Distribution Learning in Semantic Communication

• Distribution learning in semantic communication is the process of transmitting probability distributions that represent latent semantic information rather than raw symbol sequences.
• It reformulates fidelity through semantic rate–distortion measures, addressing practical challenges such as channel noise, distribution shifts, and communication rate constraints.
• Key methods include learning posteriors over hypotheses, adapting to sequential observations, and aligning latent representations across agents for robust inference.

Searching arXiv for recent and foundational papers on distribution learning in semantic communication. arXiv search query: "distribution learning semantic communication sequential observations". Distribution learning in semantic communication denotes a class of formulations in which the communicated object is not merely a symbol sequence but a probability distribution that encodes task-relevant meaning, model uncertainty, reasoning behavior, or latent semantic structure. In the current literature, this includes optimizing a posterior over a hypothesis class from examples and then communicating that posterior under a rate constraint, recovering an unknown prior over meanings from sequential received symbols, and matching or adapting distributions over reasoning paths, vocabulary outputs, or latent representations under distribution shift and channel noise (Pase et al., 2023, Lahoud et al., 14 Aug 2025). The unifying feature is that fidelity is evaluated in semantic or task space rather than by symbol-wise reconstruction.

1. Problem formulations and semantic objects

A canonical formulation treats a concept as an unknown and potentially stochastic map that is observed only through examples. In the time-sequence setting, one observes $n$ i.i.d. draws $C_1,\dots,C_n \sim P_C$, where each $C_i\in\mathcal C$ is itself a conditional distribution $p_{C_i}(Y\mid X)$ on $\mathcal X\times\mathcal Y$. The concept is never observed directly; instead, for each $i$ one collects a dataset

$$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$

with all samples i.i.d. given $C_i$. A finite hypothesis class is fixed as

$\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$

with $\Phi(\mathcal Y)$ the set of all distributions on $C_1,\dots,C_n \sim P_C$0, and a generic prior distribution on $C_1,\dots,C_n \sim P_C$1 denoted $C_1,\dots,C_n \sim P_C$2 (Pase et al., 2023).

The learning stage maps each dataset $C_1,\dots,C_n \sim P_C$3 to a belief over models. A possibly randomized learning algorithm

$C_1,\dots,C_n \sim P_C$4

produces a posterior or belief on $C_1,\dots,C_n \sim P_C$5. Model quality is evaluated through a bounded per-sample loss $C_1,\dots,C_n \sim P_C$6, extended to beliefs by

$C_1,\dots,C_n \sim P_C$7

The corresponding true loss under concept $C_1,\dots,C_n \sim P_C$8 is

$C_1,\dots,C_n \sim P_C$9

In this setup, the source to be communicated is the learned distribution $C_i\in\mathcal C$0, and the receiver reconstructs a belief $C_i\in\mathcal C$1 whose semantic quality is measured by the true-risk gap rather than by parameter-space distance (Pase et al., 2023).

This differs from classical statistical learning in a specific way stated explicitly in the literature. In classical distribution learning, one fixes $C_i\in\mathcal C$2, observes i.i.d. data $C_i\in\mathcal C$3, and minimizes empirical or regularized risk to pick a point estimate $C_i\in\mathcal C$4 or a posterior $C_i\in\mathcal C$5, with no communication constraint and with generalization bounds controlling $C_i\in\mathcal C$6. In semantic communication, a communication-rate constraint is imposed on how much information about $C_i\in\mathcal C$7 can be conveyed to a remote receiver; the posterior distribution itself becomes the source, and fidelity is measured by $C_i\in\mathcal C$8 rather than by symbol accuracy or parameter error (Pase et al., 2023).

2. Posterior communication and semantic rate–distortion

The semantic distortion between transmitter and receiver beliefs for a single concept is defined as

$C_i\in\mathcal C$9

This converts posterior transmission into a rate–distortion problem: the transmitter must send enough bits so that the receiver’s distribution $p_{C_i}(Y\mid X)$0 remains close to the transmitter’s target $p_{C_i}(Y\mid X)$1 in semantic distortion (Pase et al., 2023).

