Papers

In classical information theory, a source is modeled by a single, precisely known probability distribution. However, in the increasingly complex communication networks full of unanticipated, nonstationary, and heterogeneous random events, the assumption of precise and well-defined probability distributions to describe random variables appears somewhat idealized. Therefore, it is important to characterize the uncertainty of distributions of source messages, subject to relaxing the assumption of deterministic probability models for analyzing information sources in information theory. Based on the nonlinear expectation theory, a novel axiomatical system that extends classical probability theory, this paper investigates the information sources whose distributions themselves are uncertain, and refers to them as uncertain-distribution sources. We generalize the fundamental concept information entropy to nonlinear information entropy, which describes the measurement of the amount of information contained in a uncertain-distribution source. By using the strong law of large numbers under sublinear expectation, we establish a nonlinear source coding theorem, which not only shows that the nonlinear information entropy is the upper bound for the infimum of achievable coding rate of uncertain-distribution sources under the maximum error probability criterion, but also determines a cluster point of the coding rate of uncertain-distribution sources under the minimum error probability criterion. Our findings reveal that the introduction of nonlinear expectation theory allows for a more comprehensive understanding of information sources.

In a world where valuable artifacts are increasingly created, completed, or processed by LLMs, the central economic question is not only what the LLM can produce, but what value remains in the inputs (i.e., the prompts) we provide to it. Given a prompt, hint, critique, problem statement, or partial solution that helps an LLM produce an artifact $z$—a proof, program, design, or scientific hypothesis—how should we measure the value of that input? Intuitively, an input is valuable when it makes the target artifact easier for the model to generate: either by increasing its sampling probability, or by reducing the thinking time needed to find it. We propose a computational Levin–Kolmogorov complexity approach to this problem, by appropriately replacing the universal Turing machine in the classical definitions by the LLM itself. Concretely, we introduce an LLM-relative notion of probabilistic Levin–Kolmogorov complexity $pKt$—treating the model's thinking as the random tape of the program, and charging logarithmically for it in Levin's manner—and define prompt value as algorithmic mutual information with respect to $pKt$. This captures the intuition above: a prompt having $b$ bits of value for an artifact $z$ makes $z$ $2^b$ times “easier to obtain”, by multiplying the success probability by $2^b$, by dividing the required computation by $2^b$, or by any corresponding tradeoff between probability and computation. In contrast to the classical notion of algorithmic mutual information, ours is efficiently estimable. We additionally show that, under a natural reproduction experiment, a prompt value of \(b\) bits means that reproducing \(z\) without the prompt has median token cost \(2^b\) times that of reproducing it with the prompt.

In this paper, we define and analyze the quantized maximal correlation, an extension of the notion of maximal correlation restricted to functions taking values in sets of bounded cardinality. We derive an upper bound on the quantized maximal correlation by showing that the correlation between any quantized functions of $X$ and $Y$ is related to the MMSE distortion in quantization of a particular linear combination of random variables. Following this, we leverage rate-distortion techniques and anti-concentration inequalities to further bound this MMSE, which results in explicit bounds on the quantized maximal correlation. Unlike the quantized maximal correlation itself, which does not generally tensorize, our bounds on the mean squared error do tensorize, resulting in a dimension-free upper bound on the quantized maximal correlation for product distributions. Our results also lead to improved bounds on the isoperimetric constants of reversible Markov chains and product chains, strengthening classical results such as those by Alon and Milman.

We propose a task-aware semantic split learning (SL) framework for wireless edge-cloud inference, in which the reliability of transmitted latent representations is dynamically adapted to their relevance for the downstream task. An autoencoder (AE)-based physical (PHY) layer enables end-to-end learning of the communication interface, while unequal error protection (UEP) is realized via mutual information (MI)-driven prioritization of latent components during training. The gradient of the estimated MI with respect to each latent component serves as a sensitivity-based proxy for task relevance, providing a fully learning-driven prioritization that adapts to both the data distribution and the downstream task. We further show that this prioritization translates into measurable physical-layer effects: MI-guided UEP assigns significantly higher transmit power to the most task-critical latent components compared to the equal error protection (EEP) baseline. Experiments on real-world IoT sensing data demonstrate consistent gains over equal and fixed-UEP baselines across SNR regimes. Additional analysis confirms ranking stability, estimator robustness and generalization across datasets and task types, indicating broad applicability of the proposed framework.

