The maximum entropy state
We give an algorithm for calculating the maximum entropy state as the least fixed point of a Scott continuous mapping on the domain of classical states in their Bayesian order.
math.PR↗
SEARCH · Search arXiv
Results for “math.CA”
Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Improving the decoding performance of CA-polar codes
We investigate the use of modern code-agnostic decoders to convert CA-SCL from an incomplete decoder to a complete one. When CA-SCL fails to identify a codeword that passes the CRC check, we apply a code-agnostic decoder that identifies a codeword that satisfies the CRC. We establish that this approach gives gains of up to 0.2 dB in block error rate for CA-polar codes from the 5G New Radio standard. If, instead, the message had been encoded in a systematic CA-polar code, the gain improves to more than 1.5 dB. Leveraging recent developments in blockwise soft output, we additionally establish that it is possible to control the undetected error rate even when using the CRC for error correction.
cs.IT↗
Mathematical and numerical analysis of quantum signal processing
Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of quantum singular value transformation (QSVT), which is often regarded as one of the most important quantum algorithms of the past decade, with a wide range of applications in scientific computing, from Hamiltonian simulation to solving linear systems of equations and eigenvalue problems. In this article we survey recent advances in the mathematical and numerical analysis of QSP. In particular, we focus on its generalization beyond polynomials, the computational complexity of algorithms for phase factor evaluation, and the numerical stability of such algorithms. The resolution to some of these problems relies on an unexpected interplay between QSP, nonlinear Fourier analysis on $\mathrm{SU}(2)$, fast polynomial multiplications, and Gaussian elimination for matrices with displacement structure.
quant-ph↗
Positivity loss in bandlimited spectral reproduction on spheres
How small can the positivity loss be for an $N$-bandlimited spectral operator that exactly reproduces all modes up to degree $L$? For spherical polynomial approximation on $\mathbb S^d$, we prove that the smallest possible excess of the uniform operator norm above 1, equivalently the least positivity loss, is of sharp order $\left({L}/{(N+1)}\right)^2$ when $1\le L< N$. The lower bound follows from a Fejér peak test and a concentration estimate for bandlimited kernels, while a matching upper bound is obtained by correcting a positive Jackson operator with a smooth filter. We illustrate the result in three settings. On the circle, taking $N=sL-1$, this determines the sharp order of the generalized-projection constant above 1 and identifies the gap between the $s^{-1}$ excess of delayed de la Vallée--Poussin means and the optimal $s^{-2}$ order. For filtered hyperinterpolation, whose operator norm has long been known to be uniformly bounded, we give a quantitative lower bound on its separation from the positivity threshold 1. Finally, we identify an operator-level obstruction to maximum principles.
math.NA↗
Logarithmic Chowla Correlations Across All Shift Scales
Let $λ(n)=(-1)^{Ω(n)}$ be the Liouville function. We prove a fixed power-logarithmic bound for its logarithmically weighted two-point correlations across the full shift range. There is an absolute $c>0$ such that every sufficiently large $x$ admits a single set $\mathcal E_x\subseteq[1,x]$ with $|\mathcal E_x\cap[1,H]|\ll_A H(\log x)^{-A}$ $(1\le H\le x)$ for every fixed $A>0$, while $\max_{\substack{1\le h\le x\ h\notin\mathcal E_x}}\sup_{1\le y\le x}\left|\sum_{n\le y}\frac{λ(n)λ(n+h)}{n}\right|\ll(\log x)^{1-c}$. The same exceptional-set formulation extends, without an upper cutoff, to all positive integer shifts. Earlier full-range theorems average over the shift; here a fixed saving holds pointwise outside one set whose density in every initial segment is smaller than every fixed negative power of $\log x$. The new middle-scale argument combines a general-good-modulus Liouville deletion lemma with a linear bad-modulus score, a progression Fourier estimate, and a Mellin-localized dilation that separates divisor-dependent endpoints. Maximal fixed-moment bounds evacuate the low prefix and control the long-shift range. Assuming GRH for primitive Dirichlet $L$-functions, we also prove, uniformly for $h\in\mathbb N$ and $1\le y\le x$, $\left|\sum_{n\le y}\frac{λ(n)λ(n+h)}{n}\right|\le\log(2\min{h,y})+O((\log x)^{1-c_{\mathrm G}})$ for an absolute $c_{\mathrm G}>0$, with no exceptional shifts.
