Papers

Machine learning models can achieve strong test performance while relying on demographic or acquisition-related shortcuts. We propose counterfactual (CF) marginalisation as a test-time evaluation procedure for assessing robustness of classification models to such variables. Given a CF image generator, we intervene on nuisance parent variables such as age or sex, generate CF versions of each test image, and average predictions over a target intervention distribution. This produces intervention-aware predictions that marginalise demographic effects while preserving patient-specific latent information. We use these predictions to define metrics for CF risk, calibration, stability and worst-case sensitivity. We demonstrate this framework's utility for quantitative robustness evaluation.

In continual reinforcement learning, carefully managing the stability-plasticity tradeoff remains a core challenge. Recent work by Abel et al. (2025) formalized this dilemma by defining plasticity as the generalized directed information from an agent's observations to its actions, and empowerment as the generalized directed information from its actions to its observations. This formulation successfully reframes the traditional stability-plasticity tradeoff as an empowerment-plasticity tradeoff. However, while extensive literature exists on optimizing for empowerment, there is currently no research addressing the optimization of plasticity under this new definition. This paper presents preliminary work toward optimizing plasticity within Markov decision processes. We show that there exists a Bellman optimality equation for optimizing plasticity similar to previous work for empowerment.

We develop an exact almost-sure learning theory for smooth parametric models trained by regularly weighted empirical risk minimization on long-range dependent data. The training observations are generated from a fixed finite window of a stationary Gaussian sequence, and the sample weights are regularly varying. If the loss gradient at the population minimizer has Wiener-chaos rank $m$ and a nonzero low-frequency coefficient, then, in the long-memory interior regime, the finite-lag score reduces on the iterated-logarithm scale to a single weighted Hermite chaos. This yields an almost-sure Bahadur representation, an exact limsup law for the learned parameter, and, for $m\ge2$, the functional cluster set of the complete learning trajectory. The polynomial learning exponent is determined by the memory parameter and the chaos rank and is invariant under the admissible power weighting, whereas the sharp pathwise constant and cluster geometry depend on the weights. In the rank-one case, global optimization over the admissible power exponents shows that every optimizer is positive. Time-series prediction and classification examples illustrate the results.

Multilingual large language models (LLMs) are increasingly used for open-ended text generation, yet their behaviour in low-resource languages remains poorly understood. In this work, we question how correct and reliable is the generation of multilingual LLMs when used for the task of story generation. We consider Urdu language as a representative low-resource language. We generate Urdu-Stories, a corpus of 93 stories generated using three contemporary LLMs (GPT-5.1, Qwen-3-Max, DeepSeek-3.1). We manually annotate the errors present in them under a nine-label linguistic, semantic, and cultural taxonomy. Our notable findings suggest that LLMs often make basic errors of grammar and semantics. The stories lack coherence, have unnatural repetition and show pervasive cultural shallowness. We further show using few-shot prompting that the cultural and context errors largely remain unresolved. Our findings highlight the limitations of current LLMs as a reliable source of content generation and information retrieval for low-resource languages.

Standard cross-entropy loss causes neural networks trained on ordinal classification tasks to hedge predictions toward center classes, a failure mode we term center-class hedging. This occurs because predicting the middle class minimizes expected symmetric loss, making it the path of least resistance regardless of the true label. Existing ordinal losses address related problems such as large-error penalization and rank consistency, but none directly suppresses center-class hedging as a function of where the true label lies relative to the ordinal center. We propose the Adaptive Margin Ordinal Loss (AMOL), a multiplicative weight applied to per-class loss terms of the form $m(k,y) = 1 + \alpha \cdot (1 - |k-c|/c) \cdot (|y-c|/c)$, where $c$ is the center class, $k$ is the candidate class, and $y$ is the true label. The weight encodes a joint condition: it is large only when the candidate class is near center and the true label is far from center, collapsing to standard behavior otherwise. We further introduce the Center-Hedging Rate (CHR) as a diagnostic metric that directly quantifies this failure mode. Across four ordinal classification benchmarks and five random seeds, AMOL achieves the best or tied-best Quadratic Weighted Kappa (QWK) on all four datasets compared to cross-entropy, OLL, and SORD baselines. An asymmetric variant (AMOL-asym) eliminates center-class hedging entirely on the Abalone dataset ($\text{CHR} = 0.000 \pm 0.000$ across all five seeds, $n \approx 266$ extreme-class test samples per run), compared to $0.074 \pm 0.005$ for standard cross-entropy.

