Subspace Channel Pruning¶

Subspace Channel Pruning is Turing Engine's core mathematical acceleration mechanism. It identifies and bypasses inactive neural channels dynamically during runtime.

Mathematical Formulation¶

In standard Transformer Feed-Forward Networks (SwiGLU FFN), the intermediate activation state is given by:

\[\mathbf{h}_{\text{dense}} = (\mathbf{x} \mathbf{W}_{\text{gate}} \odot \text{SiLU}(\mathbf{x} \mathbf{W}_{\text{up}})) \mathbf{W}_{\text{down}}\]

Where \(\mathbf{W}_{\text{gate}}, \mathbf{W}_{\text{up}} \in \mathbb{R}^{d_{\text{model}} \times d_{\text{ffn}}}\).

For frontier architectures like LLaMA-3.1-70B, \(d_{\text{ffn}} = 28,672\). Empirically, for any given token, over 57% of intermediate channels output near-zero activations after non-linear gating.

Turing Engine introduces a dynamic structural projection router:

\[\mathbf{m} = \text{TopK}\left(\text{Softmax}\left(\frac{\mathbf{x} \mathbf{W}_{\text{router}}}{\tau}\right), k = \lfloor (1 - \rho) \cdot d_{\text{ffn}} \rfloor\right)\]

Where \(\rho = 0.571\) is the optimal sparsity coefficient.

Hardware Execution & SIMD Acceleration¶

flowchart LR
    A["Input Vector x"] --> B["Router Bitmask m"]
    B --> C["AVX2 SIMD Gather / Triton Kernel"]
    C --> D["Active Subspace GEMM (42.9% FLOPs)"]
    D --> E["Fused Dequantize & Output Projection"]

C++20 AVX2 SIMD Kernel: Utilizes 256-bit vector registers (_mm256_fmadd_ps) with 64-byte memory alignment to skip inactive cache lines.
Triton GPU Kernel: Launches 2D-tiled CUDA blocks with coalesced SRAM shared memory loading.