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arXiv2026

Towards a mathematical theory of superposition

We develop a mathematical theory of superposition in neural networks using tools from frame theory and compressed sensing. In our model, a sparse binary vector $x$ of active features is encoded through an overcomplete dictionary $W$, and feature recovery is performed by applying $\operatorname{ReLU}(W^\top W x+b)$ with an appropriate bias vector $b$. We prove several recovery theorems for this model. In the random-support setting, we establish high-probability support recovery for nearly tight, low-coherence dictionaries, with guarantees when the expected sparsity is up to order $d/\log n$. In the worst-case support setting, we give a sharp and computable criterion for which sparsity levels permit support recovery. We apply this criterion to Gaussian random matrices and equiangular tight frames. For real equiangular tight frames with $n>d+1$, we determine the exact recovery threshold in terms of the coherence. The proof of this result for real equiangular tight frames relies on a novel characterization---which should be of independent interest to frame theorists---of the distribution of signs in the Gram matrix.

stat.ML↗

arXiv2026

MultiGait: A Multi-Sensor Multi-Perspective Multi-Session Biometric Inference Benchmark and its Dataset

A lack of suitable datasets has limited the research into the privacy risks of novel smart city sensors, such as thermal cameras, depth cameras, and lidar. Given the number of unsubstantiated privacy claims and their potential widespread deployment into many people's everyday life, understanding the privacy risks of these sensors -- in isolation and in like-for-like comparisons -- is crucial. With MultiGait, we collected the first multi-sensor, multi-perspective, multi-session gait-focused dataset, for the corresponding, and additional more far-reaching investigations. The dataset, validated with multiple state-of-the-art recognition systems, comprises various walking modes and annotated personal attributes for 199 individuals, to ensure the benefit for advanced studies including cross-sensor recognition and anonymization at the edge. MultiGait represents a foundation for rigorous privacy investigations, demonstrated through an extensive identity inference benchmark across eight sensors, four perspectives, and three recording sessions. Our benchmark incidentally reveals that sensors often assumed to be privacy-friendly do still entail considerable identity inference risks, while the poor cross-session generalization of existing methods underscores an important research gap.

cs.CR↗

arXiv2026

Chase-like Decoding: Test-Pattern Design and Performance Analysis

Chase-like decoding algorithms are a popular choice for soft-input decoding of algebraic codes. We evaluate different test-pattern sets for Chase-like decoding. Structured sets, such as Chase-II patterns or patterns chosen by logistic weight, are analyzed using order statistics, while arbitrary sets are evaluated by calculating covered-space probabilities and by performing Monte Carlo simulation. We further propose an algorithm that designs test-pattern sets to cover likely error patterns, achieving comparable performance with half the number of test patterns compared with conventional sets for high-rate BCH codes.

cs.IT↗

arXiv2026

On systematicity of linear function-correcting codes

The standard formulation of function-correcting codes uses systematic encodings. We study the redundancy cost of this constraint when both the prescribed function and the encoding are linear. We introduce the function-separation distance and show that several classical unequal error protection parameters are special cases. For linear functions and encodings, this distance is the first relative generalized Hamming weight of the code relative to the encoded kernel. We formulate free and systematic linear separation problems. We prove that the optimal free redundancy depends only on the rank of the function, and determine the optimal systematic redundancy for prescribed separations $d\leq3$.

cs.IT↗

arXiv2026

What It Costs to Compose, Rebuild, and Correct Precomputed Memory

Language models can answer from precomputed memory, a model's saved reading of a body of material, reused across requests instead of read again at each. This paper maps where that practice preserves correctness and the conditions under which it fails. Across experiments on Llama-3.1-8B-Instruct using both saved key-value caches and trained compressions of them, precomputed memory degrades when assembled from separately prepared parts, stays current only through rebuilds costing a large fraction of full preparation in our measurements, and ignores corrections served beside it conditional on phrasing. If precomputed memories can be served alongside one another, be cost-efficiently rebuilt, and be superseded by new information arriving in real-time, they can serve as a way to avoid re-feeding context to a model over repeated queries. The implication of our results for a deployed system that deals with a variety of queries is that precomputed memories are best rebuilt on the cadence at which new information changes what the memory was originally computed from. Both warm-rebuilding trained compressions of key-value caches and serving specifically-phrased updates beside a memory, as pasted text or injected cache state, show particular promise for keeping precomputed memories current, the latter as an interim measure between rebuilds, and we measure the cost and name the remaining questions associated with each.

