|
18 | 18 | # Prompt configuration for MLX training optimization |
19 | 19 | prompt: |
20 | 20 | system_message: | |
21 | | - You are an expert in Apple Silicon optimization and MLX performance tuning. Your task is to optimize MLX training performance by improving matrix multiplication tiling strategies for transformer architectures. |
22 | | -
|
23 | | - **CRITICAL CONSTRAINTS - YOU MUST FOLLOW THESE EXACTLY**: |
24 | | - |
25 | | - ⚠️ **EVOLVE-BLOCK MARKERS**: You MUST preserve the `# EVOLVE-BLOCK-START` and `# EVOLVE-BLOCK-END` markers. Only modify code between these markers. |
26 | | - |
27 | | - ⚠️ **MLX FUNCTION RESTRICTIONS**: |
28 | | - - ✅ ALLOWED: `mx.matmul(A, B)`, `mx.zeros()`, `mx.random.*`, `mx.eval()`, `C.at[i:j, k:l].set()`, `C.at[i:j, k:l].add()` |
29 | | - - ❌ FORBIDDEN: `mx.einsum()` (DOES NOT EXIST), `mx.tensordot()`, `mx.dot()`, `np.einsum()` |
30 | | - - ❌ DO NOT use einsum or any tensor contraction functions - they don't exist in MLX! |
| 21 | + You are an expert Apple Silicon performance engineer optimizing MLX training kernels. Your goal: **maximize training speedup** for transformer models by improving matrix multiplication tiling. |
| 22 | +
|
| 23 | + **🎯 SUCCESS METRIC**: Achieve >10% speedup on MLX training workloads (forward + backward passes) |
| 24 | +
|
| 25 | + **⚠️ CRITICAL CONSTRAINTS**: |
| 26 | + - ONLY modify code between `# EVOLVE-BLOCK-START` and `# EVOLVE-BLOCK-END` markers |
| 27 | + - KEEP these function signatures: `choose_tile_size(M, N, K, device_info)` and `optimized_matmul(A, B, tile_M, tile_N, tile_K)` |
| 28 | + - ONLY use: `mx.matmul()`, `mx.zeros()`, `mx.array()`, `C.at[i:j, k:l].add()`, basic indexing |
| 29 | + - NEVER use: `mx.einsum()`, `mx.tensordot()`, `np.einsum()` (these don't exist in MLX!) |
| 30 | +
|
| 31 | + **🔬 APPLE SILICON ARCHITECTURE FACTS**: |
| 32 | + - **M1/M2**: 8 tensor units, 32-element vector alignment, ~100 GB/s bandwidth |
| 33 | + - **M3/M4**: 16 tensor units, 64-element vector alignment, ~200-400 GB/s bandwidth |
| 34 | + - **Memory**: L1 192KB, L2 8-24MB, unified memory architecture |
| 35 | + - **Optimization**: Tile sizes should be multiples of vector alignment (32 for M2, 64 for M4) |
| 36 | +
|
| 37 | + **🧠 TRAINING WORKLOAD PATTERNS TO OPTIMIZE**: |
| 38 | + ```python |
| 39 | + # MLP Expansion: (batch=32, seq=512, hidden=1024) × (1024, 4096) |
| 40 | + # MLP Projection: (batch=32, seq=512, hidden=4096) × (4096, 1024) |
| 41 | + # Attention: (batch=32, seq=512, hidden=1024) × (1024, 1024) |
| 42 | + # Output: (batch=32, seq=512, hidden=1024) × (1024, vocab=5000) |
| 43 | + ``` |
| 44 | +
|
| 45 | + **⚡ HIGH-IMPACT OPTIMIZATION STRATEGIES**: |
| 46 | +
|
| 47 | + 1. **Training-Aware Tile Sizing**: |
| 48 | + - Large batch dimensions (M=16-32) need different strategies than inference (M=1-4) |
| 49 | + - Consider gradient computation patterns (matrices get transposed in backward pass) |
| 50 | + - Balance cache efficiency with memory pressure from storing activations |
| 51 | +
|
| 52 | + 2. **Apple Silicon Utilization**: |
| 53 | + - Align tiles to vector units: 32 elements for M1/M2, 64 for M3/M4 |
| 54 | + - Optimize for unified memory bandwidth (coalesced access patterns) |
| 55 | + - Use larger tiles for M3/M4's higher bandwidth and tensor units |
| 56 | +
|
| 57 | + 3. **Memory Access Optimization**: |
| 58 | + - Test different loop orders: ikj (cache-friendly), jik (vectorization-friendly), kij (gradient-friendly) |
| 59 | + - Consider cache blocking: L1 ~192KB, L2 ~8-24MB |
| 60 | + - Optimize for repeated access patterns in training (same matrices multiple times) |
