We need to talk about scaling LLMs. For some reason, the standard advice has become “just throw more VRAM at the problem,” and it is killing performance. Specifically, most developers hit a brick wall at the very last step of training: the Cross-Entropy Loss. You’ve likely seen the infamous “Out of Memory” (OOM) error right when you thought you were done. The culprit is the logit bottleneck, and the solution is using Fused Kernels.
The Logit Bottleneck Problem
When you train a model like Llama 3, you are dealing with a vocabulary of 128,256 tokens. To predict the next token, we project the hidden state into this massive space. For a modest batch size, the intermediate logit tensor can easily exceed 80GB of VRAM. Furthermore, writing billions of logits to VRAM only to read them back milliseconds later for loss calculation is a massive waste of data movement.
I have spent years optimizing WooCommerce checkouts and custom APIs, and the principle is the same: reduce the round trips. In the world of GPU programming, we do this by fusing operations into a single kernel. If you are interested in high-performance computing, you might also want to check out my guide on mastering FP8 performance.
Why Fused Kernels are the Answer
A Fused Kernels approach combines the linear projection and the cross-entropy calculation into a single GPU program. Consequently, we avoid materializing the full logit matrix in global memory. Instead of an O(V) memory bottleneck, we use tiling to perform calculations in small blocks that fit directly into the GPU’s registers. This is where Triton’s fused softmax logic becomes a lifesaver.
The Naive Approach (The Memory Killer)
# This is what PyTorch does by default
logits = input @ weight.T # Huge memory allocation here
loss = cross_entropy(logits, targets)The Fused Triton Approach
By writing a custom kernel, we calculate the target logit and the log-sum-exp (LSE) on the fly. We iterate over the hidden dimension and the vocabulary dimension in tiles. Specifically, we use the online softmax algorithm to maintain numerical stability without ever needing the full tensor. This refactor is what allows libraries like Unsloth to achieve such massive memory reductions.
@triton.jit
def bbioon_fused_linear_ce_kernel(X_ptr, W_ptr, Y_ptr, LSE_ptr, ...):
# Program ID handles one row (token) at a time
row_idx = tl.program_id(0)
# Tiled Dot Product for Target Logit
# We only load small blocks into registers
for v_idx in range(0, V, V_BLOCK):
w_tile = tl.load(W_ptr + col_offsets)
logits = tl.dot(x_tile, w_tile)
# Online Max and Sum updates happen here
# No massive O(V) matrix in VRAMWar Story: The Atomic Traffic Jam
I honestly thought I’d seen every way a kernel could fail. When I first implemented this, I relied heavily on tl.atomic_add for the backward pass gradients. However, on an A100, this created a massive “traffic jam.” Thousands of threads were trying to update the same weight gradient addresses simultaneously. The hardware serializes these updates, and suddenly your “optimized” kernel is slower than the native PyTorch version. Specifically, the lesson here is that Fused Kernels need smart grid strategies—like using dedicated kernels for weight gradients—to truly ship production-grade performance.
Look, if this Fused Kernels stuff is eating up your dev hours, let me handle it. I’ve been wrestling with WordPress and AI integrations since the early days, and I know where the bottlenecks hide.
Final Takeaway
Transitioning from standard PyTorch ops to custom Triton kernels isn’t just a “nice to have”—it’s a requirement for training large models on consumer hardware. Specifically, by slashing peak memory usage by 84%, you can increase your batch sizes and train faster. Furthermore, understanding the math behind the backward pass ensures your gradients remain precise. If you’re building agentic systems, take a look at the Liger-Kernel implementation for more inspiration. Stop guessing, start profiling, and ship better code.