We establish a central limit theorem in Rényi divergence for independent and identically distributed lattice random variables $X_1, \cdots, X_n$ with zero mean, unit variance, and maximal span $h>0$. Let $S_n=(X_1+\cdots+X_n)/\sqrt n$. Let $Z_n$ denote the standard Gaussian distribution quantized on the support lattice of $S_n$. For every $\alpha>1$, with $\beta=\alpha/(\alpha-1)$, we prove that the Rényi divergence $D_\alpha(S_n\|Z_n)\to 0$ if and only if the divergence is finite at some convolution level and the strict sub-Gaussian condition $$ \mathbb E e^{tX}<e^{\beta t^2/2},\quad t\in\mathbb R,~ t\ne0 $$ holds. Under these conditions, we further derive an Edgeworth-type asymptotic expansion of the divergence to arbitrary order. These results provide a lattice counterpart of the Rényi entropic central limit theorem for continuous random variables due to Bobkov, Chisyakov and Götze (Ann. Probab. 47 (2019), 270–323).

In the theory of error correcting codes, list-decoding refers to the following problem. Given a code $C \subseteq \Sigma^N$ and a received word $y \in \Sigma^N$, find all codewords $c \in C$ so that $\delta(c,y) \leq \rho$, where $\delta$ is relative Hamming distance and $\rho \in (0,1)$. Codes that approach the optimal trade-off between the rate $R := \log_{|\Sigma|}(|C|) / N$ and the list-decoding radius $\rho$ are said to achieve capacity.By now, there are constructions of capacity-achieving list-decodable codes with fast near-linear-time list-decoding algorithms, but most existing work has not considered space complexity. In a recent line of work, Cook and Moshkovitz (2024, 2025, 2026) initiated the study of low-space deterministic algorithms for error correcting codes. In particular, in their 2026 paper, they gave a construction of list-decodable codes with deterministic near-linear-time and sublinear space list-decoding algorithms. However, these codes were far from achieving capacity. In this paper, we present list-decodable codes approaching capacity with deterministic time- and space-efficient list-decoding algorithms. More precisely, for any $R \in (0,1)$ and any arbitrarily small constant $\tau > 0$, we present a family of codes $C\subseteq \Sigma^N$ with rate $R$ that are deterministically list-decodable up to radius $\rho = 1 - R - \tau$, in time $N^{1 + \tau}$ and space $N^{\tau}$ with constant output list size and constant alphabet size. Our results can be extended to capacity-achieving list-recoverable codes.

We present a combinatorial proof of Simonis type MacWilliams identity for harmonic higher weight distributions of linear codes. Furthermore, we investigate the statistical moments of the harmonic higher weight enumerators for random linear codes. Defining the enumerators via rank functions of the generator matrices of linear codes, we prove that its expectation vanishes for all non-trivial harmonic functions due to the inherent symmetry of random matrices, and we also derive an explicit, non-trivial formula for the covariance.

