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arxiv: 2604.19993 · v1 · submitted 2026-04-21 · 💻 cs.AR · cs.LG

Recognition: unknown

Algorithm and Hardware Co-Design for Efficient Complex-Valued Uncertainty Estimation

Zehuan Zhang , Mark Chen , He Li , Wayne Luk
Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:55 UTC · model grok-4.3

classification 💻 cs.AR cs.LG
keywords complex-valued neural networksBayesian inferencedropoutuncertainty quantificationFPGA acceleratorsneural architecture searchhardware-software co-designalgorithm-hardware co-design
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The pith

Bayesian dropout enables uncertainty quantification directly in complex-valued neural networks with hardware-efficient implementations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to bring uncertainty estimation to complex-valued neural networks by extending dropout-based Bayesian methods to handle complex arithmetic. This is important for applications like signal processing where complex numbers are natural but confidence in predictions has been hard to obtain. The dual nature of complex values creates new opportunities for mixing real and imaginary components across layers, which an automated search exploits to find configurations that are both accurate and hardware-friendly. A framework then generates optimized FPGA accelerators from these designs, delivering large speedups and low power use compared to GPU baselines. If successful, this makes complex-valued models practical for embedded or real-time systems that require both accuracy and reliability estimates.

Core claim

We propose, for the first time, dropout-based Bayesian Complex-Valued Neural Networks (BayesCVNNs) to enable uncertainty quantification for complex-valued applications, exhibiting broad applicability and efficiency for hardware implementation due to modularity. As the dual-part nature of complex values broadens the design space with novel layer-mixing and part-mixing configurations, an automated search identifies optimal setups for real and imaginary parts. A framework generates customized FPGA-based accelerators using optimized building blocks, with experiments showing the best configurations attain higher performance with lower hardware costs.

What carries the argument

dropout-based variational inference extended to complex-valued layers combined with automated search over layer-mixing and part-mixing configurations

Load-bearing premise

That dropout remains a valid variational approximation to Bayesian inference when the network weights and operations are complex-valued rather than real-valued.

What would settle it

Observing whether the uncertainty estimates from BayesCVNNs are well-calibrated on a complex-valued test set, or whether the automatically searched configurations use fewer hardware resources than the best manually designed ones while maintaining or improving accuracy.

Figures

Figures reproduced from arXiv: 2604.19993 by He Li, Mark Chen, Wayne Luk, Zehuan Zhang.

Figure 1
Figure 1. Figure 1: Bayesian Layer Configurations. By contrast, in real domains, the Bayesian layer configuration is fixed. Therefore, BayesCVNNs exhibit a 3 𝑁 times larger design space than BayesNNs in real domains, offering flexibility to explore trade-offs between accuracy, uncertainty, and hardware costs. 4 Framework for Accelerator Generation A framework is developed to produce the optimal model configura￾tion and genera… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the Framework. 4.3 Hardware Mapping Existing Qkeras libraries do not support complex layers. To enable the construction of BayesCVNNs, we develop a set of building blocks with hardware mapping schemes. According to operational characteristics, complex layers can be categorized into three classes. The first class includes complex convolutional and complex fully connected layers, both requiring f… view at source ↗
Figure 3
Figure 3. Figure 3: Pseudocode of Bernoulli Dropout. 5 Experiments and Evaluation The proposed BayesCVNNs are implemented using PyTorch 1.9.0. Vivado-HLS 2019.2 is used for hardware implementation. QKeras 0.9.0 is used for quantization. The produced C-synthesis reports provide the performance of latency and resource consumption. The place-and-route optimizations are implemented by Vivado 2019.2 for the final designs. The FPGA… view at source ↗
Figure 4
Figure 4. Figure 4: Search Results of Complex-Valued Tasks. 5.2 Analysis of Mapping Schemes The performance difference between the two mapping schemes comes from the exploited reusability. To quantitatively investigate the effects, we take complex fully connected layers as an exam￾ple. We generate and synthesize the core operations, i.e. four sub￾operations, with varying input and output dimensions. The input dimension is set… view at source ↗
Figure 5
Figure 5. Figure 5: Resource and Latency of Mapping Schemes. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Resource Utilization of Different Models. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

