<p>Design and optimize <strong>high-performance Triton kernels</strong> for <strong>GDPA (Gated Dot-Product Attention)</strong> computation on GPU. This problem focuses on implementing efficient attention kernels with gated Q and K tensors using Triton's JIT compilation system.</p>
<h3>The Challenge</h3>
<p>You must optimize several critical aspects:</p>
<ul>
<li><strong>Gated attention computation</strong>: Efficient computation of scaled dot-product attention with gated Q and K tensors</li>
<li><strong>Gating mechanism</strong>: Applying sigmoid gates to Q and K tensors before attention computation</li>
<li><strong>Memory access patterns</strong>: Efficient loading and storing of Q, K, V, GQ, GK tensors</li>
<li><strong>Numerical stability</strong>: Handling softmax operations with proper numerical stability using streaming softmax</li>
<li><strong>Block tiling</strong>: Optimal block sizes for GPU execution across different sequence lengths</li>
<li><strong>Performance benchmarking</strong>: Achieving speedup over baseline PyTorch implementations</li>
</ul>
<h2>Optimization Targets</h2>
<p>1. <strong>Primary</strong>: Maximize geometric mean speedup over baseline (higher is better)
2. <strong>Secondary</strong>: Ensure correctness across diverse sequence lengths and attention heads
3. <strong>Tertiary</strong>: Minimize kernel launch overhead and memory usage</p>
<h2>API Specification</h2>
<p>Implement a <code>Solution</code> class that returns a Triton kernel implementation:</p>
<pre><code class="language-python">class Solution:
def solve(self, spec_path: str = None) -> dict:
"""
Returns a dict with either:
- {"code": "python_code_string"}
- {"program_path": "path/to/kernel.py"}
"""
# Your implementation
pass</code></pre>
<p>Your kernel implementation must provide a <code>gdpa_attn</code> function:</p>
<pre><code class="language-python">import torch
import triton
import triton.language as tl
<p>def gdpa_attn(
Q: torch.Tensor,
K: torch.Tensor,
V: torch.Tensor,
GQ: torch.Tensor,
GK: torch.Tensor
) -> torch.Tensor:
"""
GDPA attention computation with gated Q and K tensors.</p>
<p>Args:
Q: Query tensor of shape (Z, H, M, Dq) - float16
K: Key tensor of shape (Z, H, N, Dq) - float16
V: Value tensor of shape (Z, H, N, Dv) - float16
GQ: Query gate tensor of shape (Z, H, M, Dq) - float16
GK: Key gate tensor of shape (Z, H, N, Dq) - float16</p>
Returns:
Output tensor of shape (Z, H, M, Dv) - float16
"""
# Your implementation
pass</code></pre>
<h2>Input Specifications</h2>
<h3>Tensor Shapes</h3>
<table>
<thead>
<tr>
<th>Tensor</th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><strong>Q</strong></td>
<td><code>(Z, H, M, Dq)</code></td>
<td>Query tensor</td>
</tr>
<tr>
<td><strong>K</strong></td>
<td><code>(Z, H, N, Dq)</code></td>
<td>Key tensor</td>
</tr>
<tr>
<td><strong>V</strong></td>
<td><code>(Z, H, N, Dv)</code></td>
<td>Value tensor</td>
</tr>
<tr>
<td><strong>GQ</strong></td>
<td><code>(Z, H, M, Dq)</code></td>
<td>Query gate tensor</td>
</tr>
<tr>
<td><strong>GK</strong></td>
<td><code>(Z, H, N, Dq)</code></td>
<td>Key gate tensor</td>
</tr>
</tbody>
</table>
<h3>Dimension Details</h3>
<ul>
<li><strong>Z</strong>: Batch size (typically 1)</li>
<li><strong>H</strong>: Number of attention heads (typically 8)</li>
<li><strong>M</strong>: Query sequence length (tested with 512, 1024)</li>
<li><strong>N</strong>: Key/value sequence length (equals M for GDPA attention)</li>
