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arXiv2026

It's the Problem, Not the Path: Budget and Difficulty Confounds in LLM Reasoning Trajectories

Reasoning traces of large language models are widely read as containing "breakthrough" moments and early-legible fates. Both readings rest on measurements missing a counterfactual control at the level of the claim; we supply both controls. First, a restart-controlled truncation probe separates when a solution fits the continuation budget from when a prefix carries value that fresh computation cannot buy, comparing per-anchor continuation solve rates against from-scratch restart curves at matched total generated-token budget. Applied to 178 problem-model cells (89 MATH problems x two small open models, an outcome-blind but difficulty-targeted cohort), exactly 1 of 178 cells survives as prefix-limited; restart dose-response separates a compute-starved model from a capability-limited one; and wherever the matched budget lies inside the restart grid, continuing the model's own prefix beats restarting (9 of 9) -- predominantly compute compression rather than expanded reachability. Second, a pre-registered, difficulty-controlled test finds no detectable outcome information in early-window internal signals beyond a problem-difficulty baseline, and two generation-free analyses of public corpora show why this control is needed: a trace-blind difficulty proxy reaches AUROC 0.873 on 192K DeepSeek-R1 generations -- inside the published probe range -- and a closely matched reconstruction of the closest published early-window positive recovers a comparable pooled result (0.849) while within problem it is statistically indistinguishable from chance at all ten anchors (0.496 at t=4); a post-hoc within-targeted probe finds only a small average residual, concentrated in three low-failure problems. High pooled probe AUROCs cannot by themselves establish within-attempt information; a question-only baseline or within-problem evaluation is required.

cs.LG↗

arXiv2026

Four-Entropic Matroids Are Quaternary

For an integer $q\ge2$, a matroid is $q$-entropic if its rank function, multiplied by $\log q$, is the joint-entropy function of random variables on a $q$-element alphabet. We prove that a matroid is $4$-entropic if and only if it is representable over $\F_4$. The corresponding statements for alphabet sizes two and three were known. The proof combines minor closure and the excluded-minor characterization of quaternary matroids with structural properties of quasigroups of order four. Thus arbitrary four-symbol partition representations yield no matroids beyond the quaternary ones. As an application, every access structure admitting an ideal perfect scheme with a uniform four-symbol secret and four-symbol active shares also admits an ideal $\F_4$-linear scheme.

math.CO↗

arXiv2026

Smart Enough to Go Extinct? An Evolutionary Challenge to the Value of General Intelligence and Its Ethical Implications for AGI

The pursuit of artificial general intelligence (AGI) rests on a seemingly self-evident premise: that general intelligence, the kind of flexible, domain-general cognitive capacity exemplified by Homo sapiens, is extraordinarily valuable. This paper subjects this premise to critical scrutiny. We first present the intuitive case for the value of general intelligence before mounting an evolutionary challenge. We argue that, on evolutionary timescales, its adaptive value is far from empirically established. Numerous taxa, from cyanobacteria to horseshoe crabs, have persisted for hundreds of millions or even billions of years without anything resembling general intelligence, while Homo sapiens has existed for roughly 300,000 years and already faces self-generated existential risks. Mass extinction events do not preferentially favour cognitively sophisticated species. We argue that general intelligence may be the only biological strategy that generates existential threats to the species possessing it, an existential risk paradox with no parallel among non-intelligent survival strategies. Unlike prevailing accounts of AI risk that trace the danger to misalignment, we locate it in structural features of general intelligence itself, implying that even well-aligned AGI would inherit this liability. If the long-term evolutionary value of general intelligence is uncertain or negative, this raises ethical questions about engineering AGI and, more urgently, creating artificial consciousness. Drawing on deontological ethics and the precautionary principle, we argue that this uncertainty imposes a duty of caution: if we create a new kind of intelligent being, we bear responsibility for ensuring the conditions under which it can flourish.

