OpenRaiser/Intern-Atlas huggingface dataset:
Estimating the Decoding Failure Rate of Binary Regular Codes Using Iterative Decoding
Venue: arXiv cs.CR 2026
Year: 2026

Providing closed-form estimates of the decoding failure rate of iterative decoders for low- and moderate-density binary parity-check codes has attracted significant interest in the research community. Recently, interest in this topic has increased due to the use of iterative decoders in post-quantum cryptosystems, where the desired decoding failure rates (DFRs) are less than or equal to $2^{-128}$ and impossible to estimate via Monte Carlo simulations. We propose a new technique that provides accurate DFR estimates for a two-iteration (parallel) bit-flipping decoder that can be used for cryptographic purposes. We estimate the bit-flipping probabilities at the second decoder iteration and the syndrome weight distribution before and after the first iteration as a function of the code parameters and error weight. We validate our results numerically by comparing the modelled and simulated syndrome weights, the incorrectly guessed error bit distribution at the end of the first iteration, and the DFR after two iterations in both the floor and waterfall regimes. Finally, we apply our method to estimate the DFR of the LEDAcrypt cryptographic system, a post-quantum key encapsulation method that employs a two-iteration bit-flipping decoder. We show that the DFR estimate resulting from the chosen code parameters can be improved by a factor larger than $2^{70}$ with respect to previous estimation techniques, when $128$-bit security is required. This allows for a $20$% reduction in public key and ciphertext sizes at no security loss. We note that our results can be applied to the post-quantum cryptosystem known as Bit Flipping Key Encapsulation (BIKE) replacing the current ``BIKE-flip decoder'' with the two-iteration decoder and consequently endowing BIKE with the property of indistinguishability under an adaptive chosen-ciphertext attack (IND-CCA$2$), provably.
Knowledge Problems in Protocol Analysis: Extending the Notion of Subterm Convergent
Venue: arXiv cs.LO 2026
Year: 2026

We introduce a new form of restricted term rewrite system, the graph-embedded term rewrite system. These systems, and thus the name, are inspired by the graph minor relation and are more flexible extensions of the well-known homeomorphic-embedded property of term rewrite systems. As a motivating application area, we consider the symbolic analysis of security protocols, and more precisely the two knowledge problems defined by the deduction problem and the static equivalence problem. In this field restricted term rewrite systems, such as subterm convergent ones, have proven useful since the knowledge problems are decidable for such systems. Many of the same decision procedures still work for examples of systems which are "beyond subterm convergent". However, the applicability of the corresponding decision procedures to these examples must often be proven on an individual basis. This is due to the problem that they don't fit into an existing syntactic definition for which the procedures are known to work. Here we show that many of these systems belong to a particular subclass of graph-embedded convergent systems, called contracting convergent systems. On the one hand, we show that the knowledge problems are decidable for the subclass of contracting convergent systems. On the other hand, we show that the knowledge problems are undecidable for the class of graph-embedded systems. Going further, we compare and contrast these graph embedded systems with several notions and properties already known in the protocol analysis literature. Finally, we provide several combination results, both for the combination of multiple contracting convergent systems, and then for the combination of contracting convergent systems with particular permutative equational theories.
Compiling High-Level Neural Network Specifications into VNN-LIB Queries
Venue: arXiv cs.LO 2026
Year: 2026

The formal verification of traditional software has been revolutionised by verification-orientated languages such as Dafny and F* which enable developers to write high-level specifications that are automatically compiled down to low-level SMT-LIB queries. In contrast, neural network verification currently lacks such infrastructure, often requiring users to express requirements in formats close to the low-level VNN-LIB query format. This gap persists because targeting VNN-LIB presents unique algorithmic challenges when compared to targeting SMT-LIB: VNN-LIB is restricted to a fixed finite set of variables representing the input and outputs of the network, and even toy neural network specifications have an extremely large number of variables. In this paper, we present the first algorithm for compiling high-level neural network specifications into optimised VNN-LIB queries. Our algorithm is numerically sound and supports a far rich logical fragment than existing tools, including transformations of variables, first-class quantifiers, and specifications involving multiple networks or multiple applications of the same network. We implement this algorithm within the Vehicle framework and demonstrate that its performance is asymptotically optimal for benchmark specifications.
Topology-Informed Graph Transformer
Venue: arXiv cs.LG 2026
Year: 2026

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.
Beyond DAGs: A Latent Partial Causal Model for Multimodal Learning
Venue: arXiv cs.LG 2026
Year: 2026

