looks like that's not shared publicly yet. There are certainly many NP-hard and large combinatorial or analytical optimization problems still out there that are worth being able to tackle with new technology. Personally, I care about problems in EDA and semiconductor design. Adiabatic quantum computing was one technology with the promise of solving optimization problems (and quantum computing is still playing out with only small-scale solutions at the moment). Hoping that these new "thermodynamic computing" startups also might provide some cool technology to explore these problems with.
- kaelan123 2y ago
  Indeed, other solving other optimization problem is an interesting avenue. All I can say is stay tuned!
  - stefanpie 2y ago
    Hey thanks for the reply! I'm assuming your the first author on the paper; if so, the signup button on the Normal Computing website is not working at the moment (at least for me, even with ad blocker turned off).
G3rn0ti 2y ago
Sounds great until > requires an analog thermodynamic computer Wait. What? Perhaps a trained physicist can comment on that. Thanks.
- uoaei 2y ago
  I believe one example would be quantum annealers. Where "programming" involves setting the right initial conditions and allowing thermodynamics to bring you to an optimum via relaxation.
  - mikewarot 2y ago
    Dwave[1] does compute that way already. [1] https://www.dwavesys.com/ https://www.dwavesys.com/
    - kaelan123 2y ago
      One key difference is the system is entirely classical (not quantum) and noise-resilient (see the last appendix).
- CamperBob2 2y ago
  The paper describes it pretty well in appendix C. A matrix of integrators is constructed with a bunch of opamps, RC time constants (using digital potentiometers, presumably) and a multichannel ADC/DAC interface to the PC. Essentially a dedicated differential-equation solver. So it's a combination of old-school analog computation and modern GPU-based code. Takes longer in practice due to the overhead of interfacing with the hardware and waiting for the integrators to settle, but the authors are claiming that an optimized implementation could outperform a purely-digital solution, as I understand it, by accelerating convergence. The core idea being that conventional gradient descent is a linear operation at heart, while the gradients actually being traversed are curved surfaces that have to be approximated with multiple unnecessary steps if everything is done in the digital domain. The trouble, as everybody from Seymour Cray onward has learned the hard way, is that CMOS always wins in the end, simply because the financial power of an entire industry goes into optimizing it.
  - stefanpie 2y ago
    I didn't realize they included details about the hardware. Lie you said these just look like analog computers, compute in memory, analog arrays, which have also made a resurgence with deep leaning.
cs702 2y ago
Cool and interesting. The authors propose a hybrid digital-analog training loop that takes into account the curvature of the loss landscape (i.e., it uses second-order derivatives), and show with numerical simulations that if their method is implemented in a hybrid digital-analog physical system, each iteration in the training loop would incur computational cost that is linear in the number of parameters. I'm all for figuring out ways to let the Laws of Thermodynamics do the work of training AI models, if doing so enables us to overcome the scaling limitations and challenges of existing digital hardware and training methods.
thomasahle 2y ago
The main point of this is that natural gradient descent is a second-order method. The main GD update equation is: ∇̃L(θ) = F⁻¹∇L(θ) which requires solving a linear system. For this, you can use the methods from the author's previous paper [Thermodynamic Linear Algebra](https://arxiv.org/abs/2308.05660 https://arxiv.org/abs/2308.05660). Since it's hard to implement a full neural network on a thermodynamic computer, the paper suggests running one in parallel to a normal GPU. The GPU computes F and ∇L(θ), but offloads the linear system to the thermo computer, which runs in parallel to the digital system (Figure 1). It is important to note that the "Runtime vs Accuracy" plot in Figure 3 uses a "timing model" for the TNGD algorithm, since the computer necessary to run the algorithm still doesn't exist.
- 3abiton 2y ago
  It really gives nice way to think about gradient descent.
esafak 2y ago
Not having read the paper carefully, could someone tell me what the draw is? It looks like it is going to have the same asymptotic complexity as SGD in terms of sample size, per Table 1. Given that today's large, over-specified models have numerous, comparable extrema, is there even a need for this? I wouldn't get out of bed unless it were sublinear.
danbmil99 2y ago
Wasn't Geoffrey Hinton going on about this about a year ago?
gnarbarian 2y ago
this reminds me of simulated annealing which I learned about in an AI class about a decade ago. https://en.wikipedia.org/wiki/Simulated_annealing https://en.wikipedia.org/wiki/Simulated_annealing
rsp1984 2y ago
Leveraging thermodynamics to more efficiently compute second-order updates is certainly cool and worth exploring, however specifically in the context of deep learning I remain skeptical of its usefulness. We already have very efficient second-order methods running on classical hardware [1] but they are basically not being used at all in practice, as they are outperformed by ADAM and other 1st-order methods. This is because optimizing highly nonlinear loss functions, such as the ones in deep learning models, only really works with very low learning rates, regardless of whether a 1st or a 2nd order method is used. So, comparatively speaking, a 2nd order method might give you a slightly better parameter update per step but at a more-than-slightly-higher cost, so most of the time it's simply not worth doing. [1] https://andrew.gibiansky.com/blog/machine-learning/hessian-free-optimization/ https://andrew.gibiansky.com/blog/machine-learning/hessian-f...
- 6gvONxR4sf7o 2y ago
  Agreed that it's very cool, and also about how hard it is to make second order methods worthwhile. We're just using such huge datasets that sometimes it's hard to even get a decent estimate of the gradient for a minibatch. Getting a useful estimate of second order information over the dataset is even harder, especially when the whole point of using minibatches is computational feasibility.
  - kaelan123 2y ago
    Those are valid points! Hessian-free (HF) optimization is a really nice method, but as you say remains costly so people don't use it. The key idea in this paper is that if you are able to solve linear systems faster by using an analog device, the cost of a HF-like method is brought down, so the method can become competitive. About the noise, it is true that the second-order information will be noisier than the gradient for a given batch size (and a lot of results out there for HF optimization are with impractically large batch sizes). In the paper we use relatively small batch sizes (eg 32 for the fine-tuning example) and show that you can still get an advantage from second-order information. Of course it would be interesting to study in more detail how noisy 2nd order information can be, and on more datasets.
mirekrusin 2y ago
I don't get it, gradient descend computation is super frequent, state/input changes all the time, you'd have to reset heat landscape very frequently, what's the point? No way there is any potential speedup opportunity there, no? If anything you could probably do something with electromagnetic fields, their interference, possibly in 3d.
killerstorm 2y ago
What's our current best guess of how animal neurons learn?
- soloist11 2y ago
  [dead]
- canjobear 2y ago
  http://www.scholarpedia.org/article/Spike-timing_dependent_plasticity http://www.scholarpedia.org/article/Spike-timing_dependent_p...