<li><strong>Dq</strong>: Query/key feature dimension (typically 64)</li>
<li><strong>Dv</strong>: Value feature dimension (typically 64)</li>
</ul>
<h3>Data Type</h3>
<ul>
<li>All inputs are <strong><code>torch.float16</code></strong></li>
<li>All inputs are on <strong>CUDA device</strong></li>
</ul>
<h2>Output Specifications</h2>
<ul>
<li><strong>Shape</strong>: <code>(Z, H, M, Dv)</code> - matches query batch/head dimensions</li>
<li><strong>Dtype</strong>: <code>torch.float16</code></li>
<li><strong>Device</strong>: Same as input (CUDA)</li>
</ul>
<h2>GDPA Algorithm</h2>
<p>The Gated Dot-Product Attention algorithm consists of:</p>
<h3>Step 1: Apply Gating</h3>
<pre><code class="language-python">Qg = Q * sigmoid(GQ)
Kg = K * sigmoid(GK)</code></pre>
<h3>Step 2: Scaled Dot-Product Attention</h3>
<pre><code class="language-python">scale = 1.0 / sqrt(Dq)
scores = (Qg @ Kg.transpose(-2, -1)) * scale
attn_weights = softmax(scores, dim=-1)
output = attn_weights @ V</code></pre>
<h2>Correctness Requirements</h2>
<ul>
<li><strong>Numerical correctness</strong> verified against PyTorch baseline implementation</li>
<li><strong>Relative tolerance</strong>: 1e-2</li>
<li><strong>Absolute tolerance</strong>: 5e-3</li>
<li><strong>All test cases must pass</strong> for any score above 0</li>
<li>Gating must be correctly applied before attention computation</li>
</ul>
<h2>Scoring (0-100)</h2>
<p>Performance is measured against <strong>GPU baseline implementations</strong>:</p>
<pre><code class="language-python">geometric_mean_gpu_time = geometric_mean(gpu_baseline_times)
geometric_mean_answer_time = geometric_mean(answer_times)
<h1>Linear interpolation</h1>
target_time_0 = geometric_mean_gpu_time # 0 points (1x GPU baseline)
target_time_100 = geometric_mean_gpu_time / 3.0 # 100 points (3x speedup)
score = 100 * (target_time_0 - geometric_mean_answer_time) / (target_time_0 - target_time_100)</code></pre>
<h3>Score Interpretation</h3>
<table>
<thead>
<tr>
<th>Performance</th>
<th>Score</th>
<th>Speedup vs GPU Baseline</th>
</tr>
</thead>
<tbody>
<tr>
<td>Baseline performance</td>
<td>0 points</td>
<td>1.0x</td>
</tr>
<tr>
<td>2x speedup</td>
<td>50 points</td>
<td>2.0x</td>
</tr>
<tr>
<td>3x speedup</td>
<td>100 points</td>
<td>3.0x</td>
</tr>
<tr>
<td>4x speedup (exceptional)</td>
<td>>100 points</td>
<td>>3.0x</td>
</tr>
</tbody>
</table>
<strong>Note:</strong> Score is linearly interpolated between 1x (0 points) and 3x (100 points) GPU baseline.
<h2>Evaluation Details</h2>
<h3>Test Configuration</h3>
<ul>
<li><strong>Test cases</strong>: M = 512, 1024 (with N = M)</li>
<li><strong>Warmup phase</strong>: 10 iterations to stabilize GPU clocks and caches</li>
<li><strong>Random seed</strong>: Fixed seed (0) for reproducible data generation</li>
<li><strong>Strict correctness</strong>: Any test failure results in score of 0</li>
</ul>
<h3>Timing Methodology</h3>
<p>1. Generate input tensors on GPU
2. Warm up with 10 iterations
3. Measure time for actual computation
4. Verify correctness against reference
5. Compute geometric mean across test cases</p>
<h2>Implementation Tips</h2>
<h3>Performance Optimization</h3>
<p>1. <strong>Use Triton's block pointers</strong> (<code>tl.make_block_ptr</code>) for efficient memory access
2. <strong>Implement streaming softmax</strong> for numerical stability and memory efficiency