cs.CY↗

arXiv2026

A Nuclear-Norm Lower Bound for Dithered Scalar Quantization of Matrix Products

We consider the problem of minimizing error in quantized matrix multiplication $C=AB$. Scalar quantization of the factors introduces rounding errors whose scale depends on the maximum absolute entries -- the ranges -- of their rows and columns. These ranges determine the quantization grid steps. To reduce the error, we optimize over product-preserving transformations that alter the factor ranges and grid steps without changing $C$. Specifically, we seek the smallest leading expected squared error over invertible inner changes of basis and orthogonal outer rotations. Under independent, zero-mean subtractive dither noise on an unbounded lattice, we prove the output-only bound $E_{\rm lead} \ge (c_A+c_B)/K \Vert AB\Vert_*^2$, where $K$ is the inner dimension, $c_A$ and $c_B$ are normalized noise variances, and $\Vert AB\Vert_*$ is the nuclear norm. The bound is tight: an SVD-aligned Hadamard construction attains the infimum whenever a Hadamard matrix of order $K$ exists, including every power of two, while an SVD-aligned DCT construction is within a factor of two for every $K$. Without outer rotations, Gram-matrix balancing minimizes factorization energy, and finite-set flattening achieves the bound within $C\log(K(m+n))$. For power-of-two $K$, conditional expectations deterministically select the Hadamard signs in $O((m+n)K^2)$ exact-real operations. Synthetic experiments verify both constructions and illustrate the tradeoff between regularization and conditioning. These results characterize the full-gauge optimum and quantify the cost of preserving row and column indices.

cs.IT↗

arXiv2026

Learning the Channel Gain from Anywhere to Anywhere via Cross-environment Transformer Estimators

Channel-gain maps provide the channel gain between any two locations in a geographical region. They find numerous applications, from resource allocation and interference control to path planning for autonomous vehicles. Channel-gain map estimation (CGME) is considerably more challenging than conventional radio map estimation (RME) because channel-gain maps are functions over a 6-dimensional input space. This calls for specialized methods, which currently rely on the (inaccurate) radio tomographic model or require a prohibitively large number of measurements since they do not exploit any spatial structure. This paper overcomes this issue by leveraging spatial patterns that channel-gain maps exhibit across environments, as dictated by the laws of physics and typical environmental characteristics (e.g. building materials and layouts). Adopting a metalearning perspective, a transformer-based estimator is proposed to implicitly learn this common structure from measurements collected in multiple environments. This enables CGME in new environments from significantly fewer measurements (five times less in our experiments). To maximize learning efficiency, the transformer is composed with a feature map that enforces the invariances of CGME, such as those following from reciprocity. Numerical experiments corroborate the merits of the proposed estimator relative to existing methods.

eess.SP↗

arXiv2026

Deep Reinforcement Learning for Optimization of STAR-RIS Phase and Energy Splitting Coefficients in OTFS-NOMA Framework

This paper considers a downlink communication framework comprising a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided by orthogonal time frequency space (OTFS) and non-orthogonal multiple access (NOMA) technologies. Further, delay-Doppler mobility in such frameworks renders classical alternating optimization impractical for per-coherence interval reconfiguration. To mitigate such issues, the STAR-RIS phase-shift and energy-splitting design is formulated as a constrained, non-convex sum-rate maximization problem with closed-form maximum ratio transmission beamforming and fixed NOMA power allocation. To circumvent the per-interval re-optimization burden, a deep reinforcement learning (DRL) approach is adopted that maps observed channel realizations to STAR-RIS configurations through a single forward pass. Specifically, Beta-Space Soft Actor-Critic (SAC-BSE), a maximum entropy DRL agent, is proposed. Simulation results, with two NOMA-multiplexed users on each STAR-RIS branch, confirm rapid convergence, limit the sum-rate degradation to roughly 10\% across a 128-fold user-speed range, and yield consistent gains over OTFS-only, NOMA-only, STAR-RIS-only, fixed-split, and mode-switching baselines as transmit power and the number of STAR-RIS elements increase.

cs.IT↗

arXiv2026

Counterexamples to Charpin's Conjecture on BCH codes

We construct an infinite family of $q$-ary primitive narrow-sense BCH codes whose minimum distance strictly exceeds the Bose distance; in fact, the gap between the two can be arbitrarily large as the length of the code tends to infinity. The key idea is to embed these BCH codes in a suitably large punctured generalized Reed--Muller code, whose codeword weights obey divisibility conditions supplied by Ax's theorem. This divisibility forces the minimum distance of the BCH codes far above the Bose distance. In particular, our family disproves a longstanding conjecture of Charpin asserting that this difference is at most four.