200 points by jasondavies 2y ago

I know they mainly present results on deep learning/neural network training and optimization, but I wonder how easy it would be to use the same optimization framework for other classes of hard or large optimization problems. I was also curious about this when I saw posts about Extropic (https://www.extropic.ai/ https://www.extropic.ai/) stuff for the first time. I tried looking into any public info on their website about APIs or software stack to see what's possible beyond NN stuff to model other optimization problems. It looks like that's not shared publicly yet. There are certainly many NP-hard and large combinatorial or analytical optimization problems still out there that are worth being able to tackle with new technology. Personally, I care about problems in EDA and semiconductor design. Adiabatic quantum computing was one technology with the promise of solving optimization problems (and quantum computing is still playing out with only small-scale solutions at the moment). Hoping that these new "thermodynamic computing" startups also might provide some cool technology to explore these problems with.

kaelan123 2y ago
Indeed, other solving other optimization problem is an interesting avenue. All I can say is stay tuned!
- stefanpie 2y ago
  Hey thanks for the reply! I'm assuming your the first author on the paper; if so, the signup button on the Normal Computing website is not working at the moment (at least for me, even with ad blocker turned off).

G3rn0ti 2y ago

Sounds great until > requires an analog thermodynamic computer Wait. What? Perhaps a trained physicist can comment on that. Thanks.

uoaei 2y ago
I believe one example would be quantum annealers. Where "programming" involves setting the right initial conditions and allowing thermodynamics to bring you to an optimum via relaxation.
- mikewarot 2y ago
  Dwave[1] does compute that way already. [1] https://www.dwavesys.com/ https://www.dwavesys.com/
  - kaelan123 2y ago
    One key difference is the system is entirely classical (not quantum) and noise-resilient (see the last appendix).
CamperBob2 2y ago
The paper describes it pretty well in appendix C. A matrix of integrators is constructed with a bunch of opamps, RC time constants (using digital potentiometers, presumably) and a multichannel ADC/DAC interface to the PC. Essentially a dedicated differential-equation solver. So it's a combination of old-school analog computation and modern GPU-based code. Takes longer in practice due to the overhead of interfacing with the hardware and waiting for the integrators to settle, but the authors are claiming that an optimized implementation could outperform a purely-digital solution, as I understand it, by accelerating convergence. The core idea being that conventional gradient descent is a linear operation at heart, while the gradients actually being traversed are curved surfaces that have to be approximated with multiple unnecessary steps if everything is done in the digital domain. The trouble, as everybody from Seymour Cray onward has learned the hard way, is that CMOS always wins in the end, simply because the financial power of an entire industry goes into optimizing it.
- stefanpie 2y ago
  I didn't realize they included details about the hardware. Lie you said these just look like analog computers, compute in memory, analog arrays, which have also made a resurgence with deep leaning.

