AI 与机器学习2024arxiv.org
热力学自然梯度下降
Thermodynamic Natural Gradient Descent
进阶 · 约 60 分钟读完前置知识：自然梯度与 Fisher 信息矩阵、二阶优化方法、热力学计算基础
导读
这篇论文提出用模拟热力学计算机来实现自然梯度下降（一种二阶优化方法）：由于自然梯度更新需要求解 F⁻¹∇L 这样的线性系统，作者借助其此前关于热力学线性代数的思路，让 GPU 计算 Fisher 矩阵 F 和梯度，而把线性系统求解卸载到一台并行的热力学计算机。结论上，论文展示了深度学习训练的初步结果，但所需的模拟热力学硬件目前尚不存在，性能对比基于时序模型估算。
HN 关注点：HN 读者既被“热力学计算加速二阶优化”的新颖思路吸引，也质疑其依赖尚不存在的模拟硬件、以及二阶方法在深度学习中是否真有用。
HN 评论精选
这几条评论里：质疑 2 补充 2
补充详解核心思路：GPU 负责算 F 与梯度，线性求解卸载到并行热力学计算机，但性能图基于时序模型而非真实硬件。
这篇论文的核心在于自然梯度下降是二阶方法，其更新为 ∇̃L(θ) = F⁻¹∇L(θ)，需要解一个线性系统，可用作者上一篇论文 arXiv 2308.05660 里的方法。由于在热力学计算机上实现完整神经网络很难，该论文建议让它与普通 GPU 并行运行：GPU 计算 F 和 ∇L(θ)，把线性系统求解卸载给热力学计算机，两者并行（图1）。要注意，图3的“运行时间 vs 精度”图采用的是 TNGD 算法的“时序模型”，因为运行该算法所需的计算机尚不存在。
thomasahle查看英文原文
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). 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.
质疑质疑二阶方法在深度学习中的实用性：实践中被 ADAM 等一阶方法胜出，成本收益不划算。
利用热力学更高效地计算二阶更新确实很酷、值得探索，但具体到深度学习，我仍怀疑其实用性。我们已有在经典硬件上高效运行二阶方法[1]，但它们在实践中几乎没人用，因为会被 ADAM 等一阶方法比下去。原因是优化高度非线性的损失函数（如深度学习模型）只有在很低学习率下才真正有效，无论一阶还是二阶。所以相对而言，二阶方法每步或许给出略好的参数更新，但代价高得多，多数时候根本不值得。[1] Hessian-free optimization 链接
rsp1984查看英文原文
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/
补充好奇该框架能否推广到 EDA/半导体设计等组合优化问题，并提及 Extropic 与绝热量子计算。
我知道论文主要展示的是深度学习/神经网络训练与优化方面的结果，但我好奇同一优化框架能否轻易用于其他类型的困难或大规模优化问题。第一次看到 Extropic（extropic.ai）相关帖子时我也想到这点。我去他们官网找 API 或软件栈的公开信息，看能否对 NN 以外的问题建模，似乎还没公开。外面肯定还有很多值得用新技术攻克的 NP-hard 和大规模组合/解析优化问题。我个人关心 EDA 和半导体设计中的问题。绝热量子计算曾是承诺解决优化问题的技术（量子计算目前仍只有小规模解）。希望这些新的“热力学计算”创业公司也能提供些酷技术来探索这些问题。
stefanpie查看英文原文
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/) 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.
质疑对方案必须依赖尚不存在的模拟热力学计算机感到困惑与惊讶。
听起来很棒，直到看到“需要一个模拟热力学计算机”。等等，什么？或许受过训练的物理学家能评论一下。谢谢。
G3rn0ti查看英文原文
Sounds great until > requires an analog thermodynamic computer Wait. What? Perhaps a trained physicist can comment on that. Thanks.
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