LLM agents increasingly rely on external skills retrieved at runtime, making skill selection from large repositories a critical challenge. We present a production skill router over 34,396 skills and a large-scale study of skill retrieval using limited real supervision and synthetic data. We found that the synthetic-data fine-tuning improves in-distribution retrieval but it causes catastrophic forgetting on real and out-of-distribution (OOD) data. We evaluate several forgetting mitigation fine-tuning approaches inspired by continual learning, including embedding-anchor regularization, Learning without Forgetting (LwF), Elastic Weight Consolidation (EWC), and L2-initialization. The results show that these approaches not only retain the performance on OOD skills retrieval but also improve the retrieval on synthetic in-distribution skills by 13.98% for 0.6B Qwen retriever and reranker. Our results provide a practical benchmark and a robust fine-tuning recipe for scarce, multi-positive supervision.

Accurate plant growth estimation is essential for greenhouse monitoring, yet obtaining labeled data remains costly and time-consuming. To address this, we propose a few-shot regression framework that combines Vision Transformer (ViT) feature embeddings, clustering-based task construction, and gradient-based meta-learning, and show that task construction in embedding space is a primary driver of performance. The approach leverages an unlabeled image pool to organize data into structured tasks using fuzzy c-means clustering, enabling efficient learning from a small number of labeled samples. We systematically evaluate meta-learning methods and show that second-order methods (e.g., Model-Agnostic Meta-Learning variants such as MAML++) outperform classical baselines in the few-shot regime. Furthermore, intra-cluster support selection has a limited and dataset-dependent impact. Experiments on two plant datasets show that structured task design combined with meta-learning enables reliable plant growth estimation under severe label scarcity.

The growing reliance on Low-Earth Orbit (LEO) satellite communication systems has increased the need for intelligent methods capable of detecting cyberattacks across complex and dynamic space environments. Unlike conventional network intrusion detection, satellite systems generate heterogeneous information across radio-frequency (RF) links, onboard hardware, and orbital operations. However, many existing approaches either rely on terrestrial intrusion datasets or evaluate individual observations independently, limiting their ability to capture temporal attack behavior specific to LEO satellites. In this work, we conduct a systematic study of deep-learning-based cyberattack detection using the recently introduced satellite-specific UNSW-IoTSAT dataset. We investigate structured learning architectures that preserve hardware, orbital, and RF information, including a Subsystem-Fusion MLP and a hierarchical multimodal Transformer that models both cross-subsystem interactions and temporal evolution. We further evaluate leakage-resistant row-level and temporal settings, along with cross-satellite generalization, to characterize how model architecture and evaluation protocol influence satellite cyberattack detection. Experimental results demonstrate the value of structured multimodal modeling and rigorous evaluation, with the hierarchical Transformer achieving up to 91.66% accuracy and 85.63% macro F1 under the leakage-resistant evaluation protocol.

Autoregressive language models can be used to transform a payload text into a stegotext of identical token length by preserving per-position rank information across contexts - a methodology we formalize as Contextual Autoregressive Rank Transcoding Steganography (CARTS). While the Calgacus construction of Norelli et al. demonstrated this phenomenon experimentally, no formal security analysis existed. This paper provides the first rigorous treatment of CARTS. We show its exact correctness under deterministic model assumptions, introduce a rank-coordinate representation in which keys act as bijections on rank-vector space, define relevant security notions and the computational problems naturally associated with the construction - context search, key collisions, message equivocation, and non-commutativity of the encoding maps - and study the theoretical relationships between them, including the characterization of message equivocation in terms of context search, and the tension between key collisions and message equivocation. An empirical study on Llama 3 8B confirms exact recovery of the original payload in all tested cases, finds no key collisions under random key generation, establishes that a hand-crafted collision is local rather than global, and finds no commuting key pairs - suggesting resistance to the attack vectors studied. This work opens a formally grounded research agenda for the constructive use of language models in cryptography and privacy-preserving communication.

