Lightweight GEMM Framework

• Lightweight GEMM frameworks are design principles delivering efficient matrix multiplication by fusing low-overhead hardware, compiler, and software optimizations.
• They minimize data packing, hide latency through preloading and double buffering, and maximize compute utilization across diverse deep learning and HPC workloads.
• Empirical results demonstrate 3.6×–16.4× throughput speedup and up to 99.3% utilization through innovations like analytical performance models and input-aware tiling.

A lightweight GEMM (General Matrix–Matrix Multiplication) framework refers to an architecture, software stack, or design principle that delivers efficient matrix multiplication with low system overhead, reduced ancillary resource requirements, or minimal performance tuning effort, primarily targeting performance-critical domains such as deep learning, high-performance computing, and embedded systems. The lightweight property is achieved through streamlined hardware, compiler, or software designs that reduce configuration complexity, eliminate unnecessary data movement, and sustain high compute utilization across diverse workloads.

1. Conceptual Foundations and Motivations

Lightweight GEMM frameworks address common sources of inefficiency encountered in both large-scale and resource-constrained environments. Traditional GEMM implementations either maximize throughput but incur packing and scheduling overhead (e.g., classic BLAS libraries), or are tailored to narrow scenarios but lack flexibility. The motivation is to sustain near-peak utilization with minimal extra logic or manual tuning, often through:

• Minimizing or eliminating data packing stages when they become bottlenecks (notably for small matrices or high-frequency kernel invocations).
• Fusing configuration, control, and memory access mechanisms such that they occur in parallel with computation, hiding their latency entirely.
• Exposing a concise, parameterized API or architectural interface that enables easy adaptation to new problem shapes or hardware, while preserving reproducibility and extensibility.

Designs such as OpenGeMM, IAAT, tritonBLAS, GEMMFIP, and frameworks reusing BLIS-style loop-nest structures exemplify these principles (Yi et al., 14 Nov 2024, Yao et al., 2022, Swann et al., 3 Dec 2025, Xu et al., 2023).

2. Hardware and Architectural Approaches

At the hardware level, lightweight GEMM frameworks such as OpenGeMM prioritize ease of programmability, tight coupling of memory with compute, and controller minimalism. Key elements include:

• Parameterized MAC arrays: For example, an $M_u\times N_u\times K_u$ multiplier–accumulator array unrolling all tile dimensions in hardware for maximal parallelism.
• Minimalist RISC-V host: OpenGeMM employs an RV32I "Snitch" core that only manages configuration and control status registers (CSRs), comprising just ~1% of area and ~2.4% of system power.
• Tightly coupled, multi-banked scratchpad: Banks (e.g., 32, 64 bits wide, 1,056 words deep, 16/32 read/write ports) are programmable for high bandwidth, and controlled by address generators (AGUs) to avoid bank conflicts.
• Dedicated data streamers: Hardware loops with programmable strides enable autonomous, strided memory access by overlapping data movement with compute.
• Configuration pre-loading, double-buffering, and output buffering: Key mechanisms hide configuration and IO latency behind computation, ensuring all MAC units remain active for a maximal fraction of time (Yi et al., 14 Nov 2024).

These designs achieve 81.89%–99.34% utilization across CNN and Transformer workloads, with 3.58×–16.40× normalized throughput speedup over the Gemmini baseline and measured efficiency of 4.68 TOPS/W using INT8 datatypes.

3. Compiler and Software-Level Lightweight Frameworks

Lightweight design at the compiler or software layer focuses on reducing tuning cost and maximizing portability:

• Analytical Performance Modeling: tritonBLAS models compute and memory latency for each potential tiling configuration directly as a function of GPU architecture parameters (register/shared memory/caches, bandwidth, matrix-core instruction shape). The best tile is then predicted by closed-form evaluation, without any runtime search or empirical kernel timing (Swann et al., 3 Dec 2025).
  • For example, given the blocking parameters $(M_b, N_b, K_b)$, key cost terms include:
  • Compute latency per tile: $$T_{\text{comp}} = N_{\text{MI}} \times L_{\text{MI}}$$
  • Memory latency: $$T_{\text{mem}} = \max\{T_{L1},\,T_{L2},\,T_{\text{DRAM}}\}$$
  • Overall latency: $$T_{\text{GEMM}} = \omega \times T_{\text{tile}}(M_b,N_b,K_b)$$
  • Model selection runs up to $200,000\times$ faster than autotuning, giving 94.7% of peak at zero search cost.
• Input-Aware Tiling and Kernel Autogeneration: For small GEMM (IAAT), the framework precomputes hundreds of hand-tuned microkernels covering all block sizes, layouts, and data types. At runtime, an input-driven tiler assigns problem blocks to the closest matching kernel, eliminating packing and boundary overhead (Yao et al., 2022).
• Fused Packing and Unified Microkernels: GEMMFIP fuses data-packing with computation inside the microkernel, resulting in a single code path for both small and large matrices, thus eliminating costly runtime heuristics and the traditional dual-path logic of classic BLAS libraries (Xu et al., 2023).
• Code Generation for Fast Matrix Multiplication: Families of Strassen-like or FMM algorithms are represented symbolically ($[U,V,W]$ triples), and code generation fuses linear combinations directly into packing and micro-kernel steps; no task-based parallelism or large-temporary buffers are needed (Huang et al., 2016).

