Configurable & Hybrid FMA

• Configurable and hybrid FMA are adaptive MAC architectures that dynamically select computational paths to optimize energy, performance, and numerical stability in diverse applications.
• They enable significant reductions in power consumption and resource usage in DNN accelerators, FFT processors, and speech enhancement pipelines through run-time reconfiguration.
• Practical implementations demonstrate up to 95% power savings and improved accuracy, highlighting their effectiveness for real-time, edge-constrained deployments.

Configurable and hybrid FMA (Fused Multiply Accumulate) refers to hardware and algorithmic paradigms that dynamically adapt the structure, scheduling, or execution paths of multiply-accumulate (MAC) operations. This is achieved through mechanisms allowing run-time selection among multiple operational paths (configurability) and the combination of different computational styles or resources (hybridity). Contemporary research demonstrates configurable and hybrid FMA designs in contexts ranging from deep neural network (DNN) accelerators to signal-processing kernels such as FFT butterflies and robust augmentation in feature spaces for CNNs. Key objectives are to minimize resource usage, provide algorithmic flexibility, and enhance numerical stability or model robustness in constrained edge or real-time environments.

1. Hybrid Data-Multiplexing in DNN Accelerators

The HYDRA architecture exemplifies hybrid and configurable FMA by implementing a layer-multiplexed DNN accelerator for edge deployments (Kumar et al., 2024). HYDRA’s core is a 1-D array of $N$ FMA units coupled with a single, time-shared activation function (AF), governed by a minimal FSM.

• Data/Weight Multiplexing: Inputs $x_1,\ldots,x_N$ and weights $w_1,\ldots,w_N$ are streamed via time-multiplexed buses from input/weight banks into the N FMA units, enabling iterative layer-wise computation.
• PISO and AF Sharing: After N MAC cycles, the outputs, $s_N$, are staged in a parallel-in-serial-out (PISO) shift register. The single AF block (e.g., ReLU, sigmoid) is time-shared across the N outputs, serially computing activations.
• FSM and Layer Multiplexing: A 6-state FSM sequencially cycles through IDLE→LOAD_WEIGHTS→COMPUTE→SERIALIZE→ACTIVATE→DONE, reading configuration registers per layer (parameters $n(l)$, bit-width, activation type), enabling rapid layer context switches without DSP block reallocation or resynthesis.
• Reconfiguration Latency: For each layer, reconfiguration latency is $T_{cfg} \approx n(l) + 2$ cycles, negligible relative to total layer compute time.

Significance: HYDRA achieves >90% reductions in dynamic power consumption, LUT and register usage versus prior SOTA layer-multiplexed designs, with an area overhead of only $(N-1)$ times for bandwidth, AF, and layer architecture. Throughput is sustained at 35.21 GOPS/W at 100 MHz on edge-class FPGAs/ASICs, demonstrating viable real-time DNN inference for resource-constrained nodes (Kumar et al., 2024).

2. Configurable and Hybrid FMA in FFT and Signal Processing

Hybrid FMA is crucial in digital signal processing (DSP), where minimal FMA kernels achieve maximal arithmetic efficiency. In radix-2 FFT computation, factorization of the butterfly—$A=a+Wb$, $B=a-Wb$—into minimal FMA instructions has historically encountered singularities in the twiddle-factor ratios.

• Classical Linzer–Feig Factorization: Extracts $\omega_i = \sin\theta$, precomputes $x_1,\ldots,x_N$0. Singular at $x_1,\ldots,x_N$1 since $x_1,\ldots,x_N$2, which is addressed via epsilon-clamping but with degraded precision.
• Cosine-Based Factorization: Uses $x_1,\ldots,x_N$3, precomputes $x_1,\ldots,x_N$4, introducing a singularity at $x_1,\ldots,x_N$5.
• Dual-Select (Hybrid) FMA Strategy: For each $x_1,\ldots,x_N$6, dynamically select the factorization (sin- or cos-based) such that $x_1,\ldots,x_N$7:

$x_1,\ldots,x_N$8

This eliminates all singularities, reduces the maximal ratio to unity, and requires only one flag-bit per twiddle in the kernel’s lookup table.

Numerical Impact: In FP16, the maximal rounding error is improved by 235×, with the worst-case error bound for $x_1,\ldots,x_N$9 reduced from $w_1,\ldots,w_N$0 to $w_1,\ldots,w_N$1 (Bergach, 1 Apr 2026). This is achieved without additional inner-loop overhead, making dual-select butterflies a canonical example of configurable and hybrid FMA for DSP.

3. Layer and Algorithmic Configurability Mechanisms

Configurable FMA is also central to general purpose and application-specific accelerators that support multiple operation modes, precision scaling, and topology switching.

• FSM-Based Layer Control: HYDRA’s control FSM reads per-layer configuration from RAM (number/type of FMAs, bit-width, bias, activation). No statically dedicated hardware per layer is required; context switching involves only register and MUX changes.
• Universal Data Paths: The same FMA array is re-used for both convolutional and fully-connected layers; only sequencing of fetches and weight pattern change.
• Zero-Area Overhead: All configurations are achieved using static wiring, with extra control logic being a negligible fraction of overall hardware cost (Kumar et al., 2024).

