da4ml: Distributed Arithmetic for Machine Learning

da4ml is a static computation graph to RTL/HLS design compiler targeting ultra-low latency applications on FPGAs. It as two major components:

• A fast and performant constant-matrix-vector multiplications (CMVM) optimizer to implement them as efficient adder trees. Common sub-expressions elimination (CSE) with graph-based pre-optimization are performed to reduce the firmware footprint and improve the performance.
• Low-level symbolic tracing frameworks for generating combinational/fully pipelined logics in HDL or HLS code. da4ml can generate the firmware for almost all fully pipelined networks standalone. Alternatively, da4ml also be used as a plugin in hls4ml to optimize the CMVM operations in the network.

Key Features

• Optimized Algorithms: Comparing to hls4ml's latency strategy, da4ml's CMVM implementation uses no DSO and consumes up to 50% less LUT usage.
• Fast code generation: da4ml can generate HDL for a fully pipelined network in seconds. For the same models, high-level synthesis tools like Vivado/Vitis HLS can take up to days to generate the HDL code.
• Low-level symbolic tracing: As long as the operation can be expressed by a combination of the low-level operations supported, adding new operations is straightforward by "replaying" the operation on the symbolic tensor provided. In most cases, adding support for a new operation/layer takes just a few lines of code in numpy flavor.
• Automatic model conversion: da4ml can automatically convert models trained in HGQ2 <https://github.com/calad0i/hgq2>_.
• Bit-accurate Emulation: All operation in da4ml is bit-accurate, meaning the generated HDL code will produce the same output as the original model. da4ml's computation is converted to a RISC-like, instruction set level intermediate representation, distributed arithmetic instruction set (DAIS), which can be easily simulated in multiple ways. da4ml also provides a fast C++ based DAIS interpreter to run bit-exact inference on the traced models for verification and benchmarking.
• hls4ml integration: da4ml can be used as a extension in hls4ml to optimize the CMVM operations in the network by setting strategy='distributed_arithmetic' for the strategy of the Dense, EinsumDense, or Conv1/2D layers.

Installation

pip install da4ml

Note: da4ml is now released as binary wheels on PyPI for Linux X86_64 and MacOS ARM64 platforms. For other platforms, please install from source.

Getting Started

• See the Getting Started guide for a quick introduction to using da4ml.
• See JEDI-linear project which is based on da4ml

License

LGPLv3. See the LICENSE file for details.

Citation

If you use da4ml in a publication, please cite our TRETS'25 paper with the following bibtex entry:

@article{sun2025da4ml,
    author = {Sun, Chang and Que, Zhiqiang and Loncar, Vladimir and Luk, Wayne and Spiropulu, Maria},
    title = {da4ml: Distributed Arithmetic for Real-time Neural Networks on FPGAs},
    year = {2025},
    publisher = {Association for Computing Machinery},
    address = {New York, NY, USA},
    issn = {1936-7406},
    url = {https://doi.org/10.1145/3777387},
    doi = {10.1145/3777387},
    journal = {ACM Trans. Reconfigurable Technol. Syst.},
    month = nov,
}