In the long-blocklength limit, the minimum rate to achieve average distortion at most $p_{C_i}(Y\mid X)$2 is characterized by

$p_{C_i}(Y\mid X)$3

With a fixed pre-data distribution $p_{C_i}(Y\mid X)$4, the same bound is expressed through average Kullback–Leibler divergence: $p_{C_i}(Y\mid X)$5 These characterizations make the communication of learned beliefs an information-theoretic source-coding problem whose source alphabet is a family of posterior distributions rather than raw observations (Pase et al., 2023).

A complementary bound controls the distortion–rate function under a max-distortion criterion. If $p_{C_i}(Y\mid X)$6 for all $p_{C_i}(Y\mid X)$7, and $p_{C_i}(Y\mid X)$8 denotes the excess rate relative to the rate $p_{C_i}(Y\mid X)$9 needed to send the unconstrained optimal $\mathcal X\times\mathcal Y$0, then

$\mathcal X\times\mathcal Y$1

The proof outline uses strong coordination, total variation control of changes in expected loss, Pinsker and Bretagnolle–Huber inequalities, and a Pythagorean KL-projection argument (Pase et al., 2023).

The coordination interpretation is central. Empirical coordination asks that the type of the pairs $\mathcal X\times\mathcal Y$2 converges to a desired $\mathcal X\times\mathcal Y$3, and the minimum rate is $\mathcal X\times\mathcal Y$4, corresponding exactly to the average-distortion formulation. Strong coordination asks that the joint law of $\mathcal X\times\mathcal Y$5 converges in total variation to the i.i.d. product $\mathcal X\times\mathcal Y$6; with enough common randomness, the required rate is the same $\mathcal X\times\mathcal Y$7, and strong coordination guarantees the per-model distortion bound $\mathcal X\times\mathcal Y$8. A recurrent misconception is therefore that average semantic distortion automatically yields stronger per-instance guarantees. The formal connection in fact distinguishes empirical and strong coordination, and the two coincide in rate only under the conditions stated above (Pase et al., 2023).

3. Sequential observations, identifiability, and learnability

A second line of work studies distribution learning in the literal sense of learning an unknown meaning prior from repeated observations of a semantic channel. The semantic source has vocabulary $\mathcal X\times\mathcal Y$9 with unknown prior $i$0, the encoder alphabet is $i$1, and the encoder–channel–decoder chain induces an effective transmission matrix

$i$2

The receiver observes $i$3 i.i.d. from $i$4 and forms the empirical frequency

$i$5

The distribution-learning task is to recover $i$6 by solving

$i$7

When $i$8, the unique least-squares solution is

$i$9

(Lahoud et al., 14 Aug 2025).

The identifiability condition is exact: the prior $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$0 is identifiable from $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$1 if and only if $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$2. If $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$3, then $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$4 is invertible and the inverse mapping is unique. If $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$5, there exists a nonzero vector in the kernel of $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$6, so multiple valid priors can induce the same received distribution. This makes full column rank a necessary and sufficient condition for learnability (Lahoud et al., 14 Aug 2025).

Once $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$7, the finite-sample estimator satisfies

$$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$8

Thus convergence is $$S_i=\{z_{i,1},\dots,z_{i,m}\},\qquad z_{i,j}=(x_{i,j},y_{i,j})\sim p_{C_i}(X)\,p_{C_i}(Y\mid X),$$9, with constants governed by the smallest singular value $C_i$0. If semantic distortion is defined through a bounded per-meaning distortion $C_i$1, and if $C_i$2 is the semantic distortion gap between using the estimated prior and the true prior, then

$C_i$3

Estimation error therefore translates directly into semantic distortion degradation, again with explicit dependence on $C_i$4 (Lahoud et al., 14 Aug 2025).