3. <strong>Tune block sizes</strong> (e.g., BLOCK_M, BLOCK_N, BLOCK_K) for different sequence lengths
4. <strong>Minimize memory transactions</strong> through proper tiling strategies
5. <strong>Leverage warp-level primitives</strong> for maximum parallelism</p>
<h3>Numerical Stability</h3>
<ul>
<li>Use <strong>online softmax</strong> algorithm to avoid overflow</li>
<li>Compute max and sum in a streaming fashion</li>
<li>Scale appropriately: <code>scale = 1.0 / sqrt(Dq)</code></li>
</ul>
<h3>Memory Considerations</h3>
<ul>
<li><strong>Register usage</strong>: Balance between parallelism and register spilling</li>
<li><strong>Shared memory</strong>: Use efficiently for tiling</li>
<li><strong>Global memory coalescing</strong>: Ensure contiguous access patterns</li>
</ul>
<h2>Example Kernel Structure</h2>
<pre><code class="language-python">@triton.jit
def gdpa_attention_kernel(
Q, K, V, GQ, GK, Out,
stride_qz, stride_qh, stride_qm, stride_qd,
# ... other strides
M, N, Dq, Dv, H,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_Dq: tl.constexpr,
BLOCK_Dv: tl.constexpr,
):
# Compute block indices
# Load Q, K, V, GQ, GK blocks
# Apply gating: Qg = Q * sigmoid(GQ), Kg = K * sigmoid(GK)
# Compute attention: scores = Qg @ Kg.T * scale
# Apply softmax and matmul with V
# Store output
pass</code></pre>
<h2>Resources</h2>
<ul>
<li><strong>Triton Documentation</strong>: [https://triton-lang.org](https://triton-lang.org)</li>
<li><strong>Flash Attention Paper</strong>: Understanding efficient attention mechanisms</li>
<li><strong>GPU Performance Primer</strong>: CUDA programming best practices</li>
</ul>
<h2>Common Pitfalls</h2>
<p>1. �?Not using streaming softmax �?numerical instability
2. �?Poor block size choices �?low occupancy
3. �?Inefficient memory access patterns �?memory bottleneck
4. �?Ignoring warmup �?inconsistent timing results
5. �?Incorrect gating implementation �?wrong results</p>
<h2>Success Criteria</h2>
<p>�?All correctness tests pass
�?Achieve at least 1.5x speedup over baseline (>50 points)
�?Kernel works for both M=512 and M=1024
�?Numerical stability across all test cases</p>
<hr>
<h2>Problem Metadata</h2>
<strong>Domain:</strong> High-Performance Computing (HPC) / GPU Programming
<strong>Framework:</strong> Triton JIT Compilation
<strong>Hardware:</strong> NVIDIA GPU with CUDA support
<hr>
<h2>Model Information</h2>
<p><strong>Model:</strong> Grok 4</p>
<p><strong>Score:</strong> 95.3</p>
<h3>Solution Code</h3>
<pre><code>import torch
import triton
import triton.language as tl
@triton.jit
def gdpa_attn_kernel(
Q_ptr, K_ptr, V_ptr, GQ_ptr, GK_ptr, Out_ptr,
Z, H, M, N, Dq, Dv,
stride_Q_z, stride_Q_h, stride_Q_m, stride_Q_d,
stride_K_z, stride_K_h, stride_K_n, stride_K_d,
stride_V_z, stride_V_h, stride_V_n, stride_V_d,
stride_GQ_z, stride_GQ_h, stride_GQ_m, stride_GQ_d,
stride_GK_z, stride_GK_h, stride_GK_n, stride_GK_d,
stride_Out_z, stride_Out_h, stride_Out_m, stride_Out_d,
BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_D: tl.constexpr,
):
pid_z = tl.program_id(0)
pid_h = tl.program_id(1)
pid_m = tl.program_id(2)
z = pid_z
h = pid_h
m_start = pid_m * BLOCK_M
m_offsets = m_start + tl.arange(0, BLOCK_M)
m_mask = m_offsets < M
# Load Q and GQ
d_offsets = tl.arange(0, BLOCK_D)
Q_ptrs = Q_ptr + z * stride_Q_z + h * stride_Q_h + m_offsets[:, None] * stride_Q_m + d_offsets[None, :] * stride_Q_d
Q_mask = m_mask[:, None] & (d_offsets[None, :] < Dq)
