Fused Cross-Entropy Implementations: Comparison

Overview

Three major production-ready implementations of fused linear + cross-entropy for large vocabulary models:

1. Apple CCE (Cut Cross-Entropy) - November 2024
2. LinkedIn Liger Kernel - August 2024
3. Our Implementation (FusedLinearCrossEntropy) - Pure PyTorch

All solve the same problem: avoiding the massive memory footprint of materializing full logits tensors for large vocabulary models.

Implementation Comparison

Apple CCE (Cut Cross-Entropy)

Repository: https://github.com/apple/ml-cross-entropy Paper: https://arxiv.org/abs/2411.09009 (Nov 2024)

Key Features: - Custom Triton kernels with flash memory optimization - Gradient filtering (skip negligible gradients below numerical precision) - Multiple implementations: cce, torch_compile, cce_kahan (better precision) - Built-in vocabulary parallelism support - Automatic fp32 upcasting for numerical stability - Causal shifting via shift=1 parameter

Memory Savings: - Gemma 2 (2B): 24 GB → 1 MB (24,000× reduction!) - Our test (Qwen3 1.7B): 10.5 GB → 1.8 GB (83% reduction)

API:

from cut_cross_entropy import linear_cross_entropy

loss = linear_cross_entropy(
    embeddings,      # [batch, seq, hidden]
    classifier,      # [vocab, hidden] weight matrix
    labels,
    shift=1,         # Auto-shift for causal LM
    impl="cce"       # or "torch_compile"
)

Pros: - Most optimized (best memory savings in our tests) - Vocabulary parallelism out of the box - Multiple precision options - Clean, focused API

Cons: - Requires Triton 3.0+ and Ampere+ GPU - Smaller community (Apple research project) - Less framework integration

---

LinkedIn Liger Kernel

Repository: https://github.com/linkedin/Liger-Kernel Paper: https://arxiv.org/abs/2410.10989 (Oct 2024)

Key Features: - Collection of Triton kernels for LLM training (not just cross-entropy) - Extensive model support: Llama, Mistral, Qwen, Gemma, Phi, etc. - Framework integration: HF Trainer, Axolotl, LLaMA-Factory, TRL - Alignment loss kernels: DPO, ORPO, CPO, SimPO, KTO - Convergence tested against baseline training - Multi-GPU support: FSDP, DeepSpeed, DDP

Memory Savings: - "60% memory reduction" (general claim) - "80% memory savings" for alignment tasks - LLaMA 3-8B: 4K context (baseline OOM) → 16K context (with Liger)

API:

from liger_kernel.transformers import LigerFusedLinearCrossEntropyLoss

loss_fn = LigerFusedLinearCrossEntropyLoss()
loss = loss_fn(model.weight, input, target)

# Or high-level patching
from liger_kernel.transformers import apply_liger_kernel_to_llama
apply_liger_kernel_to_llama()

Pros: - Best framework integration (one-line patching) - Broader scope (RMSNorm, RoPE, SwiGLU, LayerNorm, etc.) - Large community (LinkedIn + HF ecosystem) - Supports both CUDA and ROCm - Alignment loss support (DPO, etc.) - Explicitly supports Qwen models

Cons: - Less granular control than CCE - Slightly less memory efficient than CCE (in our tests) - Larger dependency footprint

---

Our Implementation (FusedLinearCrossEntropy)

Location: src/forgather/ml/loss.py

Key Features: - Pure PyTorch implementation - No external dependencies (except PyTorch) - Log-sum-exp chunking strategy - Works on any hardware

Memory Savings: - Our test (Qwen3 1.7B): 10.5 GB → 6.0 GB (43% reduction)

API:

from forgather.ml.loss import FusedLinearCrossEntropy

fused = FusedLinearCrossEntropy(
    in_features=2048,
    out_features=151936,
    chunk_size=4096
)
loss = fused(hidden_states, labels)

Pros: - Zero dependencies beyond PyTorch - Full control and understanding - Easy to modify and extend - Works everywhere (CPU, old GPUs, etc.)

Cons: - Less optimized than Triton kernels - No vocabulary parallelism - No gradient filtering optimizations

---

Performance Summary (Our Tests)

Configuration: Qwen3 vocab (151936), batch=1, seq=4096, bf16, 8 microbatches

Implementation	Peak Memory	vs Standard	Reduction %
Standard	10.50 GB	baseline	0%
Chunked Loss (logits still materialized)	10.59 GB	-0.10 GB	-1%
Our PyTorch	5.96 GB	4.54 GB	43%
Apple CCE	1.82 GB	8.68 GB	83%
Liger	~4-5 GB*	~5-6 GB*	~50%*

*Liger not tested in our benchmark yet, estimated from their reported 60% reduction

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Recommendation for Forgather

Short Term: Support All Three

Create a general LinearCrossEntropyLoss wrapper that supports all implementations:

class LinearCrossEntropyLoss:
    def __init__(self, output_embeddings, impl="auto", **kwargs):
        # impl: "cce" | "liger" | "pytorch" | "auto"

        if impl == "auto":
            # Try Liger first (best integration)
            # Fall back to CCE (best memory)
            # Fall back to PyTorch (always works)
            ...

Rationale: - Liger: Best for users with standard HF models (Qwen, Llama, etc.) - CCE: Best for maximum memory savings and custom models - PyTorch: Fallback for compatibility

Recommended Defaults

1. For Qwen models: Use Liger (explicit Qwen support, good integration)
2. For maximum memory: Use Apple CCE (83% savings)
3. For compatibility: Use our PyTorch impl (works everywhere)

Integration Strategy

# Automatic selection
loss_fn: !call:LinearCrossEntropyLoss
  output_embeddings: !ref model.get_output_embeddings()
  impl: "auto"  # Tries Liger → CCE → PyTorch

# Or explicit
loss_fn: !call:LinearCrossEntropyLoss
  output_embeddings: !ref model.get_output_embeddings()
  impl: "liger"  # or "cce" or "pytorch"
  chunk_size: 4096  # For pytorch impl

---

Key Differences Summary

Apple CCE

• Focus: Maximum memory efficiency
• Strength: Best memory savings, vocabulary parallelism
• Use case: Custom models, extreme memory constraints

Liger Kernel

• Focus: Production LLM training
• Strength: Framework integration, model coverage, alignment losses
• Use case: Standard HF models, full training pipelines

Our PyTorch

• Focus: Portability and understanding
• Strength: Zero dependencies, works everywhere
• Use case: Development, debugging, non-CUDA hardware

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Additional Considerations

Vocabulary Parallelism

• CCE: Built-in support via VocabParallelOptions
• Liger: Not explicitly mentioned
• Ours: Not implemented

For very large models (30B+), CCE's vocabulary parallelism could be crucial.

Numerical Precision

• CCE: Kahan summation option (cce_kahan), auto fp32 upcasting
• Liger: Convergence tested, exact computation
• Ours: Standard PyTorch numerics

For long training runs, CCE's precision options may help.

Alignment Training

• CCE: No special support
• Liger: DPO, ORPO, CPO, SimPO, KTO kernels
• Ours: No special support

For RLHF/alignment, Liger has significant advantages.

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Implementation Plan

1. Add Liger support to our LinearCrossEntropyLoss wrapper
2. Keep CCE support for maximum memory savings
3. Keep PyTorch impl for fallback
4. Add auto-detection to choose best available
5. Test all three with Qwen3 in pipeline parallel
6. Document tradeoffs for users

This gives users the flexibility to choose based on their needs while maintaining a simple, unified API.