AnalogFed: Federated Analog Systems & Circuit Discovery

• AnalogFed is a multi-faceted federated learning approach that leverages analog over-the-air aggregation and hybrid analog-digital communication for efficient model updates.
• It exploits the wireless channel’s superposition property to perform on-air computations, thereby enhancing spectrum utilization and reducing transmission delay.
• The framework extends to privacy-preserving discovery of analog circuit topologies using generative AI, enabling collaborative design without exposing proprietary data.

In recent arXiv literature, “AnalogFed” denotes a family of federated-learning systems in which analog signaling, over-the-air computation (AirComp), or hybrid analog-digital communication is integral to the training loop, and, in a distinct 2025 usage, a federated generative-design framework for analog circuit topology discovery. Across the wireless-learning papers, the central idea is to exploit the superposition property of the wireless multiple access channel so that aggregation is performed “in the air,” or to combine such analog aggregation with selective digital transmission when uncoded analog updates are too noise-sensitive (Sun et al., 2019, Xia et al., 2020, Fujihashi et al., 2022, Abrar et al., 2024, Yao et al., 2024). In the analog-design-automation paper, the same term is used for privacy-preserving collaborative training of a generative model over proprietary circuit-topology datasets, without sharing raw private data (Li et al., 20 Jul 2025).

1. Multiple usages of the term

The literature does not use “AnalogFed” in a single, uniform sense. In some papers it is a convenient label for analog over-the-air federated learning; in others it refers to hybrid communication schemes that mix analog and digital components; in another, it denotes personalized federated learning for mmWave analog beamforming; and in the most explicit naming instance it is the title of a federated framework for analog circuit topology generation (Sun et al., 2019, Fujihashi et al., 2022, Isaksson et al., 2023, Li et al., 20 Jul 2025).

Usage in the literature	Representative paper	Defining feature
Analog over-the-air FL	"Energy-Aware Analog Aggregation for Federated Learning with Redundant Data" (Sun et al., 2019)	wireless MAC used as a computation primitive
Hybrid digital-analog FL	"Federated AirNet: Hybrid Digital-Analog Neural Network Transmission for Federated Learning" (Fujihashi et al., 2022)	digital baseline plus analog residual
Analog-digital scheduled FL	"Analog-digital Scheduling for Federated Learning: A Communication-Efficient Approach" (Abrar et al., 2024)	each device scheduled to OTA analog or orthogonal digital
Analog circuit topology discovery	"AnalogFed: Federated Discovery of Analog Circuit Topologies with Generative AI" (Li et al., 20 Jul 2025)	collaborative topology discovery without sharing raw private data

A common thread across the wireless works is that the server typically needs an aggregate rather than individually decoded client messages. This suggests an “aggregation-first” design philosophy in which the PHY layer is optimized for summation, averaging, or approximate reconstruction of model updates, rather than for reliable per-user packet recovery.

2. Over-the-air analog federation in wireless learning

The canonical AnalogFed-style wireless model treats the uplink multiple access channel as an analog aggregation device. In the AirComp-based FedSplit formulation, the server receives

$$\bm{y}^t = \sum_{n=1}^N h_n^t\bm{x}_n^t + \bm{w}^t,$$

and, after channel inversion and rescaling over the active set $\mathcal B^t$, recovers

$$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$

The same paper couples this analog MAC model with FedSplit proximal updates and a threshold-based device-selection rule

$$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$

so that weak channels do not dominate the common scaling factor $\alpha^t$ (Xia et al., 2020).

A broader comparison between digital and analog wireless FL makes the conceptual distinction explicit: the fundamental difference between the two paradigms lies in whether communication and computation are jointly designed. Digital schemes decouple communication from the FL task, whereas analog schemes allow AirComp and therefore efficient spectrum utilization. In that framework, analog transmission has fixed per-round delay

$T_{\mathrm{A}}=\frac{dM}{B},$

which does not grow with the number of active devices, but it is sensitive to imperfect CSI, channel inversion, and aggregation distortion (Yao et al., 2024).