Complex-Valued Neural Networks (CVNNs) have significant advantages in handling tasks that involve complex numbers. However, existing CVNNs are unable to quantify predictive uncertainty. We propose, for the first time, dropout-based Bayesian Complex-Valued Neural Networks (BayesCVNNs) to enable uncertainty quantification for complex-valued applications, exhibiting broad applicability and efficiency for hardware implementation due to modularity. Furthermore, as the dual-part nature of complex values significantly broadens the design space and enables novel configurations based on layer-mixing and part-mixing, we introduce an automated search approach to effectively identify optimal configurations for both real and imaginary components. To facilitate deployment, we present a framework that generates customized FPGA-based accelerators for BayesCVNNs, leveraging a set of optimized building blocks. Experiments demonstrate the best configuration can be effectively found via the automated search, attaining higher performance with lower hardware costs compared with manually crafted models. The optimized accelerators achieve approximately 4.5x and 13x speedups on different models with less than 10% power consumption compared to GPU implementations, and outperform existing work in both algorithm and hardware aspects. Our code is publicly available at: https://github.com/zehuanzhang/BayesCVNN.git.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes the first dropout-based Bayesian Complex-Valued Neural Networks (BayesCVNNs) for predictive uncertainty quantification in CVNNs. It introduces an automated search over layer-mixing and part-mixing configurations to optimize accuracy and hardware cost, together with a modular FPGA accelerator generation framework that produces custom accelerators from optimized building blocks. Experiments are said to show that the search finds superior configurations and that the resulting accelerators deliver ~4.5× and 13× speedups versus GPU baselines at <10% power.

Significance. If the central claims are substantiated, the work would provide a practical route to uncertainty-aware complex-valued models together with hardware co-design, which is relevant for signal-processing and communications applications. Public release of the code is a clear positive.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Experiments): the claim that the automated search attains “higher performance with lower hardware costs” and that accelerators achieve 4.5×/13× speedups rests on unspecified datasets, baselines, uncertainty calibration metrics (e.g., ECE, NLL), and synthesis results. Without these details the experimental support for the co-design claim cannot be evaluated.
  2. [§3] §3 (BayesCVNN construction): the paper applies real-valued dropout (layer-wise or part-wise) inside complex multiplication and addition to obtain a variational posterior, yet provides no calibration study, comparison against exact inference, or analysis of whether the induced variational family respects the circular geometry of complex posteriors. This assumption is load-bearing for the entire uncertainty-quantification claim.
minor comments (2)
  1. [§3] Notation for real/imaginary part mixing and the precise definition of the search space (layer-mixing vs. part-mixing) should be formalized with a small table or diagram early in §3 to improve readability.
  2. [Abstract] The abstract states “outperform existing work in both algorithm and hardware aspects” without naming the prior CVNN or Bayesian hardware papers being compared; a short related-work paragraph or table would clarify the novelty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments highlight important areas for clarification and strengthening, particularly around experimental details and theoretical justification of the variational approximation. We address each point below and commit to revisions that improve the manuscript without misrepresenting our contributions.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Experiments): the claim that the automated search attains “higher performance with lower hardware costs” and that accelerators achieve 4.5×/13× speedups rests on unspecified datasets, baselines, uncertainty calibration metrics (e.g., ECE, NLL), and synthesis results. Without these details the experimental support for the co-design claim cannot be evaluated.

    Authors: We agree that the abstract and experimental section would benefit from greater specificity to allow full evaluation of the claims. In the revised version, we will explicitly name the datasets (complex-valued signal processing and communications benchmarks used in §4), detail the GPU baselines (including hardware platforms and software implementations), report uncertainty calibration metrics such as ECE and NLL alongside accuracy, and expand the synthesis results with concrete FPGA metrics (resource utilization, latency, power). These additions will directly support the co-design performance claims. revision: yes

  2. Referee: [§3] §3 (BayesCVNN construction): the paper applies real-valued dropout (layer-wise or part-wise) inside complex multiplication and addition to obtain a variational posterior, yet provides no calibration study, comparison against exact inference, or analysis of whether the induced variational family respects the circular geometry of complex posteriors. This assumption is load-bearing for the entire uncertainty-quantification claim.

    Authors: We acknowledge the importance of validating the variational approximation. Our method extends the established real-valued dropout variational inference to CVNNs via layer-wise and part-mixing strategies applied to complex operations. Exact inference is intractable for networks of this size (as is standard in the BNN literature), precluding direct comparison. In the revision we will add: (i) a discussion of how the part-mixing and layer-mixing configurations preserve key complex properties, (ii) empirical calibration results using ECE and NLL, and (iii) analysis of the induced posterior relative to circular symmetry. This strengthens the uncertainty-quantification foundation while preserving the paper's focus on the novel co-design. revision: partial

Circularity Check

0 steps flagged

No circularity: novel BayesCVNN construction and search evaluated empirically

full rationale

The paper introduces dropout-based variational inference for complex-valued networks as a new construction, along with an automated search over layer-mixing and part-mixing configurations whose outputs are measured against external GPU baselines and manual designs. No derivation step reduces to a self-definition, fitted parameter renamed as prediction, or load-bearing self-citation chain; the central claims rest on empirical validation rather than tautological equivalence to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the unstated premise that dropout variational inference transfers to complex arithmetic without invalidating the uncertainty estimates and that the expanded mixing search space contains practically superior points. No free parameters, axioms, or invented physical entities are explicitly introduced in the abstract.

pith-pipeline@v0.9.0 · 5521 in / 1243 out tokens · 56924 ms · 2026-05-10T00:55:36.855274+00:00 · methodology

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