Q = tl.load(Q_ptrs, mask=Q_mask, other=0.0)
GQ_ptrs = GQ_ptr + z * stride_GQ_z + h * stride_GQ_h + m_offsets[:, None] * stride_GQ_m + d_offsets[None, :] * stride_GQ_d
GQ = tl.load(GQ_ptrs, mask=Q_mask, other=0.0)
GQ_sig = 1.0 / (1.0 + tl.exp(-GQ.to(tl.float32)))
Qg = Q * GQ_sig.to(Q.dtype)
# Initialize accumulators
l = tl.full((BLOCK_M,), -float('inf'), dtype=tl.float32)
acc = tl.zeros((BLOCK_M, BLOCK_D), dtype=tl.float32)
denom = tl.zeros((BLOCK_M,), dtype=tl.float32)
denom = tl.zeros((BLOCK_M,), dtype=tl.float32)
scale = tl.rsqrt(tl.full((), Dq, dtype=tl.float32))
for n_start in tl.range(0, N, BLOCK_N):
n_offsets = n_start + tl.arange(0, BLOCK_N)
n_mask = n_offsets < N
# Load K and GK
K_ptrs = K_ptr + z * stride_K_z + h * stride_K_h + n_offsets[:, None] * stride_K_n + d_offsets[None, :] * stride_K_d
K_mask = n_mask[:, None] & (d_offsets[None, :] < Dq)
K = tl.load(K_ptrs, mask=K_mask, other=0.0)
GK_ptrs = GK_ptr + z * stride_GK_z + h * stride_GK_h + n_offsets[:, None] * stride_GK_n + d_offsets[None, :] * stride_GK_d
GK = tl.load(GK_ptrs, mask=K_mask, other=0.0)
GK_sig = 1.0 / (1.0 + tl.exp(-GK.to(tl.float32)))
Kg = K * GK_sig.to(K.dtype)
# Compute attention scores
attn = tl.dot(Qg, tl.trans(Kg), out_dtype=tl.float32) * scale
# Load V
V_ptrs = V_ptr + z * stride_V_z + h * stride_V_h + n_offsets[:, None] * stride_V_n + d_offsets[None, :] * stride_V_d
V_mask = n_mask[:, None] & (d_offsets[None, :] < Dv)
V = tl.load(V_ptrs, mask=V_mask, other=0.0)
V_fp32 = V.to(tl.float32)
# Streaming softmax update
attn_max = tl.max(attn, axis=1)
new_m = tl.maximum(l, attn_max)
exp_attn = tl.exp(attn - new_m[:, None])
alpha = tl.exp(l - new_m)
acc = acc * alpha[:, None] + tl.dot(exp_attn, V_fp32, out_dtype=tl.float32)
denom = denom * alpha + tl.sum(exp_attn, axis=1)
l = new_m
# Store output
denom = tl.maximum(denom, 1e-9)
acc = acc / denom[:, None]
Out_ptrs = Out_ptr + z * stride_Out_z + h * stride_Out_h + m_offsets[:, None] * stride_Out_m + d_offsets[None, :] * stride_Out_d
Out_mask = m_mask[:, None] & (d_offsets[None, :] < Dv)
tl.store(Out_ptrs, acc.to(tl.float16), mask=Out_mask)
def gdpa_attn(Q: torch.Tensor, K: torch.Tensor, V: torch.Tensor, GQ: torch.Tensor, GK: torch.Tensor) -> torch.Tensor:
Z, H, M, Dq = Q.shape
N = K.shape[2]
Dv = V.shape[3]
assert K.shape == (Z, H, N, Dq)
assert V.shape == (Z, H, N, Dv)
assert GQ.shape == (Z, H, M, Dq)
assert GK.shape == (Z, H, N, Dq)
Out = torch.empty_like(V[:, :, :M, :]) # (Z, H, M, Dv)
# Strides
stride_Q = Q.stride()
stride_K = K.stride()
stride_V = V.stride()
stride_GQ = GQ.stride()
stride_GK = GK.stride()
stride_Out = Out.stride()
BLOCK_M = 32
BLOCK_N = 32
BLOCK_D = 64 # Assuming Dq == Dv == 64
grid = (Z, H, triton.cdiv(M, BLOCK_M))
gdpa_attn_kernel[grid](
Q, K, V, GQ, GK, Out,
Z, H, M, N, Dq, Dv,
*stride_Q, *stride_K, *stride_V, *stride_GQ, *stride_GK, *stride_Out,
BLOCK_M, BLOCK_N, BLOCK_D,
)
return Out
class Solution:
def solve(self, spec_path: str = None) -> dict:
code = '''
import torch
import triton
import triton.language as tl
@triton.jit
def gdpa_attn_kernel(
Q_ptr, K_ptr, V_ptr, GQ_ptr, GK_ptr, Out_ptr,
Z, H, M, N, Dq, Dv,
stride_Q_z, stride_Q_h, stride_Q_m, stride_Q_d,
stride_K_z, stride_K_h, stride_K_n, stride_K_d,
stride_V_z, stride_V_h, stride_V_n, stride_V_d,
stride_GQ_z, stride_GQ_h, stride_GQ_m, stride_GQ_d,
stride_GK_z, stride_GK_h, stride_GK_n, stride_GK_d,
