We construct a universal decoder for cyclic Gaussian multiple-input multiple-output channels with intersymbol interference and unknown channel taps and spatial noise covariance. Codewords are drawn independently and uniformly from a sphere of fixed total energy. Under stated bounds on frequency variation, the decoder attains the ensemble-average error exponent of informed maximum-likelihood decoding for fixed channels and channels with growing memory. We approximate the frequency response by a constant matrix within each frequency block. For this auxiliary channel, every matched log-likelihood is affine in a common sufficient statistic. At fixed received output, we compute the statistic density of an independent competitor. The decoder selects the candidate with the smallest statistic density, equivalently minimizing a weighted sum of residual log-determinants. The density and its support volume give an upper bound on the universal competitor probability. Affinity ensures that at least half of a suitable symmetric neighborhood of the transmitted statistic has matched likelihood no smaller than that of the transmitted word. Integrating a density lower bound over this half gives the matched competitor bound. These bounds establish equality of error exponents, which a Gaussian channel comparison transfers to the original channel. The same decoder attains the matched exponent for independent frequency blocks with prescribed energies satisfying the stated conditions. For energies proportional to block length, an additional gain condition ensures that this exponent is at least that of the total-energy spherical ensemble.
A learning architecture induces a prior over its expressible models. Recent work links architectural success to a broad complexity spectrum: model probabilities spanning many orders of magnitude. Understanding how depth shapes these priors and prediction may help explain the success of neural networks and transformers. We study this connection in large-alphabet prediction through the *layered simplex architecture* (LSA), which multiplies independent uniform simplex vectors coordinate-wise and normalizes. At depth zero, the prior is concentrated on the uniform distribution; at depth one, the Bayesian predictor is Laplace's rule. Each additional layer shifts prior mass toward more concentrated distributions. We derive exact Bayesian marginal likelihood and regret expressions using reusable depth-specific kernels. Mixing over depths up to a cutoff logarithmic in alphabet size yields an explicit predictor with rigorous guarantees. For targets uniform on a specified sparse support, the mixture's prior complexity is asymptotic to the support-description cost at every fixed positive KL resolution, establishing a broad complexity spectrum. We also prove a regret lower bound for every label-invariant predictor: the expected description length of the discovered symbol set minus the source's uncertainty about its identity given its size. For Zipf sources in a growing-alphabet regime, the depth mixture attains this bound to leading order. Thus, the symbol-discovery rate determines the regret exponent. Although introduced to study depth, the LSA predictor competes with established large-alphabet methods, including Good--Turing, Ristad's law and an adaptive Dirichlet mixture, while substantially outperforming classical add-constant rules on concentrated sources.