Early analog-aggregation work already emphasized the same compute-in-the-channel perspective. In "Energy-Aware Analog Aggregation for Federated Learning with Redundant Data" (Sun et al., 2019), the received signal on sub-channel $m$ is

$$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$

so that the parameter server directly observes the sum of scheduled workers’ gradient components up to scaling and noise. That paper is also explicit that analog aggregation alone does not resolve non-IID data effects, a point that remains central in later AnalogFed variants.

3. Hybrid analog-digital extensions

A major development beyond pure over-the-air analog aggregation is the introduction of hybrid schemes that retain analog graceful degradation while adding a digitally protected backbone. Federated AirNet is the clearest example. Its transmission model is

$$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$

where the digital source encoder produces a low-rate coded BPSK baseline on the in-phase component, and the analog branch transmits residual parameters on the quadrature component. The residual is defined by

$\bm{r} = \bm{w} - \bar{\bm{w}},$

and the receiver reconstructs it by

$\mathcal B^t$0

The paper reports better image-classification accuracy than digital-only and analog-only baselines over a wide range of SNRs, with both global and local accuracy exceeding $\mathcal B^t$1 after only two transmission rounds at $\mathcal B^t$2 dB, and about $\mathcal B^t$3 Msymbols on average for model-parameter transmissions at $\mathcal B^t$4 dB (Fujihashi et al., 2022).

ADFL introduces a different hybridization axis: device-level scheduling between OTA analog upload and orthogonal digital upload. Each round begins with the scheduling metric

$\mathcal B^t$5

and the paper proves that, for a fixed number $\mathcal B^t$6 of digital devices, the $\mathcal B^t$7 devices with the smallest SM should be scheduled as digital devices. The global-gradient estimator is then

$\mathcal B^t$8

with $\mathcal B^t$9 the OTA aggregate. Under the reported MNIST setup, ADFL achieves the same accuracy as OTA in $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$0 less time and the same accuracy as BB FL Alternative in $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$1 less time in the i.i.d. case; in the non-i.i.d. case it requires $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$2 less time than BB FL Alternative to reach the same accuracy (Abrar et al., 2024).

A further communication-layer alternative is frequency-modulation aggregation for federated edge learning. That work replaces linear analog amplitude modulation with MFSK plus TBMA, yielding constant-envelope concurrent transmission, no drop in performance up to $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$3 dB, and $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$4 dB less PAPR than the analog DSB benchmark (Martinez-Gost et al., 2023). Although it is not a pure analog scheme, it preserves the superposition-based aggregation logic that motivates AnalogFed-style PHY design.

4. Energy constraints, interference, and adaptive participation

Practical AnalogFed systems are shaped by power constraints, device availability, interference, and non-IID data. "Analog Over-the-Air Federated Learning with Interference-Based Energy Harvesting" (Khel et al., 12 Sep 2025) studies an IoT setting in which devices harvest energy from in-band and out-band RF sources. In-band energy is explicitly “double-edged”: it replenishes batteries but also creates co-channel interference at the parameter server. To avoid CSI acquisition, the paper proposes variance-based denoising with

$$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$5

and an adaptive local-epoch scheduler that selects among full training, one epoch on a fractional dataset, or idling, depending on available battery energy. Its convergence analysis yields an $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$6-type decay in the average gradient norm bound, and the reported simulations show performance comparable to CSI-based denoisers while highlighting that high-power CCI severely degrades learning accuracy (Khel et al., 12 Sep 2025).

Energy-aware analog aggregation appears earlier in the redundant-data setting of (Sun et al., 2019). There, data redundancy $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$7 is introduced so that each original dataset is stored at $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$8 different workers, with each worker using only a fraction $$\hat{\bm{\theta}}^{t+1} = \frac{1}{|\mathcal{B}^t|}\sum_{n\in\mathcal{B}^t}\bm{\theta}_n^t + \frac{\bm{w}^t}{\sqrt{\alpha^t}|\mathcal{B}^t|}.$$9 of stored samples per round. Under non-IID data and energy budget $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$0 J, doubling storage from $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$1 to $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$2 improves accuracy by $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$3, and the Lyapunov-based dynamic policy schedules $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$4 of workers on average versus $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$5 for the myopic rule. The paper is explicit that the benefit comes from improved data diversity rather than from analog aggregation alone (Sun et al., 2019).