Graph Neural Networks (GNNs) are powerful models for handling attributed graphs in tasks such as classification, link prediction, and community detection, as they enable the aggregation of information from both structural and semantic sources. However, progress in community detection is hindered by the lack of high-quality datasets, since ground-truth community labels are often unavailable and most algorithms proposed in recent literature rely on the same benchmark datasets for model training and evaluation. To address this issue, attributed random graph generators are commonly employed to create synthetic graphs for assessing the strengths and limitations of GNN-based models. Nevertheless, most existing generators rely heavily on power-law degree distributions, despite recent evidence indicating that scale-free networks are rare, particularly in social network contexts. Moreover, state-of-the-art attributed graph generators provide limited flexibility, as they do not allow users to construct communities with varying densities, degree distributions, and sub-community structures. To overcome these limitations, we introduce the Synthetic Community-Aware Attributed Graph Generator (SynCo), a graph generation algorithm that allows users to control the node degree distribution and sub-community structure. We evaluate SynCo across three different tasks: graph mimicking, hyperparameter evaluation, and node clustering tuning. The results show that our model outperforms state-of-the-art approaches in synthetic graph generation and data augmentation, while preserving the original distributions of duplicated and augmented datasets, as confirmed by statistical tests well know in literature. We also demonstrate the ability of SynCo to generate nodes in large scale, up to 2.1 million nodes.

Linear probes that decode the truth from a language model's activations have been proposed as deception monitors, and a truth probe scoring below chance on a model trained to deceive is naturally read as evidence that the model hid or stopped representing the truth. We show that a fitting-label ambiguity can produce the same readout. In a controlled game, a model should report a secret bit to an ally and its complement to a rival. On compliant (ally) contexts the true bit and the answer the task prescribes are identical labels, so a probe fitted there cannot tell which of the two it measures. We call this complete agreement perfect aliasing. The labels are complements on rival contexts, so one ally-fitted probe scored against each has rival AUROCs that sum to one. Mixed fitting, on ally and rival contexts together, makes the two labels differ; randomized output codebooks also decouple the prescribed answer from the output letter. For a reward-trained Gemma-2-9B policy that answers falsely on every evaluated rival trial, the ally-fitted probe scores $0.006 \pm 0.005$ AUROC at the final layer (mean $\pm$ sample SD over three RL training seeds), while mixed-fit probes score 1.000 on the same held-out activations. Mixed fitting also uses more examples and labelled rival data, so this shows the true bit remains linearly recoverable, not that separating the labels alone explains the gain. In instructed Llama-3.1-8B, a probe refitted on one prompt variant and one frozen from a reference variant both have held-out ally accuracy 1.000 but rival truth AUROCs of 0.080 and 0.986 on the same trials. Our main experiments use one single-token game that states the bit in the prompt, so the recovered direction may read a retained copy of it; where the model must infer the bit, no tested arm deceives reliably. We study what a probe measures, not whether the model uses that information.

Conformal prediction converts point predictions into set-valued predictions with coverage guarantees under exchangeability between calibration and deployment data. We study conformal calibration transfer, where this requirement fails because labeled calibration is available only in a source space, while prediction sets are needed in a target space linked to the source through unlabeled paired observations (e.g., paired modalities or sensor changes). We propose Transported Conformal Calibration (TCC): we transport labeled source calibration into the target space using the paired data, and then correct residual post-transport mismatch using only unlabeled target inputs. We instantiate this correction with two complementary methods: TCC-KS, which uses a label-free uncertainty surrogate to detect mismatch and adjust calibration conservatively, and weighted-TCC, which reweights transported calibration toward the target domain for improved efficiency when weights are stable. We provide finite-sample target-domain coverage guarantees that adapt to an observable measure of mismatch. Across CIFAR-100-C, Tiny-ImageNet-C, and SEN12MS, we show reliable target-domain coverage transfer without labeled target calibration data, with label-free diagnostics that predict when correction is needed.

