ALIGN-FL: Alignment in FL, Systems & Hardware

• ALIGN-FL is a multi-framework approach that applies generative component sharing in federated learning to ensure privacy and accommodate heterogeneous models under non-IID conditions.
• It also features state-space alignment methods in federated system identification, using both analytic and optimization-based similarity transformations for stable model aggregation.
• Additionally, ALIGN-FL introduces an online fused alignment operator for floating-point adders, reducing hardware overhead while enhancing speed in parallel reduction tasks.

ALIGN-FL refers to multiple independent frameworks in machine learning and computer engineering, each centered around the concept of "alignment" within distributed settings—primarily federated learning (FL) and floating-point hardware design. The three most prominent usages are: (1) a federated learning system for privacy-preserving knowledge transfer via generative decoders, (2) a state alignment method for system identification in FL, and (3) an online algorithm for multi-term floating-point addition leveraging fused alignment and reduction.

1. Generative Component Sharing in Federated Learning

ALIGN-FL, as described in "ALIGN-FL: Architecture-independent Learning through Invariant Generative component sharing in Federated Learning" (Gulati et al., 15 Dec 2025), addresses robust federated learning under extreme non-IID conditions, such as cross-silo settings where client data domains are almost non-overlapping. Standard FL techniques like FedAvg and FedProx, which transfer parameters or gradients, collapse in such regimes due to the lack of shared data support. ALIGN-FL circumvents this by transmitting only the generative components (i.e., decoders) from client-trained VAEs to the server. The server, in turn, synthesizes pseudo-samples from these decoders and performs global updates.

Key elements:

• Decoupling Architecture: Clients may employ heterogeneous encoders; only the decoder parameters ($G_{c_i}^t \equiv \theta_i$) are transmitted, ensuring model heterogeneity and privacy.
• Training Procedure: Each round, clients update private VAEs (with optional privacy schemes), transmit their decoders, and the server trains a global model solely on synthetic data drawn from these decoders.
• Privacy Enhancements: Two mechanisms are supported: (a) DP-SGD with adaptive gradient clipping and formal $(\epsilon, \delta)$ guarantees; (b) Lipschitz-constrained decoders (LCD-VAE), which impose $L$-Lipschitz continuity via a gradient penalty, structurally obfuscating outliers.

Empirical results demonstrate that this strategy both outperforms traditional parameter aggregation and achieves strong privacy properties, including effective mapping of cross-domain outliers to typical samples under privacy regularization. ALIGN-FL remains effective even when clients utilize divergent architectures, and it achieves superior FID and classification accuracy compared to FedAvg, FedProx, and contrastive synthetic-data baselines. However, utility degrades for more complex data distributions, indicating limitations in scalability to high-resolution or modality-diverse conditions (Gulati et al., 15 Dec 2025).

2. State Alignment in Federated System Identification

An alternative realization is found in the "FedAlign" framework, a state-alignment-centric federated system identification approach (Keçeci et al., 15 Mar 2025). The problem arises because linear state-space models (SSMs) are defined only up to a similarity transform, i.e., multiple parameterizations can encode identical system dynamics. Naively averaging SSM parameters from multiple clients in the federated setting produces unstable, dynamically inconsistent models due to misaligned state representations.

The FedAlign approach belongs to the family of "ALIGN-FL" methodologies focused on parameter basin realignment:

• Similarity Transformation Principle: For each client model $(A_i, B_i, C_i, D_i)$, compute a transform $T_i$ mapping its state representation to a shared parameter basin.
• FedAlign-A: An analytic solution for SISO and certain MIMO systems, leveraging controllable canonical form (CCF). $T_i$ is constructed such that the transformed models converge to an aligned canonical representation.
• FedAlign-O: An optimization-based scheme for general (especially MIMO) cases, minimizing the Frobenius norm distance between transformed client models and a reference via least squares.
• Aggregation: After alignment, model averaging is justified and preserves the fundamental input-output dynamics. The global model is mapped back to each client’s basis post-aggregation.