We introduce the geodesic quantum $f$-divergences $D_f^t$, $0\leq t\leq1$, obtained from the affine-invariant geodesic between the standard and maximal relative modular operators. They reduce to the classical $f$-divergence for commuting states. The logarithmic generator yields geodesic relative entropies joining the Umegaki and Belavkin-Staszewski entropies, while the power generators yield $(t,\alpha)$-Rényi divergences joining the Petz and geometric families. Our first main result is data processing of $D_f^t$ for every finite operator-convex generator $f$ and every $t\in[0,1]$. In particular, this gives DPI for the geodesic relative entropies and for the $(t,\alpha)$-Rényi divergences when $0<\alpha<1$ or $1<\alpha\leq2$. Our second main result identifies equality in the DPI: for invertible states, every equality-determining operator-convex generator has, at each nonmaximal parameter $0\leq t<1$, exactly the Petz sufficiency class; at $t=1$, this changes to the generally larger maximal, or BS, class, which also coincides with the equality class of the divergences associated with the quadratic generator for every $t$. Our third main result is the corresponding collapse of invertible geodesic quantum Markov chains: for each of the three ordered conditional-mutual-information constructions, the $t$-quantum Markov chains are precisely the quantum Markov chains for $0\leq t<1$, whereas at $t=1$ they are the invertible BS quantum Markov chains, a class that can be strictly larger. We also determine parameter-monotonicity regimes and the intersections with the $(\alpha,z)$ family. We prove strengthened data-processing and reconstruction estimates; we compare the three conditional orientations; we establish continuity bounds under positive lower-eigenvalue assumptions together with complementary discontinuity results; and we give a capacity-per-unit-cost interpretation.

We present a reinforcement learning (RL) approach to the co-design of stabilizer sets of Quantum Error Correcting Codes (QECCs) and decoders. We show how to produce a generative model that produces Bivariate Bicycle (BB) codes based on the choice of decoder. Specifically, we fix a decoder architecture and use Proximal Policy Optimisation (PPO) to train an agent over BB codes to maximise decoder performance under a depolarising channel noise model.

Solovay reducibility is studied intensively as a tool to compare the approximability and the degree of randomness of left-c.e. reals. By definition, a real is left-c.e. if it has a left-c.e. approximation, that is, it is the limit of an effective nondecreasing sequence of rationals. If reals $\alpha$ and $\beta$ have left-c.e. approximations $a_0, a_1, \ldots$ and $b_0, b_1, \ldots$, respectively, such that the approximation ratios \[ \frac{\alpha-a_n}{\beta-b_n} \] are bounded from above by a constant, the real $\alpha$ is Solovay reducible to $\beta$. The latter is the case for any such $\alpha$ and $\beta$ and their left-c.e. approximations whenever $\beta$ is Martin-Löf random by the Kučera-Slaman Theorem [DOI:10.1137/S0097539799357441]. This result was substantially strengthened by Barmpalias and Lewis-Pye [DOI:10.1016/j.jcss.2017.06.002], who demonstrated that, under the given assumptions, the approximation ratios are not only bounded but actually converge to a limit, which does not depend on the considered left-c.e. approximations. There is a quest for a suitable extension of Solovay reducibility to the class of all reals. Promising candidates include S2a-reducibility on the set of computably approximable reals by Zheng and Rettinger [DOI:10.1007/978-3-540-27798-9_39] and monotone Solovay reducibility by Titov [DOI:10.1007/978-3-031-95908-0_33]. For the latter, Titov [DOI:10.1017/jsl.2025.10157] demonstrated that the theorems of Kučera and Slaman and of Barmpalias and Lewis-Pye extend to all reals. He conjectured further [DOI:10.1017/jsl.2025.10157, Conjecture 3.2] that similar extensions hold for S2a-reducibility in terms of its functional characterization by Kumabe, Miyabe, and Suzuki [DOI:10.3233/COM-230486]. In this work, we refute this conjecture by proving that the analogue of the Barmpalias-Lewis-Pye Limit Theorem does not hold for S2a-reducibility.

Fluid antenna arrays exploit continuous antenna repositioning within a finite aperture to provide geometry diversity beyond grid-constrained port selection. Every displacement, however, changes both the radiation response and the multiport mutual-impedance network, coupling geometry optimization with the source-voltage constraint. This paper develops an electromagnetic-aware (EM-aware) beamforming framework for planar fluid antenna arrays. Phase retrieval converts an amplitude-only shaped-beam specification into an aperture-compatible complex target, and an EM-aware orthogonal matching pursuit (OMP) method selects grid-constrained initial antenna positions. Continuous refinement then alternates exact voltage-constrained current optimization with movement-constrained projected adaptive moment estimation (Adam) updates of all physical antenna positions. Across independently perturbed symmetric dual-beam targets, the proposed method consistently improves the average mainlobe signal-to-noise ratio (SNR) and reduces the peak sidelobe level (PSLL) over a uniform array and discrete port selection.