This framework also reveals a design tension. Encoding schemes optimized for immediate semantic performance can collapse columns of $C_i$5, destroy rank, or make $C_i$6 very small. The paper formalizes this with an instantaneous design objective $C_i$7 and a learnability constraint $C_i$8, together with the requirement that $C_i$9 be large for fast learning. A Lagrangian balance is proposed by adding a penalty $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$0 for small singular values (Lahoud et al., 14 Aug 2025).

The CIFAR-10 validation illustrates the conditioning effect. With $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$1 meanings, $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$2, and identity channel so that $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$3, three full-rank encoders were studied: a well-conditioned design with $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$4 and $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$5, a moderate design with $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$6 and $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$7, and an ill-conditioned design with $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$8 and $\mathcal H=\{h:\mathcal X\to\Phi(\mathcal Y)\},$9. All three followed $\Phi(\mathcal Y)$0, but to reach $\Phi(\mathcal Y)$1 the well-conditioned system needed approximately $\Phi(\mathcal Y)$2 samples, the moderate system approximately $\Phi(\mathcal Y)$3, and the ill-conditioned system more than $\Phi(\mathcal Y)$4. At $\Phi(\mathcal Y)$5, final accuracy was $\Phi(\mathcal Y)$6, $\Phi(\mathcal Y)$7, and $\Phi(\mathcal Y)$8, respectively. This directly contradicts the common assumption that formal identifiability alone is sufficient for practical learnability; conditioning is decisive even when rank is preserved (Lahoud et al., 14 Aug 2025).

4. Adaptation under dynamic data, out-of-distribution inputs, and channel noise

Several systems interpret distribution learning as the adaptation of a semantic encoder or decoder to a changing source distribution. In a task-unaware transmitter setting, the semantic-coding network consists of an encoder $\Phi(\mathcal Y)$9, a decoder $C_1,\dots,C_n \sim P_C$00, and a fixed pragmatic function $C_1,\dots,C_n \sim P_C$01. Over an AWGN channel, the transmitter sends $C_1,\dots,C_n \sim P_C$02, the receiver observes $C_1,\dots,C_n \sim P_C$03, and reconstructs $C_1,\dots,C_n \sim P_C$04 and $C_1,\dots,C_n \sim P_C$05. The per-sample semantic distortion is

$C_1,\dots,C_n \sim P_C$06

where $C_1,\dots,C_n \sim P_C$07 measures reconstruction error and $C_1,\dots,C_n \sim P_C$08 measures task error. Training is receiver-leading: the receiver computes $C_1,\dots,C_n \sim P_C$09 and $C_1,\dots,C_n \sim P_C$10, feeds back $C_1,\dots,C_n \sim P_C$11, and the transmitter updates

$C_1,\dots,C_n \sim P_C$12

without ever seeing $C_1,\dots,C_n \sim P_C$13 or $C_1,\dots,C_n \sim P_C$14. To address dynamic data, a cycle-GAN-based data-adaptation network learns a generator $C_1,\dots,C_n \sim P_C$15 that translates newly observed data into the form of library data. The overall minimax objective is

$C_1,\dots,C_n \sim P_C$16

The framework further defines an $C_1,\dots,C_n \sim P_C$17-divergence to measure discrepancy between library and observed domains and to guide when to trigger data adaptation (Zhang et al., 2022).

Empirically, this receiver-leading and cycle-GAN-based system was reported to be adaptive to observable datasets while keeping high performance in terms of both data recovery and task execution. For SVHN$C_1,\dots,C_n \sim P_C$18MNIST at $C_1,\dots,C_n \sim P_C$19 and $C_1,\dots,C_n \sim P_C$20 dB, convergence occurred in $C_1,\dots,C_n \sim P_C$21 epochs to within $C_1,\dots,C_n \sim P_C$22 of a “retrain-all” upper bound, while the no-DA baseline was $C_1,\dots,C_n \sim P_C$23 lower. For USPS$C_1,\dots,C_n \sim P_C$24MNIST, the method reached within $C_1,\dots,C_n \sim P_C$25 of the upper bound in $C_1,\dots,C_n \sim P_C$26 epochs. For STL10$C_1,\dots,C_n \sim P_C$27CIFAR-10 at $C_1,\dots,C_n \sim P_C$28, data adaptation yielded a $C_1,\dots,C_n \sim P_C$29 absolute gain over no-DA with a gap of $C_1,\dots,C_n \sim P_C$30 to full retraining (Zhang et al., 2022).

