Shannon
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Automated Proving of Shannon-Type Entropy Inequalities via Fine-Tuned Language Models and Guided Tree Search
Announce Type: new Abstract: Proving Shannon-type entropy inequalities is a fundamental task in information theory that often requires constructing non-trivial linear combinations of known constraints, which is a combinatorial search problem that scales poorly with the number of random variables. We investigate whether small-scale large language models (0.6B--1.7B parameters), fine-tuned on atomic proof steps and combined with guided beam search, can automate this process. On a held-out test...
Unlocking Exponential and Unbounded Robust Gains in Shannon Capacity of Classical Multiple Access Channels with Causal CSIT via Quantum Entanglement Assistance
arXiv:2606.05412v1 Announce Type: new Abstract: Quantum entanglement assistance is known to improve the Shannon capacity of classical communication networks but the largest gains noted thus far are rather modest (less than 6%), motivating the question: are large capacity gains ever possible? It is shown in this work that in the presence of causal channel state information at the transmitters, quantum entanglement assistance provides a multiplicative capacity advantage that grows...
The Preisach Extremum Stack is a Shannon-Minimal Sufficient Statistic for Rate-Independent Functionals
Announce Type: new Abstract: Let R denote the class of all computable, causal functionals that are rate-independent in the classical sense (invariant under monotone time reparametrizations), and let Pi_n be the Preisach extremum stack of an input sequence u_{0:n}. We prove a characterization theorem establishing that every F in R satisfies Fu = f(Pi_n) for a computable f, and derive two information-theoretic results. First, under any probability measure on u_{0:n}, the equality I(u_{0:n};...
$q$-Exponential Random Graphs: higher-order networks from simple constraints
Announce Type: new Abstract: Exponential Random Graphs (ERGs) are among the most widely used network models, derived as principled least-bias graph ensembles that maximize Shannon entropy under constraints on the expected values of given structural properties. However, it has been recently (re)discovered that, in the absence of additional information privileging Shannon entropy, the most agnostic inferential construction should maximize the broader class of Uffink entropies. The resulting...
Love story: Locking down the 'one that got away'
Love story: Locking down the 'one that got away' Sun 31 May 2026 at 12:00pm For a long time, Shannon Giles was "the one that got away" for Carlie Davies. That all changed when she reconnected with her teenage crush two decades later. These are Carlie's words.
Finite-Resolution Information from Collision Statistics
arXiv:2606.01218v1 Announce Type: new Abstract: Collision statistics provide a finite-resolution view of information by measuring how often a fixed number of independent samples fall on the same state. These directly countable quantities form the basis of integer-order R\'enyi entropies. Here, we use low-order R\'enyi entropies to approximate Shannon entropy and mutual information, while characterizing what is necessarily lost when only finitely many collision moments are used.
Physiological and Biochemical Responses of Grafted Tomato Plants to Salinity Stress: Evidence from the Syrian Coast
The research was carried out in Tartus (Syria), in a plastic greenhouse during the season 2024- 2025. Two tomato hybrids Levovil and Shannon were grafted onto two tomato Spirit and Maxifort rootstocks. Four levels of salinity (0, 50, 100 and 150 mM NaCl) were applied on the hybrids and grafted plants.
A Note on the Kullback-Leibler Divergence in Discretized Empirical Distributions
new Abstract: When empirical objects are represented as discrete probability distributions, within-distribution summaries such as Shannon entropy and Hill-type diversity indices describe how probability mass is spread inside each object, while Kullback-Leibler (KL) divergence provides pairwise asymmetric information. This note focuses on the KL difference $\Delta_{\mathrm{KL}}(p,q)=D_{\mathrm{KL}}(p|q)-D_{\mathrm{KL}}(q|p)$. Although $\Delta_{\mathrm{KL}}$ can add information beyond...
One if by Land, Two if by Sea, Three if by Four Seas, and More to Come -- Values of Perception, Prediction, Communication, and Common Sense in Decision Making
arXiv:2601.06077v2 Announce Type: replace Abstract: This work aims to rigorously define the values of perception, prediction, communication, and common sense in decision making. The defined quantities are decision-theoretic, but have information-theoretic analogues, e.g., they share some simple but key mathematical properties with Shannon entropy and mutual information, and can reduce to these quantities in particular settings. One interesting observation is that, the value of perception...
Unsettling dance piece explores how AI is warping human relationships
Inspired by Shannon Vallor's book The AI Mirror, this compelling piece looks at how we are being affected by our deepening interactions with tech