Fluid antenna systems obtain spatial degrees of freedom by reconfiguring antenna positions within a confined region, a principle that extends to beamforming: shaped beams can be synthesized using far fewer radio-frequency feeds than candidate antenna positions. When the candidates are densely arranged, however, electromagnetic mutual coupling changes the relationship among terminal voltages, induced currents, and radiated fields, so an uncoupled model no longer describes the hardware and may activate an unsuitable set of ports, distorting the synthesized pattern. This paper develops a mutual-coupling-aware framework that converts the desired beam amplitude into a finite-aperture-compatible complex target and models the complete antenna lattice as a coupled multiport network, selecting the active ports and their source voltages through the coupled voltage-to-field response. Inactive candidate ports remain part of the network and carry induced currents, and every compared design is evaluated through the same electromagnetic model under the same source-voltage budget. Numerical results show that the mutual-coupling-aware design improves both the average mainlobe signal-to-noise ratio (SNR) and the peak sidelobe level (PSLL) over coupling-unaware selection and a fixed array, demonstrating that mutual coupling should be exploited in the design itself rather than compensated only in the final evaluation.

In recent years, owing to the high accuracy in characterizing non-separable channels prevalent in next-generation wireless applications, the classical Weichselberger channel model has gained widespread adoption in multiple-input multiple-output (MIMO) systems. However, its non-separable structure also introduces severe analytical complexity, leading to a lack of tractable mathematical frameworks in the literature and thus raises an urgent need for further research. To address the aforementioned analytical complexity, we first derive the nearest separable (double-correlated Rayleigh) fading model to the Weichselberger model under the Kullback-Leibler divergence (KLD), a problem equivalent to rank-1 nonnegative matrix factorization under the Itakura-Saito (IS) distance criterion. The results of our asymptotic analysis in the high-SNR regime reveal that the KLD-enabled approximation achieves a tighter capacity estimate than the conventional Kronecker model, especially in sparse and non-regular scattering environments. Yet, a key limitation of the KLD-enabled model is its tendency to mischaracterize the channel capacity in the low-SNR regime due to its inability to preserve total channel power. As a more robust alternative, we introduce a novel moment matching method (MMM) aimed at mapping the exact channel statistics to those of a Wishart distribution. Both the KLD-enabled and MMM-enabled separable channel directly enable the use of exact closed-form expressions for the ergodic capacity. Numerical results demonstrate that the MMM-enabled model consistently improves upon the capacity accuracy of the conventional Kronecker model across all SNR regimes.

Decorrelating a multivariate system need not destroy source-variable identity. We introduce Constrained Oblique Rotation with Anchored Loadings (CORAL), which minimizes residual cross-correlation while guaranteeing a declared minimum correlation between each transformed variable and its designated source. For a p-variable correlation matrix $R$, we show that every exact decorrelator can be written as $R^{-1/2}Q$ for some orthogonal matrix $Q$, and define $\rho_\star(R)$ as the maximum common source fidelity compatible with exact decorrelation. Constructive lower bounds and rigorous analytical upper bounds tightly bracket $\rho_\star$ at [0.972,0.976], [0.959,0.962], and [0.949,0.950] in simulations with p={6,18,50}, respectively, compared with PCA's largest achievable minimum correlation between distinct principal components and matched source variables of 0.358, 0.329, and 0.172. Corresponding intervals are [0.751,0.758] for World Development Indicators and [0.826,0.835] for wine chemistry data sets. Thus, loss of source-variable identity is not inherent to exact decorrelation but depends on the decorrelator selected. CORAL uses constrained Riemannian optimization and extends to exact support restrictions.