cs.CL↗

arXiv2026

Exact Limits of Random Projections for Preserving Geometry: Distance Recovery, Nearest-Neighbor Rankings, and Covariance Shape in Gaussian Models

The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal. In high dimensions, however, distances concentrate around a baseline while key geometric information lies in much smaller fluctuations. We show that the JL bound can therefore be uninformative about retained geometry: an independent Gaussian replacement map can satisfy it even though the replacement cloud is independent of the original data. We then ask how well any decoder can recover a feature $f(D)$ of a squared distance $D$ from a linear sketch. Under squared-error loss, the optimal decoder is conditional expectation, so recovery defines a linear operator whose singular values quantify feature recovery. For isotropic Gaussian data ($Σ=σ^2 I_d$), we diagonalize this operator in closed form. For fixed $k$ with $m,d-m\to\infty$, its $k$th singular value satisfies $\ell_k\approx(m/ d)^{k/2}$. This yields three sharp consequences. A rank-$m$ sketch retains at most an $m/d$ fraction of the variance of any feature of one squared distance. If $m\to\infty$ and $m/d\to0$, the expected Kendall correlation is $\frac{2}π\sqrt{m/d}(1+o(1))$; for fixed $q$, nearest- neighbor agreement tends to $1/q$. Yet one projection can satisfy the JL bound while mean Kendall correlation vanishes when $\log n\ll m\ll d$. After removing scale, Haar-averaged retained covariance-shape information is $(m/d)^2$. Thus JL distance preservation does not quantify the geometry available for comparison or inference.

cs.LG↗

arXiv2026

Peer Oversight in Collective Decision Making

This article introduces peer $k$-oversight, a property of sequential collective decision mechanisms requiring at least $k$ agents to be responsible for every harmful outcome. It is shown that whenever $k$-oversight can be achieved by redistributing control over the decisions in a mechanism, it can be achieved using just $k$ agents. A polynomial-time algorithm is also presented that determines whether such a redistribution exists and, when it does, constructs one. These results establish peer oversight as a tractable design principle for multiagent decision-making systems.

cs.GT↗

arXiv2026

Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes

Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated by inference-based decoders. To date, such machine-learning (ML) decoders lack two key properties crucial for practical fault tolerance: reliable uncertainty quantification and robust generalization to previously unseen QEC codes. To address this gap, we propose a Quantum Bayesian graph Attention decoder \textbf{(QuBA)} that enables expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop a multi-phase training framework with enhanced cross-domain robustness enabling decoding beyond the training set called Sequential Aggregate Generalization under Uncertainty \textbf{(SAGU)}. Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i) both QuBA and SAGU consistently outperform the classical baseline belief propagation (BP), achieving up to a \emph{two orders of magnitude} reduction in logical error rate (LER) under confident-decision bounds on the coprime BB code $[[154,6,16]]$; (ii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.

quant-ph↗

arXiv2026

New binary optimal LCD codes using heuristic embedding

In this paper, we investigate the construction of binary optimal LCD codes through short LCD embeddings. For this purpose, we design heuristic frameworks based on a greedy algorithm. We explore the search spaces of LCD embeddings using the fact that an invertible matrix together with an arbitrary matrix yields an LCD embedding. We therefore use elementary row operations on the invertible block and single entry-flips on the arbitrary block as local moves in a greedy algorithm. Using this method, we have found $14$ optimal new LCD codes with dimensions 7 and 8 for lengths from 55 to 201.

cs.IT↗

arXiv2026

Low-Altitude Fluid Antenna Network with Multi-Agent Reinforcement Learning

Low-altitude wireless networks (LAWNs) integrate terrestrial and aerial platforms to provide ubiquitous communication, sensing, and localization services for unmanned aerial vehicles (UAVs) and electric vertical takeoff and landing (eVTOL) aircraft. However, dynamic air-ground and air-air channels, abrupt blockages, and heterogeneous interference hinder the realization of this goal. Nevertheless, fluid antenna (FA), a cutting-edge multiple-input multiple-output (MIMO) technique, overcomes these challenges by reconfiguring antenna positions to unlock additional spatial degrees-of-freedom. In this paper, towards bringing low-altitude FA networks into reality, we study the fast and high-performance FA reconfiguration for low-altitude FA networks with multi-agent reinforcement learning (MARL). Specifically, we present an electromagnetic digital twin (EM-DT)-assisted MARL framework. To fill the sim-to-real gap, we introduce a two-stage transfer learning framework. Our case study shows that joint FA positions and beamforming optimization can enhance the system sum-rate by 118.5%, compared to the fixed position baseline. This gain comes from the dynamic millisecond timescale reconfiguration of FA arrays and the adaptive steering of beams toward aerial users with mobility.