cs702 2y ago

Cool and interesting. The authors propose a hybrid digital-analog training loop that takes into account the curvature of the loss landscape (i.e., it uses second-order derivatives), and show with numerical simulations that if their method is implemented in a hybrid digital-analog physical system, each iteration in the training loop would incur computational cost that is linear in the number of parameters. I'm all for figuring out ways to let the Laws of Thermodynamics do the work of training AI models, if doing so enables us to overcome the scaling limitations and challenges of existing digital hardware and training methods.

thomasahle 2y ago

The main point of this is that natural gradient descent is a second-order method. The main GD update equation is: ∇̃L(θ) = F⁻¹∇L(θ) which requires solving a linear system. For this, you can use the methods from the author's previous paper [Thermodynamic Linear Algebra](https://arxiv.org/abs/2308.05660 https://arxiv.org/abs/2308.05660). Since it's hard to implement a full neural network on a thermodynamic computer, the paper suggests running one in parallel to a normal GPU. The GPU computes F and ∇L(θ), but offloads the linear system to the thermo computer, which runs in parallel to the digital system (Figure 1). It is important to note that the "Runtime vs Accuracy" plot in Figure 3 uses a "timing model" for the TNGD algorithm, since the computer necessary to run the algorithm still doesn't exist.

3abiton 2y ago
It really gives nice way to think about gradient descent.

esafak 2y ago

Not having read the paper carefully, could someone tell me what the draw is? It looks like it is going to have the same asymptotic complexity as SGD in terms of sample size, per Table 1. Given that today's large, over-specified models have numerous, comparable extrema, is there even a need for this? I wouldn't get out of bed unless it were sublinear.

danbmil99 2y ago

Wasn't Geoffrey Hinton going on about this about a year ago?

gnarbarian 2y ago

this reminds me of simulated annealing which I learned about in an AI class about a decade ago. https://en.wikipedia.org/wiki/Simulated_annealing https://en.wikipedia.org/wiki/Simulated_annealing

rsp1984 2y ago

Leveraging thermodynamics to more efficiently compute second-order updates is certainly cool and worth exploring, however specifically in the context of deep learning I remain skeptical of its usefulness. We already have very efficient second-order methods running on classical hardware [1] but they are basically not being used at all in practice, as they are outperformed by ADAM and other 1st-order methods. This is because optimizing highly nonlinear loss functions, such as the ones in deep learning models, only really works with very low learning rates, regardless of whether a 1st or a 2nd order method is used. So, comparatively speaking, a 2nd order method might give you a slightly better parameter update per step but at a more-than-slightly-higher cost, so most of the time it's simply not worth doing. [1] https://andrew.gibiansky.com/blog/machine-learning/hessian-free-optimization/ https://andrew.gibiansky.com/blog/machine-learning/hessian-f...

6gvONxR4sf7o 2y ago
Agreed that it's very cool, and also about how hard it is to make second order methods worthwhile. We're just using such huge datasets that sometimes it's hard to even get a decent estimate of the gradient for a minibatch. Getting a useful estimate of second order information over the dataset is even harder, especially when the whole point of using minibatches is computational feasibility.
- kaelan123 2y ago
  Those are valid points! Hessian-free (HF) optimization is a really nice method, but as you say remains costly so people don't use it. The key idea in this paper is that if you are able to solve linear systems faster by using an analog device, the cost of a HF-like method is brought down, so the method can become competitive. About the noise, it is true that the second-order information will be noisier than the gradient for a given batch size (and a lot of results out there for HF optimization are with impractically large batch sizes). In the paper we use relatively small batch sizes (eg 32 for the fine-tuning example) and show that you can still get an advantage from second-order information. Of course it would be interesting to study in more detail how noisy 2nd order information can be, and on more datasets.

mirekrusin 2y ago

I don't get it, gradient descend computation is super frequent, state/input changes all the time, you'd have to reset heat landscape very frequently, what's the point? No way there is any potential speedup opportunity there, no? If anything you could probably do something with electromagnetic fields, their interference, possibly in 3d.

killerstorm 2y ago

What's our current best guess of how animal neurons learn?

soloist11 2y ago
[dead]
canjobear 2y ago
http://www.scholarpedia.org/article/Spike-timing_dependent_plasticity http://www.scholarpedia.org/article/Spike-timing_dependent_p...