aiqbench analysis
This empirical audit reveals that standard per-channel linear projections are practically equivalent to more complex alternatives for multi-channel signal transformers, largely due to the spontaneous orthogonalization of projection vectors. While shared-scalar baselines fail information-theoretically and channel-independent architectures overfit, the study confirms that elaborate encoders are only necessary for specific high-channel-count scenarios. The practical takeaway for engineers is to default to simple linear projections unless task-specific constraints demand otherwise.
An Empirical Audit of Input Encoders for Multi-Channel Signal Transformers
arXiv:2606.04752v2 Announce Type: replace Abstract: Transformers consuming multi-channel scalar signals must embed $C$ simultaneous values into one $d_{\text{model}}$-dimensional vector per time step. We audit eight input encoders -- a shared-scalar baseline, per-channel linear projections, an orthogonality regulariser, a nonlinear MLP, block-partitioned concatenation, channel-independent and channel-as-token architectures, and a projected positional encoding -- on a synthetic benchmark where channel identity is informative and on ETTh1, scored by next-step negative log-likelihood. The headline is practical near-equivalence within a wide "top tier": the standard per-channel linear projection matches every alternative up to small, statistically real but practically modest differences. A direct geometric probe attributes this to a spontaneous orthogonalisation of the per-channel projections: they end up near-orthogonal with no explicit regulariser, letting the standard linear recover channel identity from the summed embedding. Two encoders lose decisively: the shared-scalar baseline collapses for information-theoretic reasons we make explicit, and the channel-independent PatchTST-spirit baseline overfits universally on the synthetic benchmark and underperforms on both. Paired tests resolve two small gaps: projecting the sinusoidal positional encoding through a learned linear layer edges the rest at small $C$ by extending this orthogonality to the positional subspace; a nonlinear MLP stem edges them at the largest $C$, with the gap shrinking under more training data. The practical recommendation: use the standard per-channel linear projection by default; reach for something more elaborate only when the task calls for it.
Abstract:Transformers consuming multi-channel scalar signals must embed $C$ simultaneous values into one $d_{\text{model}}$-dimensional vector per time step. We audit eight input encoders -- a shared-scalar baseline, per-channel linear projections, an orthogonality regulariser, a nonlinear MLP, block-partitioned concatenation, channel-independent and channel-as-token architectures, and a projected positional encoding -- on a synthetic benchmark where channel identity is informative and on ETTh1, scored by next-step negative log-likelihood. The headline is practical near-equivalence within a wide "top tier": the standard per-channel linear projection matches every alternative up to small, statistically real but practically modest differences. A direct geometric probe attributes this to a spontaneous orthogonalisation of the per-channel projections: they end up near-orthogonal with no explicit regulariser, letting the standard linear recover channel identity from the summed embedding. Two encoders lose decisively: the shared-scalar baseline collapses for information-theoretic reasons we make explicit, and the channel-independent PatchTST-spirit baseline overfits universally on the synthetic benchmark and underperforms on both. Paired tests resolve two small gaps: projecting the sinusoidal positional encoding through a learned linear layer edges the rest at small $C$ by extending this orthogonality to the positional subspace; a nonlinear MLP stem edges them at the largest $C$, with the gap shrinking under more training data. The practical recommendation: use the standard per-channel linear projection by default; reach for something more elaborate only when the task calls for it.
21 pages, 1 figure, 8 tables. Code: this https URL
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.04752 [cs.LG]
(or arXiv:2606.04752v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.04752 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 329 words
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