Directed Acyclic Graphs (DAGs) are a standard tool in causal modeling, but their suitability for capturing the complexity of large-scale multimodal data is questionable. In practice, real-world multimodal datasets are often collected from heterogeneous generative processes that do not conform to a single DAG. Instead, they may involve multiple, and even opposing, DAG structures with inverse causal directions. To address this gap, in this work, we first propose a novel latent partial causal model tailored for multimodal data representation learning, featuring two latent coupled variables parts connected by an undirected edge, to represent the transfer of knowledge across modalities. Under specific statistical assumptions, we establish an identifiability result, demonstrating that representations learned by MultiModal Contrastive Learning (MMCL) correspond to the latent coupled variables up to a trivial transformation. This result deepens our understanding of the why MMCL works, highlights its potential for representation disentanglement, and expands the utility of pre-trained models like CLIP. Synthetic experiments confirm the robustness of our findings, even when the assumptions are partially violated. Most importantly, experiments on a pre-trained CLIP model embodies disentangled representations, enabling few-shot learning and improving domain generalization across diverse real-world datasets. Together, these contributions push the boundaries of MMCL, both in theory and in practical applications.
Unifying Graded Linear Logic and Differential Operators
Venue: arXiv cs.LO 2026
Year: 2026

Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which can describe the resource management or the complexity analysis of a program. From an other perspective, Differential Linear Logic is an extension which allows the linearization of proofs. In this article, we merge these two directions by first defining a differential version of Graded linear logic: this is made by indexing exponential connectives with a monoid of differential operators. We prove that it is equivalent to a graded version of previously defined extension of finitary differential linear logic. We give a denotational model of our logic, based on distribution theory and linear partial differential operators with constant coefficients.
On the permutation automorphisms of binary cubic codes
Venue: arXiv cs.IT 2026
Year: 2026

A binary linear code whose permutation automorphism group has a fixed point free permutation of order $3$ is called a binary cubic code. The scope of this paper is to investigate the structural properties of binary cubic codes. Let $C$ be a binary cubic $[n,k]$ code. In this paper, we prove that if $n\geq 30$ and $C$ has permutation automorphism group of order three, then $k\geq 6$. Additionally, we show that if $n < 30$ and $k\leq 4$, then the permutation automorphism group of $C$ has order greater than three. Moreover, along the way, we provide some results on the structure of the higher dimensional cubic codes. In particular, we present some results concerning the structure of the putative extremal self-dual $[72,36,16]$ code under the assumption that it is cubic.
Online Flexible Busy Time Scheduling on Heterogeneous Machines
Venue: arXiv cs.DS 2026
Year: 2026

We study the online busy time scheduling model on heterogeneous machines. In our setting, jobs with uniform length arrive online with a deadline that becomes known to the algorithm at the job's arrival time. An algorithm has access to machines, each with different associated capacities and costs. The goal is to schedule jobs on machines by their deadline, so that the total cost incurred by the scheduling algorithm is minimized. While busy time scheduling has been well-studied, relatively little is known when machines are heterogeneous (i.e., have different costs and capacities), despite this natural theoretical generalization being the most practical model for clients using cloud computing services. We make significant progress in understanding this model by designing an 8-competitive algorithm for the problem on unit-length jobs and providing a lower bound of 2 on the competitive ratio. The lower bound is tight in the setting when jobs form non-nested intervals. Our 8-competitive algorithm generalizes to one with competitive ratio $8(2p-1)/p < 16$ when all jobs have uniform length $p$.
Quantum Soft Covering with Relative Entropy Criterion
Venue: arXiv cs.IT 2026
Year: 2026

In this work, we propose a soft covering problem for fully quantum channels using relative entropy as a criterion for operator closeness. We establish covering lemmas by deriving one-shot bounds on the achievable rates in terms of smooth min-entropies. In the asymptotic regime, we show that the infimum of the rate, defined as the logarithm of the minimum rank of the encoded input state, is given by the minimal coherent information between the reference and output systems that yields the target output state. Furthermore, we present a one-shot quantum decoupling theorem that also employs a relative-entropy criterion. Due to the Pinsker inequality, our one-shot results based on the relative-entropy criterion are tighter than the corresponding results based on the trace norm considered in the literature. In addition, we establish achievable error exponents and second-order rates for quantum soft covering under both trace-distance and relative-entropy criteria.
Maximum Spectral Efficiency of Adaptive Coherent Terrestrial FSO Links
Venue: arXiv cs.IT 2026
Year: 2026