Scheduling in multiuser multiple input multiple output (MU-MIMO) systems is essential for efficient resource allocation and overall performance enhancement. In this work, a multiuser scheduling problem is formulated to maximize the product of user equipments' (UEs) aggregate satisfactions, which maintains user fairness. Solving such a combinatorial problem using exhaustive search (EX), which requires evaluating all possible multiuser groups within a massive number of resource blocks (RBs), is prohibitive. Instead, we propose an efficient users' satisfaction based scheduling approach (US-SA). In our US-SA, a low dimension sub-grouping matrix is constructed {at each frame}, which is used to schedule the best multiuser group in each time slot; satisfied users are eliminated from the scheduling process. Our US-SA performs close to the optimal EX method in terms of satisfaction, transmitted data amount, spectral efficiency, latency, and fairness with lower computational cost. Moreover, our experiments demonstrate that the proposed scheme outperforms competing techniques.

Integrated sensing and communication (ISAC) is emerging as an important direction in the Third Generation Partnership Project (3GPP) evolution toward 6G because it allows cellular networks to provide environmental awareness in addition to connectivity. This paper surveys the current 3GPP trajectory from Release~19 feasibility studies to Release~20 radio, protocol, and architecture studies, while distinguishing established requirements, ongoing study assumptions, and possible forward directions. The survey covers service requirements, sensing topologies, channel model evolution beyond 3GPP Technical Report (TR)~38.901, Radio Access Network Working Group~1 (RAN1) physical layer design, Radio Access Network Working Groups~2 and~3 (RAN2 and RAN3) system implications, and the role of sensing-assisted communication. It also synthesizes the main unresolved issues in waveform and reference signal design, multi-node coordination, sensing data reporting, service exposure, privacy, and implementation constraints. By connecting service-level motivations to physical layer, protocol, and architecture implications, the paper provides a standards-centric reading of how 3GPP may evolve toward practical 6G ISAC support.

Intelligent control of wireless propagation environments is crucial for future network capacity and reliability. Unlike circuit-controlled reconfigurable intelligent surfaces (RIS), mechanically actuated specular reflecting surfaces (SRS) offer a simpler and potentially more cost-effective alternative. In this paper, based on the tractable ray-based cascaded channel model with power-projection correction, we investigate the fundamental operational behaviors of an ideal SRS in free space. Specifically, in the angle-aligned near field, edge reflections cause non-constructive combining, resulting in a damped oscillatory convergence of the gain to an aperture-independent constant. We further obtain the far-field behavior, unbounded-aperture asymptotics, an optimal aperture size and reflection angle, and a gain-based near/far-field boundary. For misalignment, we provide accurate approximations for small and large apertures via center-point and stationary-point analyses. We also define the SRS beam pattern, derive analytical 3-dB beamwidths, and quantify the effective region where a main lobe exists. Finally, we derive a closed-form achievable-rate for an SRS-aided communication system. Numerical results validate the proposed expressions, reveal distinct near-/far-field behaviors of specular reflection, and show that SRS can outperform RIS in the far field due to continuous aperture and angular-resolution control and stronger power projection.

Iterative decoding has been central to the success of modern channel coding, where reliability information is repeatedly exchanged across decoding components to approach fundamental performance limits. This paper brings the same principle to semantic error correction by proposing iterative cross-layer semantic error correction (ICL-SEC), a framework that closes the loop between physical-layer soft channel decoder and application-layer language-model-empowered semantic decoder. In the proposed framework, a soft-input soft-output channel decoder first produces bit-level posterior probabilities, from which word-level reliabilities are derived. Words deemed reliable are exposed to a masked language model as semantic context, while unreliable words are masked. The language model then produces contextual word likelihoods, which are leveraged to generate extrinsic bit-level priors and fed back to the channel decoder for the next iteration. This iterative refinement progressively expands the set of confidently recovered words. A key contribution is our Confirm prior-update rule: once a word is judged reliable, its bits are assigned deterministic priors with probability one in subsequent iterations, making the word fully resolved side information for both the channel decoder and the language model. This successive-confirmation mechanism prevents oscillatory unmask-mask behavior and yields a reliability interpretation consistent across layers. Simulations over text transmission demonstrates that ICL-SEC substantially outperforms both conventional channel decoding and non-iterative CL-SEC. In particular, the proposed Confirm scheme reduces the bit error rate by more than two orders of magnitude relative to non-iterative CL-SEC, while also significantly improving the other five performance metrics.