A different OOD mechanism uses a multi-modal LLM to reshape an inference distribution over a reduced semantic vocabulary. Given an image $C_1,\dots,C_n \sim P_C$31, the model produces an original distribution $C_1,\dots,C_n \sim P_C$32 through a Cross-Entropy Transformation from the final-layer self-attention matrix. A context string $C_1,\dots,C_n \sim P_C$33 is built from reliable detections of an expert model, embedded as $C_1,\dots,C_n \sim P_C$34, and used to define a contextual-similarity prior

$C_1,\dots,C_n \sim P_C$35

The posterior is then obtained through a tempered Bayes-type update

$C_1,\dots,C_n \sim P_C$36

with $C_1,\dots,C_n \sim P_C$37 tuned by Bayesian optimization to minimize a regret metric built from a correction rate and a damage rate. The same system prunes tokens outside a task-specific noun-only vocabulary, which reduces support and yields $C_1,\dots,C_n \sim P_C$38. At the receiver, a generate–criticize loop iterates between a text-to-image model and an image-to-text critic until the critic accepts or a maximum iteration count is reached (Zhang et al., 2024).

In the reported COCO-based evaluation with $C_1,\dots,C_n \sim P_C$39 OOD, Plan A alone yielded near-zero accuracy on OOD classes, Plan B alone achieved approximately $C_1,\dots,C_n \sim P_C$40 on pure OOD, and the combined Plan A–Plan B system reached $C_1,\dots,C_n \sim P_C$41 Precision, $C_1,\dots,C_n \sim P_C$42 Recall, and $C_1,\dots,C_n \sim P_C$43 F1 on the full test set. Bayes reshaping lowered $C_1,\dots,C_n \sim P_C$44 by $C_1,\dots,C_n \sim P_C$45–$C_1,\dots,C_n \sim P_C$46 on average, and up to four critic iterations raised correct image generation by approximately $C_1,\dots,C_n \sim P_C$47 over a single-pass baseline. Even when test-time SNR dropped to $C_1,\dots,C_n \sim P_C$48 dB relative to $C_1,\dots,C_n \sim P_C$49 dB during training, the end-to-end semantic loss remained within $C_1,\dots,C_n \sim P_C$50 of its clean-channel value (Zhang et al., 2024).

Latent-diffusion-based systems move the learned distribution into a compact latent space. In that setting, the model learns the semantic feature distribution $C_1,\dots,C_n \sim P_C$51 through a denoising score-matching objective

$C_1,\dots,C_n \sim P_C$52

where the forward law is conditioned on channel state information. Distribution shift is addressed in two ways: an outlier-robust encoder is obtained by projected-gradient updates on worst-case semantic outliers, and a single-layer latent-space transformation adapter $C_1,\dots,C_n \sim P_C$53 performs one-shot adversarial adaptation to new domains. Low-latency denoising is then achieved through end-to-end consistency distillation. This suggests that, in noisy and nonstationary environments, distribution learning can be implemented either as explicit probability reshaping over semantic tokens or as latent-manifold alignment and denoising (Pei et al., 2024).