The AirComp-based FedSplit analysis adds a complementary robustness result. Under strong convexity and smoothness, the expected objective gap satisfies

$$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$6

which makes the finite wireless error floor explicit in terms of fading threshold $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$7, transmit power $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$8, noise variance $$\beta^t_n = \begin{cases} 0, & |h^t_n| < \gamma,\ 1, & |h^t_n| \ge \gamma, \end{cases}$$9, model dimension $\alpha^t$0, and number of active devices $\alpha^t$1 (Xia et al., 2020).

5. Application-specific usage: mmWave analog beam selection

In another strand of the literature, “AnalogFed” is tied not to analog uplink aggregation but to analog beamforming. "mmWave Beam Selection in Analog Beamforming Using Personalized Federated Learning" (Isaksson et al., 2023) formulates downlink beam selection as a multiclass classification problem. The codebook contains $\alpha^t$2 candidate beams,

$\alpha^t$3

the input is an uplink Sub-6GHz channel estimate $\alpha^t$4, and the label is the best downlink beam index. The learned model predicts $\alpha^t$5, after which the system uses $\alpha^t$6 as the downlink analog beamforming vector.

The paper argues that realistic radio data are strongly non-IID across base stations and therefore combines clustered global models, local models, and a mixture-of-experts personalization strategy. It also introduces FedLion, whose server update is

$\alpha^t$7

In the reported DeepMIMO Outdoor 1 Blockage experiments with $\alpha^t$8 clients and $\alpha^t$9 beams, the personalized approach achieves up to $T_{\mathrm{A}}=\frac{dM}{B},$0 higher accuracy than a single FL model and $T_{\mathrm{A}}=\frac{dM}{B},$1 higher than a local model. Here the “analog” qualifier refers to analog beamforming rather than analog transmission of model updates (Isaksson et al., 2023).

This application-specific use is important because it broadens the scope of AnalogFed beyond AirComp. A plausible implication is that the term has become a shorthand for federated-learning methods specialized to analog-native communication subsystems, even when the FL transport itself is not analog.

6. AnalogFed as federated analog circuit topology discovery

The most explicit and self-contained definition appears in "AnalogFed: Federated Discovery of Analog Circuit Topologies with Generative AI" (Li et al., 20 Jul 2025). That work addresses a different problem: how to train a generative model for analog circuit topology discovery when analog datasets are private, fragmented, and tied to confidential semiconductor processes. The framework uses federated learning so that clients retain local circuit datasets and exchange only model updates.

The model is a decoder-only transformer inspired by AnalogGenie, with $T_{\mathrm{A}}=\frac{dM}{B},$2 layers, $T_{\mathrm{A}}=\frac{dM}{B},$3 attention heads, vocabulary size $T_{\mathrm{A}}=\frac{dM}{B},$4, about $T_{\mathrm{A}}=\frac{dM}{B},$5M parameters, and maximum sequence length $T_{\mathrm{A}}=\frac{dM}{B},$6. Its preprocessing stack includes graph simplification, frequent-subgraph mining with gSpan over more than $T_{\mathrm{A}}=\frac{dM}{B},$7 real-world topologies spanning $T_{\mathrm{A}}=\frac{dM}{B},$8 circuit categories, and sequence optimization via the Chinese Postman Problem. The paper reports that this compression pipeline reduces sequence length by about $T_{\mathrm{A}}=\frac{dM}{B},$9 on average. Federated pretraining uses FedAvg with local update interval $m$0 steps per client per round, mini-batch size $m$1, and $m$2 communication rounds, after which clients can fine-tune locally with PPO using rewards $m$3, $m$4, $m$5, and $m$6 for invalid, valid-but-irrelevant, low-performance relevant valid, and high-performance relevant valid circuits, respectively (Li et al., 20 Jul 2025).