cs.IT↗

arXiv2026

The generalized covering radii of Melas codes

The generalized covering radii have recently emerged as fundamental parameters of linear codes with applications to database linear querying. In this paper, we study the generalized covering radii $ρ_t(M(m,q))$ of Melas codes $M(m,q)$ over any finite field $\mathbb{F}_q$. We determine $ρ_2(M(m,q))$ for all $q$, and for a general $t \ge 3$, we prove that $ρ_t(M(m,q)) \in \left\{2t,2t+1\right\}$ for $q \in \{2,3\}$ and $ρ_t(M(m,q))=2t$ for $q \ge 4$ whenever $m$ is sufficiently large. These results extend recent work on the covering radius of Melas codes.

cs.IT↗

arXiv2026

A Comprehensive Survey on Semantic Communication in Non-Terrestrial Networks: Architectures, Methodologies, and Challenges

Sixth-generation networks are expected to extend connectivity beyond terrestrial infrastructure through non-terrestrial networks (NTNs) comprising satellites, high-altitude platform stations, and unmanned aerial vehicles. However, these platforms operate in a regime that bit-fidelity-centric design handles poorly: high free-space path loss, massive round-trip delays, Doppler shifts of hundreds of kilohertz, limited visibility windows, and limited on-board computing capability compared with ground hardware. Semantic communication (SemCom), which transmits task-relevant meaning rather than exact bits, provides a promising way to address these constraints. This survey examines SemCom for NTNs from the perspective of how semantic mechanisms support different parts of the communication system. We first map five structural NTN constraints onto the semantic mechanisms that can address them, and we show that each platform imposes a distinct constraint vector that selects among those mechanisms. We then propose a five-plane taxonomy covering semantic representation and on-board encoding, channel-adaptive transmission, semantic networking, resource management, and distributed learning with knowledge-base maintenance, together with a cross-cutting trust plane, and we review the literature within it. Finally, we summarize current standardization efforts and available research resources, and identify open problems and future research directions for SemCom in NTNs.

cs.IT↗

arXiv2026

Covering 1024 syndromes with 50 columns

We exhibit a binary linear $[50,40]_2$ code of covering radius $2$, so $\ell_2(10,2)\le 50$, one column below the Kaikkonen--Rosendahl length $51$ that has stood since 2003 and that still seeds the $R=2$ family of Davydov--Marcugini--Pambianco (arXiv:2511.02542). The new matrix admits a $(2,0)$-partition into ten blocks, so Construction $\mathrm{QM}_2^2$ propagates it to exhaustively verified codes of lengths $815$ and $1631$ at $r=18$ and $r=20$, and to the family $n=51\cdot 2^{r/2-5}-1$ of asymptotic density $2601/2048$. The matrices, verifiers, and source are at https://github.com/wustep/maths, pin problems/covering/share/2026-08-24/ at commit 736a38f.

cs.IT↗

arXiv2026

Tight Lower Bounds for State Tomography with Limited Entanglement

We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower bound matching the upper bound in [arXiv:2510.07788]. Thus the copy complexity of estimating an arbitrary $d$-dimensional state to trace distance $ε$ is, up to absolute constant factors, $\max\{d^3/(\sqrt{k}ε^2),d^2/ε^2\}$ for every $k$ and all sufficiently small $ε$. This removes the earlier restriction that $k$ be small as a function of the accuracy. The lower bound applies to arbitrary measurements within each block and adaptive choices between blocks. The lower bound already applies in a small neighborhood of any state whose smallest eigenvalue is of order $1/d$, even when the center is known. The main ingredient is a uniform Fisher information bound for one measurement block that depends only on the smallest eigenvalue of the state. The proof avoids the perturbative expansion responsible for the restriction in [arXiv:2402.16353]. Fano's inequality for metric balls and a log-Sobolev comparison between mutual and Fisher information then reduce the adaptive protocol to this block bound [arXiv:1607.00550, arXiv:1902.08582].