Terrestrial free-space optical (FSO) communication systems, while designed to operate on large unlicensed optical bandwidths, are fundamentally power-constrained due to stringent eye-safety regulations. Moreover, channel fluctuations inherent to terrestrial FSO links further reduce the received optical power. Consequently, the achievable signal-to-noiseratio (SNR) per hertz could become limited -- especially for future terrestrial FSO systems based on coherent communications. This necessitates the development of efficient and adaptive communication strategies at both the optical transmitter and receiver. However, a comprehensive assessment of adaptive coherent terrestrial FSO systems remains largely unexplored in the existing literature. This paper investigates terrestrial FSO communication links employing adaptive coherent transmission and synchronous heterodyne detection-based reception operating in the shot-noise-limited regime. Specifically, we propose a novel exact closed-form expression for the average spectral efficiency limit of coherent FSO communication systems with optimal adaptive signaling over gamma-gamma turbulence channels with pointing errors. More importantly, we provide a detailed assessment of the impact of turbulence and pointing error impairments on the coherent FSO system performance, revealing several novel and counterintuitive insights. Extensive numerical results help elucidate the intricacies of analyzing these terrestrial FSO systems and clarify a few misconceptions alluded to in recent related literature.
Scaling Efficient LLMs
Venue: arXiv cs.CL 2026
Year: 2026

Recent LLMs have hundreds of billions of parameters consuming vast resources. Furthermore, the so called "AI scaling law" for transformers suggests that the number of parameters must scale linearly with the size of the data. In response, we inquire into efficient LLMs, i.e. those with the fewest parameters that achieve the desired accuracy on a training corpus. Specifically, by comparing theoretical and empirical estimates of the Kullback-Leibler divergence, we derive a natural AI scaling law that the number of parameters in an efficient LLM scales as $D^γ$ where $D$ is the size of the training data and $ γ\in [0.44, 0.72]$, suggesting the existence of more efficient architectures. Against this backdrop, we propose recurrent transformers, combining the efficacy of transformers with the efficiency of recurrent networks, progressively applying a single transformer layer to a fixed-width sliding window across the input sequence. Recurrent transformers (a) run in linear time in the sequence length, (b) are memory-efficient and amenable to parallel processing in large batches, (c) learn to forget history for language tasks, or accumulate history for long range tasks like copy and selective copy, and (d) are amenable to curriculum training to overcome vanishing gradients. In our experiments, we find that recurrent transformers perform favorably on benchmark tests.
Standardizing the Measurement of Text Diversity: A Tool and a Comparative Analysis of Scores
Venue: arXiv cs.CL 2026
Year: 2026

The diversity across outputs generated by LLMs shapes perception of their quality and utility. High lexical diversity is often desirable, but there is no standard method to measure this property. Templated answer structures and ``canned'' responses across different documents are readily noticeable, but difficult to visualize across large corpora. This work aims to standardize measurement of text diversity. Specifically, we empirically investigate the convergent validity of existing scores across English texts, and we release diversity, an open-source Python package for measuring and extracting repetition in text. We also build a platform based on diversity for users to interactively explore repetition in text. We find that fast compression algorithms capture information similar to what is measured by slow-to-compute $n$-gram overlap homogeneity scores. Further, a combination of measures -- compression ratios, self-repetition of long $n$-grams, and Self-BLEU and BERTScore -- are sufficient to report, as they have low mutual correlation with each other.
Enumeration for MSO-Queries on Compressed Trees
Venue: arXiv cs.FL 2026
Year: 2026

We study the problem of enumerating the answers to a query formulated in monadic second order logic (MSO) over an unranked forest F that is compressed by a straight-line program (SLP) D. Our main result states that this can be done after O(|D|) preprocessing and with output-linear delay (in data complexity). This is a substantial improvement over the previously known algorithms for MSO-evaluation over trees, since the compressed size |D| might be much smaller than (or even logarithmic in) the actual data size |F|, and there are linear time SLP-compressors that yield very good compressions on practical inputs. In particular, this also constitutes a meta-theorem in the field of algorithmics on SLP-compressed inputs: all enumeration problems on trees or strings that can be formulated in MSO-logic can be solved with linear preprocessing and output-linear delay, even if the inputs are compressed by SLPs. We also show that our approach can support vertex relabelling updates in time that is logarithmic in the uncompressed data. Our result extends previous work on the enumeration of MSO-queries over uncompressed trees and on the enumeration of document spanners over compressed text documents.
Dynamics of Moral Behavior in Heterogeneous Populations of Learning Agents
Venue: arXiv cs.MA 2026
Year: 2026