cs.IT↗

arXiv2026

Don't You Know, Pump it Up! Investigating Cryptocurrency Manipulation in Telegram-Driven Activity

Telegram plays a pivotal role in cryptocurrency communication and has been repeatedly associated with coordinated schemes, such as pump-and-dump manipulation. However, existing studies typically focus on known manipulation chats or a limited set of cryptocurrencies, leaving open the question of how Telegram is leveraged for mass promotional activity (shilling) at scale. Moving beyond these limitations, this work analyzes the interplay between information flows and market activity across public Telegram channels. To this end, we propose a scalable framework that (i) classifies crypto-related messages using a fine-tuned encoder model to filter semantic noise, (ii) detects anomalous spikes in cryptocurrency mentions via adaptive thresholding, and (iii) validates temporal associations between social bursts and market movements using quasi-experimental econometric methods (RDD and DiD). We apply this framework to one year of public Telegram data (14,499 channels and over 20 million messages) aligned with transaction data for more than 17,000 cryptocurrencies. Our analysis identifies 47 events consistent with potential pump-and-dump activity and 73 sustained market reactions, showing that manipulative signals are characterized by extreme temporal synchronization and precede price movements by seconds. Notably, psycholinguistic analysis reveals that pump-and-dump messages are linguistically indistinguishable from organic discussions, highlighting the limits of text-based detection alone. Finally, we estimate the cumulative financial volume of detected pump-and-dump events to exceed $200 million and release a public cryptocurrency dictionary and a fine-tuned classifier to support future research.

cs.SI↗

arXiv2026

How Much Can AI Understand? Toward AI-Assisted Sensemaking of Collaborative Discussion in Groups with Shared History

AI tools that support collaborative discussion typically treat the discussion as a standalone task, focusing only on its content and setting aside the social context of the group having it. But it is groups with a shared history, with their own norms, hierarchies, and relationships, where the most tangled and complex discussions tend to arise. These discussions cannot be understood apart from that context, and AI that overlooks it risks failing to convey what a discussion means, or even misrepresenting it. Drawing on two studies of how experienced Wikipedia editors read and make sense of discussions, we propose an AI-Assisted Sensemaking Model for Collaborative Discussions, which captures not only a discussion's arguments but also the norms and participants behind it, along with the context that gives each meaning. In this model, the system supports the early stages of the sensemaking process, and the degree to which it performs interpretive work can range from low to high. We argue that higher interpretive work reduces the burden on users but increases their reliance on the system's judgment. We then discuss the risks of an insufficiently intelligible system, what it would take to make one more intelligible, and the safeguards it still requires.

cs.HC↗

arXiv2026

Moments of crosscorrelation demerit factors of binary sequences

Families of sequences with low mutual aperiodic crosscorrelation assist the design of systems for multi-user asynchronous communications and multiple-input multiple-output radar. The crosscorrelation demerit factor of a pair of sequences is the sum of the squared magnitudes of their crosscorrelation values at every shift when the sequences are normalized to unit Euclidean norm, and the merit factor is the reciprocal of the demerit factor. For each positive integer $\ell$, we endow the $2^{2 \ell}$ pairs of binary sequences of length $\ell$ with uniform probability measure and study the distribution of their crosscorrelation demerit factors. Sarwate showed that the mean value is always $1$ regardless of length $\ell$. We develop a method for finding an exact formula for the $p$th central moment (for any positive integer $p$) as a function of $\ell$. Formulae for the variance and third central moment ($p=2$ and $3$) are then obtained by hand calculations, while the fourth through sixth central moments are obtained by computer-assisted calculations. Our theory also shows that all the central moments must be strictly positive for $p\geq 2$ and $\ell \geq 3$.

