heavyball 0.12.1

Efficient optimizers

HeavyBall

[!IMPORTANT]
The SOAP implementation was broken until 0.9.0. Please upgrade to 0.9.0 or later.

A simple package of efficient optimizers

The goal is not to thrive for completeness, full maintenance or abstraction, but instead to provide a simple largely static alternative to torch.optim with more and better optimizers.

Currently (2024-11-12, 0.11.0), the recommended optimizer is PrecondSchedulePaLMForeachSOAP.

Features

• Stochastic Rounding: FP32 convergence with BF16 parameters
• Inplace EMA: Same math, but less memory, less compute and higher stability
• Foreach: Fast multi-tensor application
• PaLM Beta2: Fast initial convergence, stable late convergence
• ScheduleFree: No learning rate schedule, but better convergence
• Preconditioner Schedule: Improved loss-per-step in early convergence, better step-per-second in late convergence (explained below)

Getting started

pip install heavyball

import torch
import heavyball

# Create a model
model = torch.nn.Linear(16, 1)

# Create an optimizer
optimizer = heavyball.PrecondSchedulePaLMForeachSOAP(model.parameters(), lr=1e-3)

x = torch.randn(128, 16)
y = torch.randn(128, 1)

for _ in range(1000):
    optimizer.zero_grad()
    loss = torch.nn.functional.mse_loss(model(x), y)
    loss.backward()
    optimizer.step()

Optimizers

Name	Description	Advantages / Disadvantages
ForeachAdamW	More efficient (speed, memory) AdamW	+ Faster than AdamW + Possibly more (numerically) stable
ForeachLaProp	More efficient (speed, memory) LaProp	+ Same cost as AdamW + Marginally better converence (better proofs) + Higher hyperparameter stability - Not a guaranteed win (can be neutral) - No "Slingshot"
ForeachADOPT	More efficient (speed, memory) ADOPT	+ Same cost as AdamW + Rigorous mathematical convergence proofs, even for challenging models (GANs) - Empirically underperforms LaProp - no bf16
ForeachSFAdamW	More efficient (speed, memory) ScheduleFree AdamW	+ Same cost as AdamW, but better eval perf + Full control over hyperparameters
PaLMForeachSFAdamW	ForeachSFAdamW with PaLM's beta2 schedule	+ Same cost as AdamW, but better eval perf + Less control, but faster early and more stable late convergence + ScheduleFree - slow early convergence
ForeachSOAP	More efficient (speed, memory) SOAP	+ Faster convergence (loss-at-step) + Full control over hyperparameters - more memory usage - more hyperparameters - higher overhead than AdamW (can be ammortized; better loss-at-second)
PaLMForeachSOAP	ForeachSOAP with PaLM's beta2 schedule	+ Faster convergence (loss-at-step) + Less control, but faster early and more stable late convergence - more memory usage - more hyperparameters - higher overhead than AdamW (can be ammortized; better loss-at-second)
SFPaLMForeachSOAP	ScheduleFree PaLMForeachSOAP	+ Fast convergence (loss-at-step) + less memory usage than PaLMForeachSOAP (more tham AdamW) - slower initial convergence than PaLMForeachSOAP (but allows higher LRs) - higher overhead than AdamW (can be ammortized)
PrecondScheduleSFPaLMForeachSOAP	SFPaLMForeachSOAP with preconditioner schedule, matching the error of PrecondEvery=2 with the cost of PrecondEvery=512	+ Better initial convergence than SFPaLMForeachSOAP + Significantly faster (sec/it) later + less memory usage than PaLMForeachSOAP (more tham AdamW) - slower initial convergence than PaLMForeachSOAP (but allows higher LRs) - higher overhead than AdamW (can be ammortized), goes to 0 with increasing number of step
PrecondSchedulePaLMForeachSOAP	PrecondScheduleSFPaLMForeachSOAP without schedule-free	+ Best initial convergence + Significantly faster (sec/it) later + high stability - more memory usage than PrecondScheduleSFPaLMForeachSOAP - higher overhead than AdamW (can be ammortized), goes to 0 with increasing number of steps
PrecondScheduleForeachSOAP	PrecondScheduleSFPaLMForeachSOAP without PaLM's beta2 schedule	+ Better initial convergence + Significantly faster (sec/it) later - more memory usage than PrecondScheduleSFPaLMForeachSOAP - higher overhead than AdamW (can be ammortized), goes to 0 with increasing number of steps

Precond Schedule

The default preconditioner schedule (f) would yield the following update intervals:

Steps	Interval, f	Total (schedule)	Total (constant, every 2)	Total (constant, every 16)
10	1.00005	10	5 (0.5x)	0 (0.0x)
100	1.026	99	50 (0.5x)	6 (0.1x)
1,000	2.0	738	500 (0.7x)	62 (0.1x)
10,000	14.3	2,168	5,000 (2.3x)	625 (0.3x)
100,000	100.2	4,049	50,000 (12.3x)	6,250 (1.5x)
1,000,000	513	7,245	500,000 (69.0x)	62,500 (8.6x)

Utils

To access heavyball.utils, you need to explicitly import heavyball.utils.
It has several handy functions:

• set_torch() sets pytorch optimization settings (TF32, opt_einsum, benchmark, ...)
• compile_mode, a string passed as-is to torch.compile(mode=compile_mode) in all compiled heavyball calls
• zeroth_power_mode, a string determining whether to use QR, newtonschulz{iterations}, or svd or eigh to approximate the eigenvectors. Eigh has the highest precision and cost