math.NT↗
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↗
Enhancing Affine Maximizer Auctions with Correlation-Aware Payment
Affine Maximizer Auctions (AMAs), a generalized mechanism family from VCG, are widely used in automated mechanism design due to their inherent dominant-strategy incentive compatibility (DSIC) and individual rationality (IR). However, as the payment form is fixed, AMA's expressiveness is restricted, especially in distributions where bidders' valuations are correlated. In this paper, we propose Correlation-Aware AMA (CA-AMA), a novel framework that augments AMA with a new correlation-aware payment. We show that any CA-AMA preserves the DSIC property and formalize finding optimal CA-AMA as a constraint optimization problem subject to the IR constraint. Then, we theoretically characterize scenarios where classic AMAs can perform arbitrarily poorly compared to the optimal revenue, while the CA-AMA can reach the optimal revenue. For optimizing CA-AMA, we design a practical two-stage training algorithm. We derive that the target function's continuity and the generalization bound on the degree of deviation from strict IR. Finally, extensive experiments showcase that our algorithm can find an approximate optimal CA-AMA in various distributions with improved revenue and a low degree of violation of IR.
cs.GT↗
Random Forest-Informed Cellular Automaton for Large-Scale Wildfire Spread Modelling
Accurate large-scale wildfire spread modelling requires models that capture both the environmental conditions associated with fire occurrence and the local dynamics of fire propagation. We propose a three-stage framework that combines a Random Forest (RF) model with a cellular automaton (CA). First, an RF model trained on the 2021 Canadian fire season estimates daily pixel-level fire-occurrence probabilities. Second, quantile gradient boosting models provide optional spread-rate priors for sensitivity analysis. Third, an RF-informed CA combines the RF probability layer with neighbourhood-driven spread on a 5 km grid. The RF model achieved AUC values of 0.725--0.795 on the 2022--2024 datasets, while the RF-informed CA achieved substantially higher spatial overlap than the evaluated CA-only baselines in the 2023 simulation. A higher-resolution simulation provides an additional qualitative assessment of local spatial errors. These results suggest that combining RF-derived probabilities with local CA spread can improve large-scale wildfire simulations under the tested conditions.
stat.AP↗
CARVY-FL: Client Anticlustering for Robust Voting in Provably Secure Federated Learning
Federated learning (FL) enables collaborative training without directly sharing raw data, but remains vulnerable to malicious clients. Voting-based FL improves robustness by partitioning clients into groups, training one model per group, and aggregating predictions by plurality voting. However, under class-disjoint non-IID data, distribution-oblivious grouping can yield highly variable certified accuracy (CA). We propose CARVY-FL, which estimates client distribution types from one-epoch model updates and uses anticlustering to increase within-group distributional diversity. Under a fixed grouping, CARVY-FL retains the voting-based CA guarantee while increasing vote margins. Experiments on MNIST and Fashion-MNIST show higher CA than FLCert. Under BadNets with model replacement, CARVY-FL improves the AUC of 100-ASR by 11.1% and 14.9%, respectively.
cs.CR↗
RL-ADA: A World-Feedback Framework for Adversarially Robust Enterprise Dialogue Agents
Deploying task-oriented dialogue agents in enterprise customer support faces a persistent annotation bottleneck: robust training requires labelled interaction data at scale, yet enterprise conversational logs are privacy-sensitive and expensive to annotate, while user behaviour evolves faster than labelling pipelines can keep pace. We present RL-ADA (Reinforcement Learning with Adversarial Dialogue Agents), a co-evolutionary training framework that eliminates this bottleneck by replacing human labels with \emph{world feedback}: consequence-based reward signals derived directly from measurable interaction outcomes. A Customer Support Agent (DA, 3B parameters) and an Adversarial Customer Agent (CA, 7B parameters) co-evolve in an adversarial arena guided by a fixed automated judge: the DA is rewarded for correctly handling multi-turn customer conversations to successful resolution, while the CA is rewarded for producing realistic, intent-concealing utterances that cause misroutes, creating asymmetric adversarial pressure through opposing but independently structured rewards. An isolation gym iteratively retrains the weaker agent on prior-failure transcripts, requiring no human annotation at any stage. In a banking customer support proof of concept, tool-routing errors are eliminated and the strict end-to-end PASS rate doubles over five co-evolutionary cycles, driven solely by automated arena reward with no labelled data. We additionally observe the emergence of \textbf{Contextual Camouflage}, an adversarial strategy in which the CA learns to embed intent within dense realistic customer detail purely from reward pressure, with direct implications for enterprise red-teaming and robustness evaluation.