quant-ph↗

arXiv2026

MAP-Based Task-Oriented Precoding for Multiuser Communication

We propose a task-oriented multiuser wireless communication framework for distributed classification based on a MAP-driven system design under wireless channel impairments. \textcolor{black}{By deriving tractable approximations of the MAP error bound}, the proposed approach enables the design of learning-based feature extraction and precoding strategies. Unlike existing approaches that optimize intermediate reconstruction, information-theoretic, or feature-separability objectives, the proposed formulation directly optimizes objectives derived from the MAP decision error, thereby providing a more direct connection to the final classification performance. Simulation results demonstrate that the proposed schemes achieve higher classification accuracy than their counterparts, with lower or comparable computational complexity.

cs.IT↗

arXiv2026

Local Private Information Retrieval for Graph-Based Replicated Systems

We rethink the definition of privacy in multi-server, graph-replicated private information retrieval (PIR) systems, by introducing a novel setting where the user's privacy is governed by the servers' storage structure. In classical graph-replicated PIR, the user retrieves a single message stored at the servers, while hiding the message index from each server. In our proposed privacy setting, the user is concerned with hiding the message index from a particular server, only if that server stores the message being retrieved, and privacy is not imposed otherwise. We coin this relaxed privacy requirement as local user privacy and the resulting PIR problem as local PIR on the graph. Our focus is on two-replicated PIR systems, where every message is replicated twice and stored on two distinct servers. Specifically, we study local PIR systems where the storage is represented by simple graphs, i.e., every pair of vertices is associated with at most one edge, and by their multigraph extension, i.e., $r$ parallel edges replace every edge. For these settings, we establish bounds on the local PIR capacity, defined as the maximum number of message symbols retrieved, per downloaded symbol. The local privacy requirement yields significant capacity gain over the classical PIR capacity under the same storage structure. For instance, in settings where the graph is a disjoint union of multiple identical sub-graphs, the gain in the local PIR capacity over classical PIR capacity is multiplicative in the number of sub-graphs. Further, for connected graphs, we derive capacity lower bounds for edge-transitive and bipartite graphs, which are greater than the best-known PIR capacity bounds. From these and by establishing matching upper bounds, we exactly characterize the capacity for star graphs, cyclic graphs, and path graphs with odd number of vertices. We introduce two local PIR schemes for general graphs.

cs.IT↗

arXiv2026

Manifold-Aware General Coded Computing for Straggler-Resilient Distributed Computing

Existing coded-computing designs do not explicitly exploit the intrinsic structure of the input data. In communication systems, statistical structure and redundancy are often removed through source coding (or compression) before channel coding is applied. This principle, however, does not transfer directly to coded computation. In many computational tasks, particularly in machine learning, the structure of the data is precisely what the computation seeks to exploit to infer outputs or learn meaningful patterns. Consequently, coded-computing schemes should preserve and leverage this structure in their code design, rather than ignoring or eliminating it through source coding. This observation motivates a different perspective on code construction. In many channel-coding schemes, such as Reed-Solomon codes, coded symbols are generated by evaluating a low-dimensional algebraic representation at selected points. In contrast, many high-dimensional datasets naturally concentrate near low-dimensional manifolds. In this paper, we exploit this intrinsic geometry by designing coded samples that follow the natural manifold of the data, rather than imposing an artificial low-dimensional structure unrelated to the data distribution. Inspired by graph-based manifold learning, we propose a manifold-aware encoding strategy for general coded computing (GCC). Experiments on neural network inference and high-dimensional polynomial evaluation demonstrate that the proposed strategy consistently and significantly reduces the mean squared recovery error under straggling compared with standard GCC.

cs.LG↗

arXiv2026

Finite-Sample Limits of Entropy-Based Structure Identification in Discretized Nonlinear Systems