stride_Out_z, stride_Out_h, stride_Out_m, stride_Out_d,
BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_D: tl.constexpr,
):
pid_z = tl.program_id(0)
pid_h = tl.program_id(1)
pid_m = tl.program_id(2)
z = pid_z
h = pid_h
m_start = pid_m * BLOCK_M
m_offsets = m_start + tl.arange(0, BLOCK_M)
m_mask = m_offsets < M
# Load Q and GQ
d_offsets = tl.arange(0, BLOCK_D)
Q_ptrs = Q_ptr + z * stride_Q_z + h * stride_Q_h + m_offsets[:, None] * stride_Q_m + d_offsets[None, :] * stride_Q_d
Q_mask = m_mask[:, None] & (d_offsets[None, :] < Dq)
Q = tl.load(Q_ptrs, mask=Q_mask, other=0.0)
GQ_ptrs = GQ_ptr + z * stride_GQ_z + h * stride_GQ_h + m_offsets[:, None] * stride_GQ_m + d_offsets[None, :] * stride_GQ_d
GQ = tl.load(GQ_ptrs, mask=Q_mask, other=0.0)
GQ_sig = 1.0 / (1.0 + tl.exp(-GQ.to(tl.float32)))
Qg = Q * GQ_sig.to(Q.dtype)
# Initialize accumulators
l = tl.full((BLOCK_M,), -float('inf'), dtype=tl.float32)
acc = tl.zeros((BLOCK_M, BLOCK_D), dtype=tl.float32)
denom = tl.zeros((BLOCK_M,), dtype=tl.float32)
scale = tl.rsqrt(tl.full((), Dq, dtype=tl.float32))
for n_start in tl.range(0, N, BLOCK_N):
n_offsets = n_start + tl.arange(0, BLOCK_N)
n_mask = n_offsets < N
# Load K and GK
K_ptrs = K_ptr + z * stride_K_z + h * stride_K_h + n_offsets[:, None] * stride_K_n + d_offsets[None, :] * stride_K_d
K_mask = n_mask[:, None] & (d_offsets[None, :] < Dq)
K = tl.load(K_ptrs, mask=K_mask, other=0.0)
GK_ptrs = GK_ptr + z * stride_GK_z + h * stride_GK_h + n_offsets[:, None] * stride_GK_n + d_offsets[None, :] * stride_GK_d
GK = tl.load(GK_ptrs, mask=K_mask, other=0.0)
GK_sig = 1.0 / (1.0 + tl.exp(-GK.to(tl.float32)))
Kg = K * GK_sig.to(K.dtype)
# Compute attention scores
attn = tl.dot(Qg, tl.trans(Kg), out_dtype=tl.float32) * scale
# Load V
V_ptrs = V_ptr + z * stride_V_z + h * stride_V_h + n_offsets[:, None] * stride_V_n + d_offsets[None, :] * stride_V_d
V_mask = n_mask[:, None] & (d_offsets[None, :] < Dv)
V = tl.load(V_ptrs, mask=V_mask, other=0.0)
V_fp32 = V.to(tl.float32)
# Streaming softmax update
attn_max = tl.max(attn, axis=1)
new_m = tl.maximum(l, attn_max)
exp_attn = tl.exp(attn - new_m[:, None])
alpha = tl.exp(l - new_m)
acc = acc * alpha[:, None] + tl.dot(exp_attn, V_fp32, out_dtype=tl.float32)
denom = denom * alpha + tl.sum(exp_attn, axis=1)
l = new_m
# Store output
denom = tl.maximum(denom, 1e-9)
acc = acc / denom[:, None]
Out_ptrs = Out_ptr + z * stride_Out_z + h * stride_Out_h + m_offsets[:, None] * stride_Out_m + d_offsets[None, :] * stride_Out_d
Out_mask = m_mask[:, None] & (d_offsets[None, :] < Dv)
tl.store(Out_ptrs, acc.to(tl.float16), mask=Out_mask)
def gdpa_attn(Q: torch.Tensor, K: torch.Tensor, V: torch.Tensor, GQ: torch.Tensor, GK: torch.Tensor) -> torch.Tensor:
Z, H, M, Dq = Q.shape
N = K.shape[2]
Dv = V.shape[3]
assert K.shape == (Z, H, N, Dq)
assert V.shape == (Z, H, N, Dv)
assert GQ.shape == (Z, H, M, Dq)
assert GK.shape == (Z, H, N, Dq)
Out = torch.empty_like(V[:, :, :M, :]) # (Z, H, M, Dv)
# Strides
stride_Q = Q.stride()
stride_K = K.stride()
stride_V = V.stride()
stride_GQ = GQ.stride()
stride_GK = GK.stride()
stride_Out = Out.stride()
BLOCK_M = 32
BLOCK_N = 32
BLOCK_D = 64 # Assuming Dq == Dv == 64
grid = (Z, H, triton.cdiv(M, BLOCK_M))
gdpa_attn_kernel[grid](
Q, K, V, GQ, GK, Out,
Z, H, M, N, Dq, Dv,
*stride_Q, *stride_K, *stride_V, *stride_GQ, *stride_GK, *stride_Out,
BLOCK_M, BLOCK_N, BLOCK_D,
)
return Out
'''
return {"code": code}
</code></pre>