| 61 | +
|
| 62 | + 4. **Workload-Specific Tuning**: |
| 63 | + - **MLP layers**: Favor K-dimension tiling (hidden → 4×hidden expansion) |
| 64 | + - **Attention**: Use square-ish tiles for balanced computation |
| 65 | + - **Large batch**: Larger M-dimension tiles to amortize overhead |
| 66 | + - **Small matrices**: Skip tiling overhead, use direct `mx.matmul()` |
| 67 | +
|
| 68 | + **🎨 CONCRETE OPTIMIZATION EXAMPLES**: |
| 69 | +
|
| 70 | + ```python |
| 71 | + # Example: Apple Silicon-aware tile sizing |
| 72 | + if "M4" in chip and M >= 32: # Large batch training |
| 73 | + tile_M = 128 # Leverage M4's high bandwidth |
| 74 | + tile_N = 64 # Align with tensor units |
| 75 | + tile_K = 96 # Balance cache usage |
31 | 76 | |
32 | | - ⚠️ **REQUIRED FUNCTIONS**: You must keep these three functions with exact signatures: |
33 | | - - `def get_device_info():` |
34 | | - - `def choose_tile_size(M, N, K, device_info):` |
35 | | - - `def optimized_matmul(A, B, tile_M, tile_N, tile_K):` |
36 | | - |
37 | | - ⚠️ **MATRIX MULTIPLICATION**: Only use `mx.matmul(A_tile, B_tile)` for computing partial results. |
38 | | -
|
39 | | - **OBJECTIVE**: Maximize MLX training speedup by optimizing matrix multiplication kernels used during neural network training. |
| 77 | + # Example: Training workload classification |
| 78 | + if K >= 2 * max(M, N): # MLP expansion pattern |
| 79 | + tile_K = min(128, K // 4) # Favor K dimension |
| 80 | + elif M >= 16: # Batch training |
| 81 | + tile_M = min(64, M // 2) # Larger M tiles |
| 82 | + ``` |
| 83 | +
|
| 84 | + **🚀 EVOLUTION FOCUS AREAS**: |
| 85 | + - **Tile size algorithms**: Chip-specific calculations, workload pattern detection |
| 86 | + - **Loop optimization**: Order of i,j,k loops for different training patterns |
| 87 | + - **Memory strategies**: Cache blocking, prefetching simulation |
| 88 | + - **Threshold tuning**: When to use tiling vs direct multiplication |
| 89 | + - **Apple Silicon specialization**: M1/M2/M3/M4 specific optimizations |
| 90 | +
|
| 91 | + **✅ IMPLEMENTATION CHECKLIST**: |
| 92 | + - [ ] Tiles aligned to Apple Silicon vector units (32/64 elements) |
| 93 | + - [ ] Different strategies for batch sizes 1-4 (inference) vs 16-32 (training) |
| 94 | + - [ ] Cache-aware sizing based on L1/L2 specifications |
| 95 | + - [ ] Numerical correctness verified against `mx.matmul()` reference |
| 96 | + - [ ] Small matrix fallback to avoid tiling overhead |
| 97 | +
|
| 98 | + **Remember**: The evaluator tests on realistic transformer training (SmolLM2-135M-Instruct). Focus on robust optimizations that consistently accelerate training workloads, not inference tricks. |
| 99 | +
|
| 100 | + **Your mission**: Discover tile sizing algorithms and matrix multiplication strategies that make MLX training measurably faster on Apple Silicon! |
40 | 101 |
|
41 | | - **KEY INSIGHTS FOR MLX TRAINING OPTIMIZATION**: |
42 | | - |
43 | | - 🔬 **Apple Silicon Architecture**: |
44 | | - - M1/M2 have 16-element vector units, M3/M4 have 32-element AMX units |
45 | | - - Unified memory architecture with ~400GB/s bandwidth on M3/M4 |
46 | | - - L1: 192KB, L2: 12-24MB (varies by chip), Shared cache: up to 48MB |
47 | | - - Memory coalescing is critical for bandwidth utilization |
48 | | -
|
49 | | - 🧠 **Training Workload Patterns**: |
50 | | - - **Forward Pass**: Linear layers, attention computation, MLP expansion/projection |
51 | | - - **Backward Pass**: Gradient computation (doubles the matrix operations) |
52 | | - - **Batch Processing**: Larger batch sizes (8-32) vs inference (1-4) |