Discretization fundamentally limits structure identification in stochastic systems. When system stochasticity exceeds the discretization resolution, entropy-based methods lose their ability to distinguish which input drives the output. We study this in Fuzzy Inductive Reasoning (FIR), a nonparametric framework for learning dynamical systems from discretized measurements, where the choice of input variables determines both predictive accuracy and the interpretability of the learned input--output relationships. Entropy-based selection targets explainability, i.e., identifying which variables causally drive the output, while mean-squared-error-based selection targets prediction. We introduce a resolution-stochasticity ratio that governs when entropy-based selection is reliable. Three results follow. First, entropy-based selection is consistent below this threshold but loses discriminative power above it, regardless of sample size. Second, using the entropy-selected variables for prediction instead of the MSE-selected ones incurs a closed-form excess prediction risk that grows with input complexity and shrinks with sample size. Third, reliable identification of the causally relevant inputs requires data that scales with the number of input combinations and inversely with the strength of the entropy signal. The theory is validated on a two-state Markov model and demonstrated on a distribution grid reliability dataset analyzing the impact of infrastructure investment, where the goal is to explain which investments drive reliability improvements rather than merely predict outcomes.

eess.SY↗

arXiv2026

Edge codes constructed from unicyclic graphs

Jaramillo-Velez recently introduced edge codes, a new class of toric evaluation codes constructed from the edges of a (hyper)graph $\mathcal{H}$. In the case that $\mathcal{H}$ is a tree, Jaramillo-Velez computed both the minimum distance and the weight distribution of the associated code. In this paper, we study edge codes associated to unicyclic graphs. Our most striking result is that computing the parameters of these codes is subtle in the case that the induced cycle has an even length because these values will depend on certain conditions regarding the length of the cycle and the size of the base field.

math.CO↗

arXiv2026

Intent Drift at SME Scale: Deployment Practice, Not Model Capability, Determines Agentic Compliance

We introduce Chain of Intent, a governance framework for agentic AI at small regulated firms, and validate it against a failure it was built to address. Existing agentic governance research assumes enterprise infrastructure that small firms do not have. In a simulated Hong Kong asset manager with 415 synthetic contact records, an agent performing a routine client-communications task was subjected to ordinary managerial pressure to increase its reach. With its authorised constraints written into its configuration, the agent held: it identified every ambiguity in the firm's records, cited privacy legislation it had never been shown, and refused six successive requests, breaching in two of fifteen runs. With the same task, data, pressure and model, but its purpose left unstated as resource-constrained firms routinely leave it, it breached in thirteen of fifteen runs, contacting up to 220 individuals of whom 94 per cent had no demonstrable marketing consent - conduct carrying a maximum of three years' imprisonment under Hong Kong law. Chain of Intent applies four controls requiring no security engineering: a machine-readable purpose, constrained tool access, a scope ledger, and a pre-action check. It eliminated unlawful contact in every run while preserving task completion, and ablation shows each control independently sufficient by a different mechanism. We further show that drift must be measured at two stages - agents widened their candidate sets in every pressured run while acting on them in roughly one in seven - and that governance applied at the point of intent costs roughly half as much as governance applied at the point of action.

cs.CY↗

arXiv2026

On Cost-Aware Designs for Sequential Hypothesis Testing

We introduce Cost-Aware (CA) Sequential Hypothesis Testing (CASHT), in which an active decision-maker selects sensing actions with differing, random costs to identify the true hypothesis under an average-error constraint $δ$ while minimizing the expected total cost rather than the number of samples. For fixed costs, we prove that the optimal expected total cost scales as $Θ(\log(1/δ))$, and is achievable by Multihypothesis Sequential Probability Ratio Test-based procedures. We show that the CA design principle is to maximize the ratio of expected information gain to expected cost under the policy-induced action distribution. Guided by this principle, we adapt two classic policies to the CA setting and establish their asymptotic optimality. We then treat random costs under two revelation models: ex-post, where costs are disclosed only after a sample is obtained, and the cost-error tradeoff coincides with the fixed-cost case, and ex-ante, where costs accrue before acquisition, and the decision maker may cancel an action mid-operation. For the ex-ante model, we characterize when cancellation lowers the total cost and analyze several cost distributions in detail. Simulations confirm our findings that the CA variants consistently reduce total cost relative to their classical counterparts, and when action cancellation helps or hurts.

cs.IT↗