The paper contains An elementary proof of Marton and Shields' obstruction to finitary coding.

This paper extends a one-shot (finite-blocklength) information-theoretic framework built on a single primitive: the pairwise error probability (PEP) of a randomized, dither-broken decoding rule, and the error spectrum it induces. A companion paper developed the framework for point-to-point channel coding – uniformity of the PEP, the error-spectrum representation of achievability and converse, and the linear-programming form of the prior-optimized minimax meta-converse. Here we show that the same primitive, read on an enlarged candidate space, governs four further settings: lossy source coding under average distortion, joint source-channel coding with list decoding, channel coding with an erasure/undetected-error option, and the two-user multiple-access channel. In each case a single spectrum yields a random-coding achievability bound and exact fixed-code identities, and we indicate how the convex – indeed linear-programming – prior optimization of the channel-coding case extends under matched decoding. The development recovers the one-shot lossy bound of Matsuta-Uyematsu and the joint source-channel bounds in the Csiszar tradition, complements the lossy bounds of Kostina-Verdu, and connects the multiuser case to the comparable achievability/converse pair through three pairwise error events.

Diffusion models learn to reverse a predefined corruption process, but sampling still requires a costly time discretization and depends on the chosen noise schedule. We study these two issues for variance-preserving diffusions with matrix-valued schedules. Our analysis transfers reverse-time discretization errors to the forward corruption law and treats two numerical schemes within a common framework. The first freezes the score and yields, through a matrix-sensitive local comparison and forward information dissipation, an ambient-dimensional step complexity with leading factor $d/\varepsilon^2$ for KL accuracy $\varepsilon^2$. The second keeps the known Gaussian drift exact and freezes the posterior mean. For data of metric-entropy dimension $k$, a forward Markov identity, an anisotropic covering estimate, and Stieltjes integration by parts give the corresponding factor $k\log k/\varepsilon^2$. In both cases, the proof identifies a local error, accumulates it through the forward evolution, and inserts the result into a common KL decomposition. The local errors further provide directional criteria for matrix schedules and an asymptotically optimal square-root adaptive grid. A high-dimensional Gaussian-mixture experiment illustrates the resulting schedule and grid improvements.

Let $d\geq 2$ and let $\bf{f}_1,\ldots,\bf{f}_m\in\mathbb C^d$. We prove that if $m\leq 2d-1$, then the intensity measurement map \[ \bf{x}\longmapsto \bigl( |\langle \bf{x},\bf{f}_1\rangle|^2, \ldots, |\langle \bf{x},\bf{f}_m\rangle|^2 \bigr) \] fails to recover almost every signal in $\mathbb C^d$ uniquely up to a global phase factor. Combined with the known generic sufficiency of $2d$ measurements, our result establishes that the minimum number of measurements required for almost-everywhere phase retrieval in $\mathbb C^d$ is exactly $2d$. This resolves an open problem in phase retrieval by determining the exact measurement threshold for almost-everywhere phase retrieval in ${\mathbb C}^d$.

Noise modulation (NoiseMod) encodes information in the variance of a transmitted noise-like waveform rather than in its amplitude, phase, or frequency, and is attractive for ultra-low-power and covert links. Its main weakness is that, unlike classical modulation, it exhibits no diversity under Rayleigh fading: its bit error probability (BEP) decays only as $1/(N_s\delta)$, where $N_s$ is the number of noise samples per bit and $\delta$ the useful-to-thermal noise variance ratio. Independently, fluid antenna systems (FAS) have been shown to recover substantial selection diversity from a single radiating element that switches among $N_p$ closely spaced ports, without extra radio-frequency chains. This paper combines the two: we equip a NoiseMod receiver with a fluid antenna and derive its average BEP. For idealized, mutually independent ports, we obtain an exact closed-form BEP via order statistics of the port envelopes. For the physically accurate, spatially correlated case governed by Jake's model, we build a semi-analytical BEP using the two-stage channel approximation of Khammassi et al. We validate both regimes against full signal-level Monte Carlo simulation and show that (i) FAS restores a diversity order that grows with the number of ports $N_p$ when ports are weakly correlated, (ii) this gain saturates once the fluid-antenna aperture $W\lambda$ is fixed and $N_p$ grows, mirroring the outage-probability saturation reported for FAS, now observed for BEP, and (iii) an intrinsic, correlation-independent (and $\delta$-independent) BEP floor set only by $N_s$ and the variance ratio $\alpha$ persists regardless of the antenna diversity order.