Implication: Highly granular run-time configurability is achieved without area or power penalty, enabling support for diverse DNN topologies and workloads in spatially constrained, power-critical environments.

4. Hybrid FMA Architectures in Speech Enhancement and Filtering

Configurable and hybrid FMA systems extend beyond arithmetic units and are featured in multi-stage filtering architectures for real-time audio enhancement in embedded scenarios.

• FoVNet for Smart Glasses: FoVNet uses a configurable field-of-view (FoV) mechanism, allowing the user or upstream module to specify a range of spatial sectors for target-speech enhancement (Xu et al., 2024).
• Hybrid Pipeline: Consists of spatial feature extraction (fixed beamforming for $w_1,\ldots,w_N$2 blocks), an ultra-lightweight neural network for mask estimation (0.2M params, 49MMACS), and a classical multi-channel Wiener filter (MCWF) for low-distortion enhancement. Perceptual quality is refined via a residual-reduction mask.
• Configurable Gating (FiLM-Style): Distinct learnable gating vectors modulate network features depending on block inclusion in desired FoV, allowing flexible adaptation to arbitrary user-specified spatial regions.
• Resource and Latency Profile: The entire pipeline remains within <60 MMACS and 16 ms end-to-end latency, with computational cost split between neural and classic FMA steps.

Significance: This hybrid combination leverages classical filtering for explainable, low-distortion enhancement and neural masking for non-linear discrimination, adapted in a user-configurable manner. It enables robust, parameter-efficient speech enhancement for augmented reality/wearable devices under real-time constraints (Xu et al., 2024).

5. Configurable and Hybrid FMA in Robust Model Training

In DNN learning, “FMA” also denotes Feature Map Augmentation: a regularization loss enforcing feature-invariance to input transformations.

• FMA Loss Specification: For each clean/augmented input pair $w_1,\ldots,w_N$3:

$w_1,\ldots,w_N$4

where $w_1,\ldots,w_N$5 is the set of regularized layers, $w_1,\ldots,w_N$6 is the activation count.

• Configurable CA Finetuning: Distortions are grouped into non-overlapping augmentation pools applied alternately per epoch (e.g., Combined$w_1,\ldots,w_N$7 and Combined$w_1,\ldots,w_N$8), ensuring robustness to multiple distortion types without dataset blow-up.
• Empirical Gains: FMA combined-augmentation finetuning yields +8.94% (CIFAR-10) and +8.04% (ImageNet) absolute accuracy on augmented sets, vastly outperforming single-augmentation or task-only protocols (Kapoor et al., 2020).

Practical Advice: Key configuration knobs include $w_1,\ldots,w_N$9 (FMA loss weight), layer subset $s_N$0 for regularization, and per-augmentation strengths. For memory-constrained settings, regularizing only mid/high-level features is effective.

6. Performance Trade-offs and Design Impact

Configurable and hybrid FMA implementations typically target fundamental reductions in power, area, and compute, with rigorously quantified trade-offs.

Metric	SOTA Layer-Muxed	HYDRA	Improvement
Slice LUTs	112,654	13,550	88.0% ↓
Slice Registers	113,648	7,962	93.0% ↓
Logic Power (W)	0.133	0.01225	91.8% ↓
Signal Power (W)	0.235	0.0117	95.1% ↓
Dynamic Power (W)	0.481	0.025	95.8% ↓
Throughput (GOPS/W)	79.68	35.21	~same order

Static power remains essentially unchanged due to same clocked silicon area; resource improvements and energy efficiency transitions are achieved through architectural re-use and hybridization rather than frequency or supply scaling (Kumar et al., 2024).

Impact: Such FMA architectures enable real-time, low-power execution—in DNN inference, digital signal processing, or filter/mask-based pipelines—on edge-class hardware without sacrificing accuracy or usability under dynamic, application-specific conditions. This suggests broad applicability in energy-, area-, and latency-bounded environments.

7. Generalizations and Future Perspectives

Configurable and hybrid FMA paradigms are extensible to other domains requiring arithmetically minimal, numerically robust, and structurally adaptive kernels.

• Higher-Radix and Other Transforms: Dual-select or multi-select FMA strategies can be applied to radix-$s_N$1 FFTs, DCT/MDCT, and chirp z-transform by runtime selection of the optimal kernel factorization per instance (Bergach, 1 Apr 2026).
• Beyond Arithmetic Units: The use of hybrid architectures that combine neural, statistical, and classical processing (as in FoVNet) is applicable in embedded sensing, speech enhancement, or anytime/adaptive inference.
• Misconceptions: Hybrid/Configurable FMA design does not impose throughput penalties or extra inner-loop complexity; the key methods manipulate only outer control, lookup tables, or top-level scheduling—not the critical arithmetic path.

A plausible implication is that the maturation of configurable and hybrid FMA design will define the scalability and flexibility envelope for future edge AI, real-time signal processing, and robust learning systems.