HeavyBall

Important

It's recommended to use heavyball.utils.set_torch() for faster training and less memory usage.

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 (2024-11-22, 0.21.0), the recommended stable optimizer is PrecondSchedulePaLMSOAP (see below). The recommended experimental optimizer is DelayedPSGDKron (tuning guide).

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 (turn it off to save memory via foreach=False)
• 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)
• Memory-efficient storage PSGD supports store_triu_as_line (default: True) and q_dtype to trade off memory usage for memory bandwidth; Other optimizers have storage_dtype, supporting lower-precision EMAs at no(?) performance drop via stochastic rounding

Getting started

pip install heavyball

import torch
import heavyball

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

# Create an optimizer
optimizer = heavyball.PrecondSchedulePaLMSOAP(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
AdamW	More efficient (speed, memory) AdamW	+ Faster than AdamW + Possibly more (numerically) stable
LaProp	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"
ADOPT	More efficient (speed, memory) ADOPT	+ Same cost as AdamW + Rigorous mathematical convergence proofs, even for challenging models (GANs) - Empirically underperforms LaProp - no bf16
SFAdamW	More efficient (speed, memory) ScheduleFree AdamW	+ Same cost as AdamW, but better eval perf + Full control over hyperparameters
PaLMSFAdamW	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
SOAP	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)
PaLMSOAP	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)
SFPaLMSOAP	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)
PrecondScheduleSFPaLMSOAP	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
PrecondSchedulePaLMSOAP	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
PrecondScheduleSOAP	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)

Memory

Second order optimizers make it difficult to estimate memory usage, as it depends on shapes and hyperparameters. To estimate your memory usage, you may use test/test_memory.py which attempts to ensure there are no regressions.
Furthermore, you can find real-world memory usage of a 300M parameters video diffusion model below:

PSGD

HeavyBall offers various configurations of PSGD:

• "PSGDKron" is the baseline, equivalent to kron_torch, but with lower compute and memory overhead.
• "PurePSGD" has no momentum, further reducing memory and compute
• "DelayedPSGD" implements SOAP/ADOPT-style off-by-one momentum, which has worse initial convergence but higher stability

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