4. Mechanisms for High Utilization and Low Overhead

Across architectures, several mechanisms commonly underpin lightweight GEMM frameworks:

• Latency Hiding: Pre-loading of configuration data (e.g., for the next tile) during the current computation round; pre-fetching and buffering to avoid compute stalls.
• Fine-Grained Data Reuse: Double-buffering, software/hardware pipelining, and programmable stride AGUs to maximize scratchpad and register file usage.
• Bank Conflict Avoidance: Strided address generation and data layout orchestration ensure all SPM banks are accessed in parallel, maximizing sustained bandwidth (Yi et al., 14 Nov 2024, Swann et al., 3 Dec 2025).
• Removable Packing: For small to medium matrices, offline code generation of dense kernel libraries (as in IAAT) eliminates dynamic data rearrangement costs entirely; microkernels consume input in its native layout (Yao et al., 2022).

A table summarizing effective mechanisms:

Mechanism	Framework Example	Impact
Config pre-loading	OpenGeMM	Maintains MAC utilization during reconfig
Analytical modeling	tritonBLAS	Removes need for runtime autotuning search
Fused packing+compute	GEMMFIP, Strassen-FMM	Eliminates redundant memory traffic
Input-aware kernel plan	IAAT	Zero-packing for small GEMM

5. Benchmarks, Metrics, and Empirical Results

Framework performance is typically measured by utilization, throughput, and energy efficiency:

• Utilization: $$U = \frac{\text{useful\_cycles}}{\text{total\_cycles}}$$; OpenGeMM reports 81.9%–99.3% across workloads.
• Normalized Throughput: $$T_{\mathrm{norm}} = \frac{\mathrm{operation\_count}}{\mathrm{execution\_time}}$$; OpenGeMM achieves 204.8 GOPS at 43.8 mW (Yi et al., 14 Nov 2024).
• Energy Efficiency: $\eta=\frac{T_{\mathrm{norm}}}{P_{\mathrm{sys}}}$, with OpenGeMM reaching 4.68 TOPS/W.
• Selection speed and performance regression: tritonBLAS analytical selection reduces parameter search time to microseconds, sustains within 3% of vendor GEMM throughput across 150,000 shapes (Swann et al., 3 Dec 2025).
• Small GEMM performance: IAAT yields 1.8×–2.5× speedup over OpenBLAS/ARMPL on $M,N,K\leq80$ (Yao et al., 2022).

Notable outcomes:

• OpenGeMM gives 3.6×–16.4× normalized throughput over Gemmini due to higher sustained temporal utilization.
• tritonBLAS's analytical selector achieves over 94% of autotuned peak with no search overhead.

6. Design Insights, Trade-offs, and Practical Guidelines

Trade-offs and insights from lightweight GEMM frameworks:

• Controller Minimalism vs. Programmability: Snitch RV32I occupies minimal die area, trading off general-purpose instruction delivery for rapid CSR communication. Full-featured RISC-V cores would exceed the MAC core in area and power.
• Banked SPM and Port Balancing: A higher number of banks widens available parallelism (e.g., 32×64 b banks in OpenGeMM), but increases die-area; programmable data layout avoids bank conflicts but may necessitate compiler data management (Yi et al., 14 Nov 2024).
• Offline vs. Online Overhead: IAAT demonstrates that shifting packing/elimination logic to offline kernel generation reduces runtime cost to a single tiling and microkernel dispatch loop; this inflates code size but is ideal for batch/batched small-matrix settings (Yao et al., 2022).
• When to Autotune vs. When to Use Analytical Selection: tritonBLAS recommends analytical selection for dynamic batched workloads and multi-arch deployment; full search (autotuning) is reserved for applications where incremental GFLOPS outweighs search cost (Swann et al., 3 Dec 2025).
• Portability: Detaching performance logic from device-specific low-level kernels, as in code-generators or compiled microkernels, facilitates extension to new backends and architectures (Huang et al., 2016, Xu et al., 2023).

7. Extension to Related Operations and Future Directions

Lightweight GEMM framework design principles are generalizable to a variety of level-3 BLAS and tensor operators:

• Convolution via GEMM: Low-memory convolution algorithms reformulate 2D convolution as a series of small GEMMs, using $O(MHW)$ (low-memory accumulation) or $O(KW)$ ("hole-punch" accumulation) workspace versus the $O(K^2CHW)$ im2col scheme. This enables efficient inference on memory-limited embedded platforms without a throughput penalty (Anderson et al., 2017).
• SYRK, TRSM, etc.: BLIS-style loop-structure frameworks with fused data movement primitives can generalize to symmetric rank-k update (SYRK) and triangular solves (TRSM), applying the same fusion of packing and compute (Xu et al., 2023).
• Compiler Scheduling and Search: Lightweight, search-based schedulers (G-BFS/N-A2C in TVM) can minimize the space of tiling factors to search <0.1% of configurations, discovering near-optimal GEMM kernels with little or no manual kernel specialization (Zhang et al., 2019).

A plausible implication is that framework modularity and configuration compactness will remain central for integrating new algorithmic advances (e.g., low-memory or fast matrix multiplication methods) into heterogeneous hardware and compiler stacks, ensuring both performance and maintainability.

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References:

OpenGeMM (Yi et al., 14 Nov 2024); GEMMbench (Lokhmotov, 2015); tritonBLAS (Swann et al., 3 Dec 2025); IAAT (Yao et al., 2022); GEMMFIP (Xu et al., 2023); TVM search (Zhang et al., 2019); Strassen-FMM codegen (Huang et al., 2016); Low-memory GEMM convolution (Anderson et al., 2017).