Pairwise relationships among mental-health symptoms are routinely summarised asscalar edge weights, which cannot express whether two symptoms carry overlapping information about a third or information that appears only in combination. Partial information decomposition (PID) addresses this gap but is computationally intractable beyond a few sources. We introduce embedding-based PID (ePID), a scalable pipeline that compresses all nonfocal symptoms into a low-cardinality discrete embedding and computes a tractable two-source PID, yielding source-unique, remainder-unique, redundant, and synergistic components for each ordered source-target pair. We benchmarked 13 candidate embeddings on synthetic Bayesian networks calibrated to PHQ-9 and on 83 real-world datasets across five PID measures. A supervised Agglomerative Conditional Information Bottleneck (ACIB) embedding recovered the reference decomposition most accurately of the 13 embeddings tested, and did so for every PID measure yielding non-negative atoms once four or more symptoms were compressed (synergy recovery r = 0.92). The two instruments then diverged sharply. In PHQ-9 networks (UK Biobank,N = 154,291; Xinxiang student sample, N = 24,292) the surrounding symptom context carried most pairwise dependence through redundant and remainder-unique channels; synergy contributed 6 to 9%, and no directed edge was synergy-dominated in either cohort. In the 28-item Interpersonal Reactivity Index, 45% of source pairs were. The identical pipeline, applied without parameter changes, therefore returned opposite profiles for the two instruments, each consistent with how that instrument was constructed. By separating overlapping from interaction-dependent information, ePID provides a scalable, model-agnostic complement to standard symptom-network methodology to distinguish redundant and synergistic contributions to observed correlations.

Training datasets for upcoming LLMs would include a significant amount of AI text/image data generated from current LLMs. In such a scenario, it is important to understand how this affects batch decompositions and thereby, the performance of the resultant new LLM. In this paper, we consider AI generated data as anomalies “linked" to main data points and study decomposition and undersampling properties of the overall random dataset. We use redundancy graphs and iteration techniques to obtain bounds for the minimum size of a strongly dissimilar (SD) decomposition and demonstrate a phase transition phenomena, wherein the minimum size is essentially determined by the main data points when the number of anomalies is small and is “taken" over by the anomalies above a certain threshold. We also establish a size criticality result for the strong similarity of a randomly undersampled dataset and illustrate our results with examples involving categorical datasets, whose overall space size is much larger than the size of the dataset.

Algorithmic Information Dynamics (AID) studies systems by perturbing them and measuring changes in algorithmic complexity, but its usual estimator, the Block Decomposition Method, is piecewise constant, restricting the calculus to finite differences. We use $K^{\mathrm{CDM}}_{\mathrm{s}F}$, a certified, differentiable estimator, to bring the calculus into learning dynamics: grokking, where a complexity order parameter is known but has not been made to act. As a transient loss kick, the estimator becomes a controller that accelerates grokking in Levin's description-length–versus-time sense, within a data-dependent Occam boundary whose finite-size trend, $f_c\sim\ln p/p$, is consistent with a coupon-collector interpretation. Ablations show that a complexity gate matches a train-loss gate in rescuing failing seeds with $27\%$ less intervention; among the tested signals, only map complexity marks the transition's completion; the certified prior and the per-parameter $\nabla K$ attribution are both fungible (a uniform-prior sensor makes bit-identical gate decisions, and random supports match $\nabla K$-selected ones above a sparsity threshold); and direct field perturbation shows a nucleation-like response to the Occam field (no linear regime is resolved over the probed amplitudes, so these measurements do not justify a fluctuation–dissipation surrogate), with a finite-field response growing by orders of magnitude toward the phase-transition. These measurements account for the empirically tuned staircase: bang–bang pulses, stall-fired and released on yield, whose iteration plausibly builds the response it exploits. The kick transfers to sparse parity and to a transformer; a sustained weight-space loss fails. The algorithmic estimator's distinct contribution is timing (when to fire and when to release), not attribution.