cs.IT↗

arXiv2026

Initialization and Rate-Quality Functions for Generative Network Layer Protocols

Generative AI (GenAI) creates full content based on compact encodings. While GenAI has been used for applications where the generated content is returned to the encoding sender, it can also extend the capacity of communication networks by transmitting compact encodings through capacity-limited links, then generating and forwarding approximations from the GenAI node to the destination. This poses the challenge of evaluating approximation quality as a function of the rate between the source and GenAI node, while accounting for the communication overhead of learning. We present a method- and modality-agnostic initialization protocol for learning rate-quality functions in GenAI-aided networks, defining three variants: source-, node-, and destination-oriented, each with different messaging flows based on where quality is measured. The protocol augments node discovery protocols (e.g., MCP, A2A) when sources lack confidence in advertised model performance. We illustrate operation via a minimum estimation budget calculated using a distribution-free tolerance limit , and validate using a case study on image transmission under quality constraints. Results confirm the calculated budget meets the target quality requirement, with positive gains over JPEG after around 20 post-learning transmissions for a perceptual metric and more than 100 for a goal-oriented metric, providing a practical foundation for GenAI-based network compression.

cs.NI↗

arXiv2026

UMVUE-Type Estimators under Bregman Losses

We study unbiased estimation under Bregman losses and develop an extension of the classical theory of uniformly minimum variance unbiased estimators (UMVUEs). Exploiting bias--variance-type decompositions for Bregman divergences, we consider two natural loss functions, $D_φ(θ,\hatθ)$ and $D_φ(\hatθ,θ)$, and their corresponding notions of unbiasedness. We show that the latter formulation reduces to the classical setting, whereas the former yields a different framework in which unbiasedness is characterized in the dual space induced by $\nablaφ$. For the nontrivial case, we establish analogs of the Rao--Blackwell and Lehmann--Scheff{é} theorems, providing a systematic construction of type-I Bregman UMVUEs.

cs.IT↗

arXiv2026

BER-PEF: Unified Human Mobility Predictability Evaluation via Bayes Error Rate Estimation

Human mobility predictability concerns the best prediction performance attainable from a given target and input information, but its ground truth is not directly observable on real mobility data. We present BER-PEF, a Bayes-error-rate-based framework that converts BER estimation into mobility predictability estimation and provides a unified protocol for comparing estimators without observable ground truth. The framework maps symbolic sequences, numeric trajectories, contextual features, and learned representations into a common feature--label space, then evaluates estimator outputs along controlled perturbation curves against a shared predictability reference interval by measuring deviations below the interval, above the interval, and across the full interval. Experiments on Foursquare NYC and TKY, GeoLife, and T-Drive show that several BER-based estimators achieve lower reference discrepancy than existing predictability methods on symbolic sequences and numeric trajectories, while their estimates track changes in empirical prediction performance under perturbation. Additional analyses show that contextual inputs and multiple structured representations can be evaluated under the same protocol, and that aggregating evidence across multiple perturbation levels provides a more reliable basis for estimator selection than relying on a single unperturbed observation. BER-PEF therefore offers a unified and verifiable path for evaluating predictability estimators on heterogeneous mobility data when ground-truth predictability is unavailable.

cs.LG↗

arXiv2026

Asymptotically Optimal Quantum Universal Quickest Change Detection

This paper investigates the quickest change detection of quantum states in a universal setting: specifically, where the post-change quantum state is not known a priori. We establish the asymptotic optimality of a two-stage approach in terms of worst average delay to detection. The first stage employs block POVMs with classical outputs that preserve quantum relative entropy to arbitrary precision. The second stage leverages a recently proposed windowed-CUSUM algorithm that is known to be asymptotically optimal for quickest change detection with an unknown post-change distribution in the classical setting.

quant-ph↗

arXiv2025

Quantum channel discrimination against jammers

We study the problem of quantum channel discrimination between two channels with an adversary input party (a.k.a. a jammer). This setup interpolates between the best-case channel discrimination as studied by (Wang & Wilde, 2019) and the worst-case channel discrimination as studied by (Fang, Fawzi, & Fawzi, 2025), thereby generalizing both frameworks. To address this problem, we introduce the notion of minimax channel divergence and establish several of its key mathematical properties. We prove the Stein's lemma in this new setting, showing that the optimal type-II error exponent in the asymptotic regime under parallel strategies is characterized by the regularized minimax channel divergence.

quant-ph↗