cs.CL↗
ECA-BLS: An Efficient Complex-Augmented Broad Learning System
Broad Learning System (BLS) is an efficient alternative to deep architectures due to its fast training, analytical learning, and strong generalization under limited data. However, existing BLS variants are confined to real-valued representations, restricting their ability to capture nonlinear interactions and second-order statistical dependencies inherent in real-world data. Notably, no prior BLS model fully exploits the complete second-order statistics that naturally emerge when data are embedded in the complex domain. To address this limitation, this paper introduces the first complex augmented Broad Learning System (CA-BLS), which transforms real-valued inputs into phase-encoded complex representations and adopts widely linear modeling to jointly leverage covariance and pseudo-covariance information via complex conjugate augmentation. This enables effective modeling of latent nonlinearities, coherence structures, and second-order dependencies inaccessible to conventional BLS formulations. To mitigate the additional computational cost of complex augmentation, an Efficient Complex Augmented BLS (ECA-BLS) is further developed, reformulating CA-BLS entirely in the real domain while preserving its exact decision function, achieving up to 75\% fewer multiplications and over 60\% fewer additions. A rigorous theoretical analysis proves the mathematical equivalence between CA-BLS and ECA-BLS, ensuring zero theoretical loss. Extensive experiments on 26 benchmark datasets from the UCI and KEEL repositories demonstrate that ECA-BLS consistently outperforms classical BLS and recent state-of-the-art randomized neural networks in accuracy, average rank, and statistical significance, establishing augmented second-order modeling as a critical and previously missing dimension of BLS research.
cs.LG↗
Practical Persistent Multi-Word Compare-and-Swap Algorithms for Many-Core CPUs
In the last decade, academic and industrial researchers have focused on persistent memory because of the development of the first practical product, Intel Optane. One of the main challenges of persistent memory programming is to guarantee consistent durability over separate memory addresses, and Wang et al. proposed a persistent multi-word compare-and-swap (PMwCAS) algorithm to solve this problem. However, their algorithm contains redundant compare-and-swap (CAS) and cache flush instructions and does not achieve sufficient performance on many-core CPUs. This paper proposes a new algorithm to improve performance on many-core CPUs by removing useless CAS/flush instructions from PMwCAS operations. We also exclude dirty flags, which help ensure consistent durability in the original algorithm, from our algorithm using PMwCAS descriptors as write-ahead logs. Experimental results show that the proposed method is up to ten times faster than the original algorithm and suggests several productive uses of PMwCAS operations.
cs.DB↗
Counterfactual Contrastive Analysis
Visual Counterfactual Explanations (VCEs) aim to explain image classifiers by generating minimally edited and realistic versions of an input image that change the classifier's prediction. Existing VCE methods are inherently classifier-dependent and therefore susceptible to classifier biases and failure modes, such as sensitivity to shortcut features and calibration errors. In this paper, we propose a classifier-free approach for visual counterfactual generation based on Contrastive Analysis (CA). Given two datasets corresponding to different classes (e.g., healthy and patients), we disentangle the generative factors that are common across the two datasets from those that are salient to each dataset, and generate counterfactual images by swapping only the salient factors. By operating directly on data distributions rather than decision boundaries, our method provides model-agnostic VCEs that are less sensitive to classifier biases. Our approach leverages the high-quality synthesis and well-structured latent space of StyleGAN2. We use the feature space F, instead than the usual W-space, to improve detail preservation. Unlike conventional CA approaches, which typically assume salient factors in only one dataset, we introduce an adapted framework and loss functions for VCE that allow multiple salient factors in each dataset. We evaluate our method on three medical imaging datasets and demonstrate superior counterfactual generation quality compared to existing approaches.
cs.CV↗
Discovering Sensorimotor Agency in Cellular Automata using Diversity Search
The research field of Artificial Life studies how life-like phenomena such as autopoiesis, agency, or self-regulation can self-organize in computer simulations. In cellular automata (CA), a key open-question has been whether it it is possible to find environment rules that self-organize robust "individuals" from an initial state with no prior existence of things like "bodies", "brain", "perception" or "action". In this paper, we leverage recent advances in machine learning, combining algorithms for diversity search, curriculum learning and gradient descent, to automate the search of such "individuals", i.e. localized structures that move around with the ability to react in a coherent manner to external obstacles and maintain their integrity, hence primitive forms of sensorimotor agency. We show that this approach enables to find systematically environmental conditions in CA leading to self-organization of such basic forms of agency. Through multiple experiments, we show that the discovered agents have surprisingly robust capabilities to move, maintain their body integrity and navigate among various obstacles. They also show strong generalization abilities, with robustness to changes of scale, random updates or perturbations from the environment not seen during training. We discuss how this approach opens new perspectives in AI and synthetic bioengineering.