We give a complete proof of the 2011 Tu–Deng conjecture. We begin from its original modular pair-count formulation, prove an equivalent cyclic Hamming weight-drop formulation, and establish the exact transfer identity that connects this count with a two-variable matrix polynomial. The proof then reduces the conjecture to normalized inequalities for the coefficients of that polynomial. A 2011 conjecture by the author which came to be called the Cusick Conjecture (it is a consequence of the Tu–Deng Conjecture) was proved by K. Cheng in 2026. The proof in the present paper extends the cyclic deletion ideas of Cheng. The new ideas might be applicable to other problems.

High-order multiple-input multiple-output (MIMO) detection requires efficient search over a large discrete symbol space while producing reliable soft information for channel decoding. This paper develops a learning-to-transition (L2T) framework that formulates MIMO detection as a stochastic sequence of complete-vector transitions. At each transition, a channel-coupled Transformer updates both the instance embedding and the sampling policy, while a blockwise autoregressive factorization captures inter-stream dependence with moderate sequential complexity. For hard-output detection, a transition network is applied recursively and trained through a residual-to-BER curriculum, which first learns the MIMO search geometry from the exact residual metric and then aligns the policy with transmitted-bit accuracy. For soft-output reception, the well-trained hard policy is cloned at the parameter level into every layer of an untied soft-input soft-output iterative detection and decoding (IDD) receiver. This tied-to-untied transfer preserves the learned zero-prior search dynamics while enabling layer- and round-specific specialization under decoder feedback. Within each IDD round, decoder priors tilt candidate generation according to Bayes' rule, and likelihood-weighted terminal hypotheses produce posterior and extrinsic log-likelihood ratios for LDPC decoding. A multi-stage training strategy further stabilizes the hard-to-soft transfer by progressively exposing the receiver to synthetic and in-loop decoder-generated priors.

We study sparse regression codes (SPARCs) for lossy compression under simple greedy encoding rules, including both correlation-based and distance-based methods. We generalize the SPARC construction, and consider the class of additive orthogonal regression codes, of which standard SPARCs are a special case. For this class of codes, we derive nonasymptotic bounds on the squared-error distortion by tracking the evolution of the encoding residual across stages. Our results highlight the role of power allocation in controlling the distortion, allowing us to optimize the allocation based on the parameters of the code. The optimized allocation improves the finite-length compression performance of SPARCs, and our bounds provide distortion guarantees for lower complexity variants of SPARCs, like signed SPARCs and $K$-sparse SPARCs.

An autonomous robot efficiently exploring an unknown environment, such as looking for water sources on Mars, faces two simultaneous demands: building an accurate information map while quickly finding the regions of greatest value, and paying for every meter of travel and the cost of every measurement it takes. Classical information-seeking and reward-seeking criteria address only one of these objectives at a time. Here, we propose Expected Free Energy (EFE), the principled action-selection objective from active inference, as a unifying criterion for budgeted robotic informative path planning. Maintaining a Gaussian-process belief over the information field, our agent plans continuous trajectories that minimize expected free energy under hard path-length constraints. The results from multiple realizations show that EFE-based planning yields accurate posterior maps and locates the highest-value regions simultaneously, outperforming information-theoretic baselines under the same settings. In robotic exploration, these unified, easy-to-tune principled information-gathering strategies facilitate autonomous deployment while enforcing efficiency and resource constraints.