5. Distribution matching for implicit reasoning and distributed deduction

Semantic communication is not restricted to explicit labels or object classes. An implicit semantic communication architecture models meaning through a semantic graph whose nodes are entities, edges are relations, and whose reasoning mechanism $C_1,\dots,C_n \sim P_C$54 is a user-specific policy for traversing the graph. The decoder’s reasoning mechanism is formulated as an MDP $C_1,\dots,C_n \sim P_C$55, with state $C_1,\dots,C_n \sim P_C$56, action $C_1,\dots,C_n \sim P_C$57 the choice of a relation, and policy $C_1,\dots,C_n \sim P_C$58. Paths are embedded into $C_1,\dots,C_n \sim P_C$59 using TransE, and a discriminator $C_1,\dots,C_n \sim P_C$60 scores them as expert-like or generated. The discriminator solves

$C_1,\dots,C_n \sim P_C$61

while the generator minimizes

$C_1,\dots,C_n \sim P_C$62

which can be rewritten as minimizing $C_1,\dots,C_n \sim P_C$63. Under optimal discriminator updates and sufficient capacity, the generated path distribution $C_1,\dots,C_n \sim P_C$64 converges to the expert distribution $C_1,\dots,C_n \sim P_C$65. This is a direct instance of distribution learning as imitation of a hidden reasoning process rather than of a visible source distribution (Xiao et al., 2022).

The experimental study used NELL-995 with approximately $C_1,\dots,C_n \sim P_C$66K entities and $C_1,\dots,C_n \sim P_C$67 relations. Under AWGN, semantic-based recovery reduced “entity-packet” error rate by up to $C_1,\dots,C_n \sim P_C$68 relative to raw transmission. GAML attained $C_1,\dots,C_n \sim P_C$69–$C_1,\dots,C_n \sim P_C$70 higher path-prediction accuracy than a genetic-algorithm baseline across sub-graphs of varying density, and discriminator and policy losses stabilized within approximately $C_1,\dots,C_n \sim P_C$71 adversarial rounds. The paper identifies a practical limitation: the current MDP depth $C_1,\dots,C_n \sim P_C$72 is fixed, so very long or deeply nested reasoning may strain sampling efficiency (Xiao et al., 2022).

A distributed variant appears in logical deduction of hypotheses. In that setting, each node $C_1,\dots,C_n \sim P_C$73 has local evidence $C_1,\dots,C_n \sim P_C$74 and posterior $C_1,\dots,C_n \sim P_C$75 over the state space $C_1,\dots,C_n \sim P_C$76, and must choose the most content-informative first-order-logic sentence $C_1,\dots,C_n \sim P_C$77 under a sentence-count budget $C_1,\dots,C_n \sim P_C$78. The node-side criterion is

$C_1,\dots,C_n \sim P_C$79

with $C_1,\dots,C_n \sim P_C$80. The server updates its posterior over constituent states by Bayes’ rule,

$C_1,\dots,C_n \sim P_C$81

and broadcasts its own most content-informative sentence. Under the stated inductive-logic prior and likelihood, a PAC-type bound shows that as accumulated evidence grows, the posterior on the minimal true constituent converges to $C_1,\dots,C_n \sim P_C$82. Theorem 4 further states that content-information selection yields a strictly tighter posterior and PAC bound than random selection: $C_1,\dots,C_n \sim P_C$83 This makes distributed semantic communication a process of sequentially learning the global state-of-the-world distribution under limited budgets (Saz et al., 9 Feb 2025).

The synthetic benchmark used $C_1,\dots,C_n \sim P_C$84 nodes, $C_1,\dots,C_n \sim P_C$85 first-order-logic sentences per node, $C_1,\dots,C_n \sim P_C$86 overlap between any pair, $C_1,\dots,C_n \sim P_C$87 unique content, and $C_1,\dots,C_n \sim P_C$88 candidate hypotheses per node. Communication budgets of $C_1,\dots,C_n \sim P_C$89 and $C_1,\dots,C_n \sim P_C$90 sentences per round were evaluated against random sentence selection. The reported uplink cost per node at $C_1,\dots,C_n \sim P_C$91 success rate was $C_1,\dots,C_n \sim P_C$92 bits for DISCD-1 versus $C_1,\dots,C_n \sim P_C$93 bits for Random-1, and $C_1,\dots,C_n \sim P_C$94 bits for DISCD-2 versus $C_1,\dots,C_n \sim P_C$95 bits for Random-2 (Saz et al., 9 Feb 2025). A common misconception is that semantic communication necessarily operates on monolithic messages. These results show instead that it can operate on iterative belief refinement over structured logical state spaces.