The evaluation uses the AnalogGenie dataset of $m$7 unique analog circuit topologies across $m$8 functional types. In centralized training, the reported generator reaches validity $m$9, scalability $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$0, versatility $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$1, novelty $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$2, MMD $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$3, Op-Amp FoM $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$4, and Power Converter FoM $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$5. Under full-dataset federated training with $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$6 clients, the corresponding values are validity $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$7, novelty $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$8, MMD $$y_m(t)=\sigma_m(t)\sum_{n\in\mathcal{B}(t)}g_{m,n}(t)+z_m(t),$$9, Op-Amp FoM $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$0, and Power Converter FoM $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$1, which the paper describes as very close to centralized performance. As the number of clients increases from $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$2 to $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$3, validity degrades modestly from $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$4 to $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$5 on the full dataset, while the paper also reports stronger degradation when both client count increases and dataset fraction is reduced (Li et al., 20 Jul 2025).

This AnalogFed variant also foregrounds security and privacy in a way that differs from wireless AirComp papers. The two protected assets are circuit IP privacy and process privacy. The paper reports that model poisoning by scaling updates $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$6 and $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$7 increases validation loss by $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$8 and $$x_{i} = x^{\langle\mathsf{d}\rangle}_{i} + \jmath\, x^{\langle\mathsf{a}\rangle}_{i},$$9, respectively, while data poisoning increases validation loss by $\bm{r} = \bm{w} - \bar{\bm{w}},$0. A defense inspired by FLDetector is used to detect, isolate, and recover from malicious clients (Li et al., 20 Jul 2025).

7. Limitations, misconceptions, and open questions

A common misconception is that analog federation is simply an uncoded, always-superior alternative to digital communication. The comparative analysis in (Yao et al., 2024) argues otherwise: analog FL is preferable when the bottleneck is bandwidth and the number of devices is large, because AirComp enables simultaneous uplink aggregation, but digital transmission is preferable when CSI is unreliable or when resource scheduling and power efficiency are more important. The same paper emphasizes that analog performance is sensitive to computational errors arising from imperfect alignment, truncation, and CSI error.

A second misconception is that analog aggregation alone resolves system heterogeneity. The redundant-data study (Sun et al., 2019) shows that non-IID data remain a major bottleneck even when analog aggregation removes the orthogonal-access overhead, which is why it introduces redundancy and Lyapunov-based worker scheduling. The mmWave beam-selection work reaches a related conclusion from another direction: a single global model is too restrictive under quantity skew, class imbalance, and concept shift, motivating clustered models, local adaptation, and mixture-of-experts personalization (Isaksson et al., 2023).

Hybrid papers complicate any simple analog-versus-digital narrative. Federated AirNet can underperform pure analog below about $\bm{r} = \bm{w} - \bar{\bm{w}},$1 dB because the digital threshold is set to $\bm{r} = \bm{w} - \bar{\bm{w}},$2 dB, yet above that regime it improves smoothly and achieves the best accuracy in higher-SNR settings (Fujihashi et al., 2022). ADFL shows that scheduling only a few low-SM devices to digital while keeping most devices on OTA can outperform both OTA-only and digital-only baselines under a delay constraint (Abrar et al., 2024). In the energy-harvesting OTA setting, high-power CCI sharply reduces accuracy, but increasing the number of active devices can partially average out the interference (Khel et al., 12 Sep 2025).

For the circuit-discovery meaning of AnalogFed, the main open issues are different. The paper states that security is not fully solved, communication cost remains a concern, heterogeneity is manageable but still present, fine-tuning depends on local labels and reward models, and the scope is focused on topology generation rather than sizing or layout (Li et al., 20 Jul 2025). Taken together, these limitations suggest that “AnalogFed” is less a single settled architecture than a research direction centered on matching federated optimization to analog-native communication or analog-domain design constraints.