Geometric Inductive Biases for Semi-Supervised Equalization: The Constellation-Aware Transformer

arXiv:2609.33695v1 Announce Type: new Abstract: Decoding signals over unknown channels with minimal pilot overhead is a critical challenge in next-generation communications. Existing deep learning approaches typically rely on generic encoders that struggle to model long-range temporal dependencies or efficiently capture the channel's physical properties from scarce data. We argue that standard architectures suffer from agnostic estimation gaps, as they must implicitly learn the constellation geometry that is already known. We introduce the Constellation-Aware Transformer (CAT), a novel architecture that explicitly injects geometric inductive biases into the equalization process. CAT is composed of a stack of custom TransFIRmer blocks, which use an "early interaction" paradigm to co-process received signals and ideal constellation symbols. Each block features a split Feed-Forward Network that applies a Finite Impulse Response (FIR)-inspired filter for deconvolution and a parallel MLP for geometric refinement. We show that this design is structurally aligned with the optimal linear (MIMO Wiener) receiver: its attention can implement a matched-filter bank, and its bidirectional FIR branch provides the non-causal filtering that block MMSE equalization requires. In the semi-supervised setting, CAT needs fewer pilots than VAE and standard Transformer baselines: on two of our three ISI channels, it reaches a lower SER with 64 pilots than they do with 128.

Abstract:Decoding signals over unknown channels with minimal pilot overhead is a critical challenge in next-generation communications. Existing deep learning approaches typically rely on generic encoders that struggle to model long-range temporal dependencies or efficiently capture the channel's physical properties from scarce data. We argue that standard architectures suffer from agnostic estimation gaps, as they must implicitly learn the constellation geometry that is already known. We introduce the Constellation-Aware Transformer (CAT), a novel architecture that explicitly injects geometric inductive biases into the equalization process. CAT is composed of a stack of custom TransFIRmer blocks, which use an "early interaction" paradigm to co-process received signals and ideal constellation symbols. Each block features a split Feed-Forward Network that applies a Finite Impulse Response (FIR)-inspired filter for deconvolution and a parallel MLP for geometric refinement. We show that this design is structurally aligned with the optimal linear (MIMO Wiener) receiver: its attention can implement a matched-filter bank, and its bidirectional FIR branch provides the non-causal filtering that block MMSE equalization requires. In the semi-supervised setting, CAT needs fewer pilots than VAE and standard Transformer baselines: on two of our three ISI channels, it reaches a lower SER with 64 pilots than they do with 128.

Machine Learning (cs.LG); Information Theory (cs.IT); Signal Processing (eess.SP)

arXiv:2609.33695 [cs.LG]

(or arXiv:2609.33695v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.33695 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Geometric Inductive Biases for Semi-Supervised Equalization: The Constellation-Aware Transformer

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