6. Multiagent semantic alignment and broader design tensions

In heterogeneous multiagent systems, distribution learning also takes the form of learning a shared semantic space and the topology over which aligned latent representations should be exchanged. In a network-sheaf formulation, each agent $C_1,\dots,C_n \sim P_C$96 observes a $C_1,\dots,C_n \sim P_C$97-dimensional latent embedding $C_1,\dots,C_n \sim P_C$98 of a shared dataset, but the embeddings are not mutually aligned. A graph $C_1,\dots,C_n \sim P_C$99 is equipped with a sheaf $C_i\in\mathcal C$00 whose node stalks and edge stalks are $C_i\in\mathcal C$01, and whose restriction maps along each edge are orthogonal transformations. Smoothness is measured by the sheaf Laplacian $C_i\in\mathcal C$02, with

$C_i\in\mathcal C$03

Learning the communication topology and alignment maps is formulated as a best-subset-selection problem: $C_i\in\mathcal C$04 where $C_i\in\mathcal C$05 are denoised sparse codes (Grimaldi et al., 2 Dec 2025).

The denoising and compression step uses a shared dictionary $C_i\in\mathcal C$06 and sparse codes $C_i\in\mathcal C$07 such that $C_i\in\mathcal C$08, with per-example sparsity constraint $C_i\in\mathcal C$09 and a log-determinant penalty on $C_i\in\mathcal C$10: $C_i\in\mathcal C$11 The resulting nonconvex problem is solved through successive convex approximation, splitting of orthogonality constraints, and ADMM-style updates, with closed-form updates for the dictionary and code blocks. Under standard SCA–ADMM assumptions, every limit point is a stationary solution of the dictionary-learning problem (Grimaldi et al., 2 Dec 2025).

The empirical observations are notable. On $C_i\in\mathcal C$12 pretrained image-classification models on CIFAR-10, varying the sparsity budget $C_i\in\mathcal C$13 produced a smooth accuracy–compression trade-off, and even with extreme sparsity such as $C_i\in\mathcal C$14 out of $C_i\in\mathcal C$15, the average classification accuracy over the recovered embeddings remained within a few points of the full latent-space performance. Without dictionary learning, per-edge Procrustes losses formed a single-mode cloud; after semantic denoising, the losses became bimodal, clearly separating homophilic from heterophilic edges. A simple greedy edge-selection then recovered the true model-family clusters and improved downstream task accuracy. The abstract summarizes the effect more generally: semantic denoising and compression facilitate AI agents alignment and the extraction of semantic clusters while preserving high accuracy in downstream task (Grimaldi et al., 2 Dec 2025).

Taken together, current results isolate several recurring tensions. One is the tension between immediate semantic performance and long-term learnability: encoder designs that improve instantaneous distortion may collapse distinguishability and degrade $C_i\in\mathcal C$16 (Lahoud et al., 14 Aug 2025). Another is the tension between shared knowledge assumptions and operational settings with task-unaware transmitters or dynamic source domains, which motivates receiver-leading training, cycle-GAN adaptation, and context-driven posterior reshaping (Zhang et al., 2022, Zhang et al., 2024). A further tension concerns the semantic object itself: the distribution to be learned may be a posterior over models, a source prior over meanings, a path distribution over reasoning trajectories, a posterior over logical states, or a shared sparse latent code. This suggests that “distribution learning” in semantic communication is best understood not as a single algorithmic primitive but as a family of inference-and-coding problems in which probability distributions are the semantic carriers, the optimization targets, and often the objects of transmission themselves.