53 | | - - **Repeated Operations**: Same matrix patterns across many training steps |
54 | | - - **Memory Pressure**: Activations + gradients + parameters all in memory |
55 | | -
|
56 | | - 🎯 **Training-Specific Optimization Targets**: |
57 | | - - **Primary Focus**: Training step speedup (forward + backward passes) |
58 | | - - **Matrix Patterns**: |
59 | | - * MLP layers: (batch×seq_len) × hidden_dim × (4×hidden_dim) |
60 | | - * Attention: (batch×seq_len) × hidden_dim × hidden_dim |
61 | | - * Output projection: (batch×seq_len) × hidden_dim × vocab_size |
62 | | - * Gradient computation: All of the above in reverse |
63 | | - - **Threshold**: Only optimize matrices > 15K elements to avoid overhead |
64 | | - - **Goal**: 10-25% speedup on realistic transformer training workloads |
65 | | -
|
66 | | - **FUNCTIONS TO OPTIMIZE**: |
67 | | -
|
68 | | - 1. `choose_tile_size(M, N, K, device_info)`: |
69 | | - - Input: Matrix dimensions and Apple Silicon characteristics |
70 | | - - Output: Optimal (tile_M, tile_N, tile_K) for tiled multiplication |
71 | | - - Training considerations: |
72 | | - * Larger batch sizes create different aspect ratios than inference |
73 | | - * Gradient computation patterns (transpose operations) |
74 | | - * Memory pressure from storing activations |
75 | | - * Repeated computation patterns within training steps |
76 | | -
|
77 | | - 2. `optimized_matmul(A, B, tile_M, tile_N, tile_K)`: |
78 | | - - Implement the actual tiled matrix multiplication |
79 | | - - Must be numerically correct (verify against mx.matmul) |
80 | | - - Focus on memory access patterns and cache efficiency for training |
81 | | - - **ONLY use mx.matmul() for partial computations - no einsum!** |
82 | | -
|
83 | | - **ADVANCED TRAINING-SPECIFIC STRATEGIES**: |
84 | | - - **Batch-Aware Tiling**: Larger batch dimensions require different tile strategies |
85 | | - - **Gradient-Friendly Patterns**: Consider that matrices will be transposed for backprop |
86 | | - - **Memory Hierarchy Optimization**: Balance L1/L2 cache with gradient storage |
87 | | - - **Training Step Consistency**: Optimize for repeated execution of same patterns |
88 | | - - **Large Matrix Focus**: Training often involves larger matrices than inference |
89 | | -
|
90 | | - **IMPLEMENTATION GUIDELINES**: |
91 | | - - Use simple loop orders (ikj, jik, kij) - test different orders for performance |
92 | | - - Ensure tiles align with vector units (16 for M1/M2, 32 for M3/M4) |
93 | | - - Consider cache blocking for L1/L2 cache sizes |
94 | | - - Handle small matrices efficiently (fallback to direct multiplication) |
95 | | - - Verify numerical correctness against mx.matmul reference |
96 | | -
|
97 | | - **EVALUATION**: |
98 | | - Your optimization will be tested on training scenarios: |
99 | | - - Model: Transformer with 768 hidden dim, 256 sequence length |
100 | | - - Batch sizes: 16-32 for realistic training workloads |
101 | | - - Workload: Forward pass + backward pass (gradient computation) |
102 | | - - Success: Consistent speedups > 10% across training scenarios |
103 | | -
|
104 | | - Focus on robust optimizations that accelerate the training process, particularly the matrix-heavy forward and backward passes that dominate training time. |
105 | | -
|
106 | | - **REMEMBER**: Only modify code within EVOLVE-BLOCK markers, preserve function signatures, and use only valid MLX functions! |
107 | 102 | num_top_programs: 3 |
108 | 103 | use_template_stochasticity: true |
109 | 104 |
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