Growing concerns about safety and alignment of AI systems highlight the importance of embedding moral capabilities in artificial agents: a promising solution is the use of learning from experience, i.e., Reinforcement Learning. In multi-agent (social) environments, complex population-level phenomena may emerge from interactions between individual learning agents. Many of the existing studies rely on simulated social dilemma environments to study the interactions of independent learning agents; however, they tend to ignore the moral heterogeneity that is likely to be present in societies of agents in practice. For example, at different points in time a single learning agent may face opponents who are consequentialist (i.e., focused on maximizing outcomes over time), norm-based (i.e., conforming to specific norms), or virtue-based (i.e., considering a combination of different virtues). The extent to which agents' co-development may be impacted by such moral heterogeneity in populations is not well understood. In this paper, we present a study of the learning dynamics of morally heterogeneous populations interacting in a social dilemma setting. Using an Iterated Prisoner's Dilemma environment with a partner selection mechanism, we investigate the extent to which the prevalence of diverse moral agents in populations affects individual agents' learning behaviors and emergent population-level outcomes. We observe several types of non-trivial interactions between pro-social and anti-social agents, and find that certain types of moral agents are able to steer selfish agents towards more cooperative behavior.
Revenue Variance Minimization: Beyond First Price Auctions
Venue: arXiv cs.GT 2026
Year: 2026

We study revenue variance in the sale of $k$ homogeneous items to risk-neutral, unit-demand bidders with independent private values. Although the Revenue Equivalence Theorem implies that standard auctions generate the same expected revenue, the distribution of revenue differs across mechanisms. Prior work shows that, in single-item environments with ex-post individual rationality (IR), the first-price auction minimizes revenue variance. We show that this result is fragile. Under interim IR, the optimality of the first-price auction breaks down in asymmetric single-item settings, and we characterize the variance-minimizing mechanisms for any implementable allocation rule in this environment. In multi-item symmetric regular environments with interim IR, we construct a mechanism that implements the efficient allocation and guarantees constant revenue while maintaining non-negative payments. Under ex-post IR, we show that revenue variance can be reduced relative to winner-pays-bid formats by introducing negative correlations in payments. Nevertheless, we show that the variance ranking between the winner-pays-bid auction and the uniform $(k+1)$-st price auction is maintained in multi-unit settings.
Unified Source-Free Domain Adaptation
Venue: arXiv cs.CV 2026
Year: 2026

In the pursuit of transferring a source model to a target domain without access to the source training data, Source-Free Domain Adaptation (SFDA) has been extensively explored across various scenarios, including Closed-set, Open-set, Partial-set, and Generalized settings. Existing methods, focusing on specific scenarios, not only address a limited subset of challenges but also necessitate prior knowledge of the target domain, significantly limiting their practical utility and deployability. In light of these considerations, we introduce a more practical yet challenging problem, termed unified SFDA, which comprehensively incorporates all specific scenarios in a unified manner. In this paper, we propose a novel approach latent Causal factors discovery for unified SFDA (CausalDA). In contrast to previous alternatives that emphasize learning the statistical description of reality, we formulate CausalDA from a causality perspective. The objective is to uncover potential causality between latent variables and model decisions, enhancing the reliability and robustness of the learned model against domain shifts. To integrate extensive world knowledge, we leverage a pre-trained vision-language model such as CLIP. This aids in the formation and discovery of latent causal factors in the absence of supervision in the variation of distribution and semantics, coupled with a newly designed information bottleneck with theoretical guarantees. Extensive experiments demonstrate that CausalDA can achieve new state-of-the-art results in distinct SFDA settings, as well as source-free out-of-distribution generalization. Our code and data are available at https://github.com/tntek/CausalDA.
Governance of Generative Artificial Intelligence for Companies
Venue: arXiv cs.AI 2026
Year: 2026

Generative Artificial Intelligence (GenAI), specifically large language models (LLMs) like ChatGPT, has swiftly entered organizations without adequate governance, posing both opportunities and risks. Despite extensive debate on GenAI's transformative potential and emerging regulatory measures, limited research addresses organizational governance from both technical and business perspectives. While frameworks for AI governance exist, it remains unclear to what extent they apply to GenAI. This review paper fills this gap by surveying recent literature to better understand the fundamental characteristics of GenAI and to adapt existing governance frameworks specifically to GenAI within organizations. To this end, it extends Nickerson's framework development process by incorporating prior conceptualizations. The resulting framework delineates scope, objectives, and governance mechanisms designed to both harness business opportunities and mitigate risks associated with GenAI integration. Overall, this research advances a focused approach to GenAI governance, offering practical guidance for companies navigating the challenges of GenAI adoption and highlighting research gaps.