Experiments on synthetic and real-world control datasets reveal FedAlign’s marked superiority over FedAvg: FedAlign delivers faster convergence, avoids instability, and maintains physical meaning in the global SSM (Keçeci et al., 15 Mar 2025). FedAlign-A is exact but sensitive to conditioning in MIMO; FedAlign-O is robust but computationally heavier due to data-dependent optimization.

3. Online Alignment in Floating-Point Adders

The "ALIGN-FL" designation also refers to a class of hardware algorithms for multi-term floating-point addition (Alexandridis et al., 29 Oct 2024), crucial in workloads such as vector dot products and matrix multiplication. Traditional methods first determine the global maximum exponent before aligning and summing mantissas (fractional parts) serially, inducing pipeline inefficiency and high hardware overhead.

The online ALIGN-FL algorithm:

• Fused Associative Operator: Defines a binary operator, $\otimes_{AF}$, acting on $(\lambda_a, o_a), (\lambda_b, o_b)$ pairs (exponent, fraction). $\otimes_{AF}$ computes $\max$, shift-aligns, and sums the operands in one step: $(E, o_a' + o_b')$ where $E = \max(\lambda_a, \lambda_b)$, $o_a' = o_a \gg (E-\lambda_a)$, $o_b' = o_b \gg (E-\lambda_b)$.
• Reduction Tree: Multiple $\otimes_{AF}$ units are wired in parallel trees (binary, radix-4, mixed-radix) for $N$-term reductions, eliminating the serial dependency on exponent-max detection.
• Associativity: The operator is mathematically associative, enabling arbitrary grouping and pipelining.
• Hardware Implications: Synthesis in 28nm demonstrates 3–23% area and 4–26% power savings, with up to ~17% delay reduction at equivalent pipeline depths. Mixed-radix trees are optimal in balancing comparator/adder/shifter fan-in and pipeline register cost.

This approach is especially advantageous in machine learning accelerators that require high-throughput and low-latency summation for large-scale reductions (Alexandridis et al., 29 Oct 2024).

4. Comparative Summary Table of ALIGN-FL Variants

Domain	Alignment Focus	Key Methodology
Federated VAE/Generative FL (Gulati et al., 15 Dec 2025)	Generative feature	Decoder-only sharing, synthetic data aggregation, DP-SGD, Lipschitz-constrained VAE decoders
Federated System Identification (Keçeci et al., 15 Mar 2025)	State-space parametrization	Similarity transformation to parameter basin (FedAlign-A: analytic, FedAlign-O: optimization-based)
Floating-Point Hardware (Alexandridis et al., 29 Oct 2024)	Exponent/fraction align	Online associative fused operator, reduction trees for parallel exponent alignment/addition

Each methodology solves a class of alignment problem—whether parameters, representations, or data—critical for coherent aggregation in distributed and parallel systems.

5. Open Challenges and Extensions

Each flavor of ALIGN-FL exposes distinct research frontiers:

• Generative FL: Tight $(\epsilon, \delta)$ composition for Lipschitz-constrained VAEs, adaptation to diffusion models or high-resolution data, and privacy-budget trade-offs per-client remain unresolved (Gulati et al., 15 Dec 2025).
• System Identification: Handling severe heterogeneity in state dimension or system order, adaptivity of alignment to evolving local models, and distributed optimization scalability are ongoing concerns (Keçeci et al., 15 Mar 2025).
• Floating-Point Adders: Extension to multi-precision, handling special values (Inf/NaN), register-latency optimization, and integration into accelerator design frameworks are active directions (Alexandridis et al., 29 Oct 2024).

A plausible implication is that alignment-centric algorithms are increasingly foundational in both machine learning and computational hardware domains, as distributed computing architectures become more prevalent and heterogeneous.