The Inference Report

Pilot-aided channel estimation is a decisive block in orthogonal frequency-division multiplexing (OFDM) receivers for both 5G New Radio (5G-NR) and Long-Term Evolution (LTE). A large body of estimators exists, from simple least-squares (LS) interpolation to statistically optimal linear minimum-mean-square-error (LMMSE) variants and, more recently, deep convolutional denoisers, yet no single estimator is uniformly best: the winner depends on the propagation scenario, the numerology, the operating signal-to-noise ratio (SNR), the mobility (Doppler), and the antenna configuration. In this paper, we quantify this fact through a unified study of eight literature estimators evaluated over the 3GPP TR~38.901 Urban-Macro (UMa), Urban-Micro (UMi), and Rural-Macro (RMa) channels generated with NVIDIA Sionna, for both 5G-NR and LTE numerologies, in single-input single-output (SISO) and $8\times2$ multiple-input multiple-output (MIMO) settings. We then propose a \emph{condition-adaptive multi-agent orchestrator} that treats each estimator as an independent agent and dispatches, per operating condition, to the agent that is best on a validation split without any genie knowledge. The orchestrator tracks the per-realization oracle to within $1.07$~dB and improves the normalized mean-square error (NMSE) over the best \emph{fixed} strategy by up to $3.6$~dB at high SNR, where the low-SNR champion is no longer optimal. Because the agents are independent, running them concurrently delivers this best-of-eight accuracy at essentially single-estimator latency: a data-parallel partition scales the wall-clock nearly as $1/K$ with $K$ workers (up to $6.9\times$), whereas naive by-algorithm partitioning is Amdahl-limited by the heaviest agent. The results substantiate multi-agent orchestration as a practical route to robust channel estimation across heterogeneous 5G-NR/LTE deployments.

The Schrödinger bridge owes its computational power to a single structural fact: by Girsanov's theorem the controlled problem is a Kullback--Leibler (KL) projection onto a fixed reference measure, solvable by alternating projections. This letter shows that the fact does not survive risk sensitivity. When the expected path cost is replaced by the entropic risk measure and both endpoint marginals are kept as hard constraints, the resulting fixed-point bridge value $J_θ$ (the soft-problem value at the multiplier that enforces the terminal constraint) admits no representation as a constrained KL minimum against any fixed path-space reference with a regular endpoint law (a class strictly larger than the uniformly elliptic diffusion references: no Markov property is required), even allowing an additive normalisation depending on the initial marginal. Moreover, no single reference generates the one-parameter family in the risk parameter. The obstruction is computed in closed form: the Gaussian bridge value violates, by exactly $θ/2$, a heat equation that any Gaussian smoothing of a fixed endpoint density must obey. In place of the projection, the theory rests on a terminal-multiplier fixed point and an asymmetric factorisation penalising the score energy of the backward factor.

We study latent-space watermarking through a pretrained generator using a prescribed latent-to-output stochastic mapping, called the renderer. A watermark encoder selects the latent input using a message and secret key. For every message and semantic context, the released output must have exactly the desired conditional output distribution. For finite alphabets, we derive rate--key inner and outer bounds and characterize the coding and coordination requirements for realizing watermark communication through the prescribed latent interface. When the target output distribution of the generator uniquely determines the corresponding latent input distribution through the renderer, a strengthened converse yields the capacity region; the same region governs explicit preservation of the pretrained latent distribution. We extend the analysis to general jointly Gaussian models and identify a sufficient statistic of the latent that captures both the watermark-bearing information available at the generated output and the latent coordination required to preserve its target distribution. For the vector Gaussian model, we further characterize the optimal allocation of the secret-key resource across the resulting modes. Finally, we turn to an emerging robustness threat that is particularly natural in generative watermarking: an adversary can regenerate the released sample to obtain a fresh realization of the same underlying content while attenuating or destroying the embedded watermark. We incorporate this robustness axis into our framework and characterize the one-pass compound capacity of the scalar Gaussian model when the semantic context is known to the encoder but hidden from the detector, while the regeneration attack may depend on that context. Extending the analysis to multiple rounds of repeated canonical regeneration, we characterize the resulting watermark-capacity decay.

We propose a pragmatic information theory unifying communication, control, and decision-making. Its core is the isoteleia mapping, formalizing equifinality: distinct semantic paths leading to the same optimal action are pragmatically equivalent. This induces a three-tier hierarchy of syntactic, semantic, and pragmatic information, each abstraction discarding task-irrelevant distinctions. We develop pragmatic entropy, up/down mutual information, channel capacity, and rate-distortion, and prove three coding theorems generalizing Shannon's classical results. We introduce pragmatic value (VoI) and cost (CoI) of information as decision-theoretic duals to rate-distortion and capacity, respectively, and formulate a Lagrangian dual framework for cross-layer optimization. The pragmatic efficiency bound $\mathcal{E}_p(λ)=\sup_R[Φ_p(R)-λ\,\mathrm{CoI}_p(R)]$ quantifies the maximum net utility any resource-constrained intelligent system can extract, thereby establishing a fundamental behavioral capacity limit---generalizing Shannon's symbol-level capacity to goal-directed action. Extensions to continuous messages yield closed-form Gaussian expressions, while dynamic settings are addressed via a Bellman equation for sequential decision-making. This framework provides a rigorous foundation for task-oriented communication, networked control, autonomous systems, and embodied AI, shifting focus from symbol fidelity to the effectiveness of information in guiding actions, and offers a unified mathematical language for next-generation intelligent systems.

To mitigate the scalability bottleneck in the radio access network (RAN) in federated edge learning (FEEL), over-the-air federated learning (AirFL) exploits waveform superposition over multiple-access channels (MACs) for analog model aggregation. However, coherent AirFL typically relies on stringent PHY-layer conditions such as accurate channel state information (CSI), tight time/frequency synchronization, and frequent transceiver calibration for signal alignment. However, these requirements, if not impossible to be met, incur substantial communication and computation overhead. In this paper, we propose a non-coherent AirFL (NCAirFL) protocol over a broadband single-antenna MAC, leveraging binary dithering, unbiased non-coherent detection, and long-term error feedback to waive the need for instantaneous CSI. For NCAirFL with general smooth non-convex objectives and a constant learning rate, we establish a convergence bound achieving the convergence rate in the same order of $\mathcal{O}(1/\sqrt{T})$ as communication-ideal FedAvg, where $T$ is the total number of communication rounds. To further improve communication efficiency under data and wireless resource heterogeneity, we also derive a lower bound on the expected single-round objective decrease in the global loss conditioned on device scheduling, building upon which a surrogate objective function is obtained for jointly optimal device selection and power control. Experimental results on MNIST and CIFAR-10 corroborate that NCAirFL achieves learning performance close to FedAvg in practical settings, with the proposed device scheduling policy substantially accelerating convergence.

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation $\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1$ is recovered as $d\to\infty$: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite $d$, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.