cs.MA↗
Beyond Object Authentication: Context-Closed Post-Quantum Authentication for the WebPKI
Post-quantum migration increases WebPKI authentication cost, but authenticating a compressed certificate object does not by itself preserve the mutable authorization context under which a relying party accepts it. We formalize \emph{context closure}: the authenticated projection accepted by a verifier must determine the selected authorization semantics it claims, relative to declared source contracts and event-coverage witnesses. We instantiate this idea with \LRp, a two-plane post-quantum construction that authenticates mutable CA-context state in an update plane while the warm path carries only state-local dependency references selected by explicit profile negotiation. In a pinned CCADB reconstruction, we obtain 44,912 path/view contexts and 16,858 physical CA lineages across Apple, Chrome, Microsoft, and Mozilla views. The core compiler yields $m_{50}=6$, $m_{95}=16$, and $m_{\max}=18$ typed dependencies. A warm LR+ selector therefore costs 296, 776, and 872 bytes at median, p95, and maximum, compared with 3,842, 5,932, and 6,350 bytes for a one-signature stateless bundle carrying the same dependency vector. The retained all-view closure state is 16.15 MB, and per-view lifecycle crossovers range from 19.60 to 50.41 median-path warm authentications/day under the stated checkpoint and update model. The implementation and evaluation artifact are available at https://github.com/nserser/LR-WebPKI
cs.CR↗
Operationalising AI Regulatory Sandboxes: Activities, Requirements, and Technical Assessment under the EU AI Act
The systematic assessment of AI systems is increasingly vital as these technologies enter high-stakes domains. To address this, the EU's Artificial Intelligence Act introduces AI Regulatory Sandboxes (AIRS): supervised environments where AI systems can be tested under the oversight of Competent Authorities (CAs), balancing innovation with compliance, particularly for startups and SMEs. Yet significant challenges remain: assessment methods are fragmented, tests lack standardisation, and feedback loops between developers and regulators are weak. This paper operationalises the AIRS lifecycle. We map the sandbox journey into 29 concrete activities, from pre-participation guidance through application, preparation, participation, exit, and post-participation monitoring, and we distinguish between a Core AIRS centred on regulatory oversight and an Extended AIRS that additionally embeds structured technical testing through an AI Technical Sandbox (AITS). From this mapping we derive 15 infrastructural and governance requirements that an AITS must satisfy, each linked to the activities it supports and, for high-risk systems, to the provider obligations set out in Articles 9-15 of the AI Act. The framework aims to address multiple stakeholders: CAs gain structured workflows for applying legal obligations; technical experts can integrate robust evaluation methods; and AI providers access a transparent pathway to compliance. We conclude by outlining the Sandbox Configurator, an open-source framework intended to instantiate AITS environments from these requirements, and by discussing how a shared technical foundation can support a scalable and innovation-friendly European infrastructure for trustworthy AI governance.
cs.CY↗
CaST-POI: Candidate-Conditioned Spatiotemporal Modeling for Next POI Recommendation
Next Point-of-Interest (POI) recommendation ranks a user's likely next location based on check-in history. Most recent rankers compress the trajectory into a single user vector and score every candidate through the same representation, ignoring that every candidate carries geographic coordinates and that the relevance of a past visit depends on where the candidate is located. Target attention from click-through-rate prediction conditions the user representation on the scored item, but its operator was developed for web items without geometry. This paper proposes CaST-POI, a candidate-conditioned POI ranker that keeps a standard target-attention reader and adds two bucketised biases to the attention logits: one for the recency of each past visit and another for its distance to the candidate being scored. Different candidates therefore read the same trajectory with different attention weights, grounded in real geographic distance rather than inferred from item embeddings. Comparing against seven sequential recommenders trained with the same split on three datasets NYC, TKY and CA under per-user leave-one-out with full-vocabulary ranking, CaST-POI improves MRR over the strongest baseline by 5.1%, 7.6% and 14.5%. Holm-corrected paired tests confirm the gains on TKY and CA. Ablation study locates the gain in the explicit revisit gate and the candidate-relative spatial bias, whereas the candidate-independent temporal bias has no measurable effect on all datasets. Code is available at https://github.com/YuZhenyuLindy/CaST-POI.
cs.IR↗
Reinforcement Learning for Symbolic Equation Solving
We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials, trigonometric) and a controlled class of restricted-open families requiring a change of variables (CoV) such as completing the square. We cast algebra as an MDP with a dynamic action space and a tree-structured policy (TreeMLP). The main policy learns from reward alone with no supervised solution traces; the CoV substitution comes from a supervised generator interchangeable with a CAS call. On closed equations the agent matches the prior best on CommonCore (0.93 greedy vs. ConPoLe's 0.925) under a single policy. On four hand-designed restricted-open families (quadratic, cubic, quartic, exponential) it reaches 0.79 beam / 0.67 greedy, exceeding the strongest non-learned search (A-star, 0.64). Learned CoV timing has content only on the exponential family, the one requiring a nested CoV, where a natural rule solves none of the held-out equations while the policy solves 75% from reward alone. At 10x scale a sharp seed-level bimodality emerges; a UCB learning-progress curriculum shows a non-significant positive trend toward mitigating it. We do not claim general open-equation solving: every open-equation result is confined to these four controlled families.
cs.LG↗