Quantum-inspired classical algorithms have dequantized several quantum machine learning routines by replacing quantum linear-algebra subroutines with classical counterparts. However, the sampler based on quantum singular value transformation (QSVT) for learning with optimized random features is not covered by existing dequantization frameworks, because the matrix to be inverted is not itself available through sampling access. In this work, we develop a classical algorithm to address this type of quantum-advantage candidate. Our method samples heavy indices, reduces the transformation to a small principal block, and outputs a sparse classical representation with operator-norm guarantees. Applying this method dequantizes the sampler for optimized random features, giving a classical sampler with prescribed accuracy and polynomially related runtime. These results show that the factorization underlying a quantum block encoding can itself provide sufficient classical structure even when sampling-and-query access to the composite matrix is unavailable.

The ambitious requirements of sixth-generation (6G) networks are driving communication systems from reliable bit delivery toward meaning-aware and task-oriented connectivity. Large models (LMs), with strong multimodal understanding and generation capabilities, have accelerated this shift and made semantic communication (SemCom) increasingly practical. Yet current LM-driven SemCom remains fragmented: semantic representations are typically tied to specific modalities, models, or tasks. While the bit provides a universal unit for digital transport, there is still no analogous unit for representing and processing semantics, which limits interoperability, theoretical unification, and scalable system design. We argue that tokens provide a natural candidate for this missing abstraction. Two trends support this: unified multimodal LMs now encode text, images, audio, video, and robot actions in one token space, while distributed LM inference already generates substantial token-level traffic through expert routing, cache transfer, and speculative decoding. Token communication (TokenCom) emerges by unifying these trends, using the LM's native processing unit as a communication abstraction above the bit level and enabling importance assignment, error handling, and resource allocation directly at token granularity. This survey traces the evolution from LM-driven SemCom to TokenCom. We review three major directions of LM-driven SemCom: source-centric semantic coding, channel semantics for physical-layer tasks, and collaborative edge-device intelligence. We then examine the token abstraction, the transmission techniques it requires, and two emerging paradigms, namely TokenCom for LM services and for embodied and agentic intelligence. Finally, we identify open challenges toward unified, scalable, and AI-native 6G communication systems.

Human video datasets offer an abundant and diverse source of interaction data that can complement expensive real-robot data. To bridge the human-to-robot embodiment gap, existing approaches either robotize videos in task-matched settings or address observation and action alignment separately. In this work, we systematically examine whether robotized human videos can serve as an effective and scalable source of robot-aligned supervision. To this end, we develop a robotization pipeline that converts heterogeneous human videos into robot-aligned observations and action trajectories while inferring missing intermediate signals across annotation levels. Using this pipeline, we construct the HuRo dataset, comprising about 630K robotized episodes and 142M processed frames from five human-video sources. Across four real-world manipulation tasks, pretraining a VLA policy on increasing amounts of robotized human-video data improves overall completion from 51.5% to 80.3% and OOD completion under spatial and visual shifts from 34.9% to 72.2%. Ablations further show that visual robotization improves OOD robustness and that end-to-end pretraining with retargeted actions outperforms visual-only transfer. Project website: https://3587jjh.github.io/HuRo.

Activation steering provides a lightweight way to control large language models (LLMs) by modifying their hidden activations at inference time. Among these approaches, norm-preserving steering aims to change model behavior without altering the activation norm, reducing the risk of representation collapse and degradation. However, existing norm-preserving methods are limited by predefined steering trajectories and by their reliance on one-step updates, which may fail to capture the complex structure of activation distributions. We propose GeoSteer, an optimization-based method for norm-preserving activation steering. GeoSteer formulates steering as a Riemannian optimization problem and updates activations through a sequence of small geodesic steps on the representation manifold. To avoid fixed steering directions, GeoSteer learns a nonlinear activation-space objective that distinguishes desired from undesired activations, and uses this function to adaptively guide each steering step. This multistep formulation yields smoother, more stable, and more consistent steering behavior while preserving the activation norm. Across TruthfulQA, RealToxicityPrompts, and UltraFeedback benchmarks, GeoSteer consistently improves over state-of-the-art activation steering baselines. These results suggest that norm-preserving steering can be made more effective by replacing predefined one-step edits with adaptive, geometry-aware optimization.

Neural networks trained past memorization frequently undergo a delayed transition to generalization, a phenomenon known as grokking. Despite theoretical progress on why this transition occurs, the quantitative structure of when it occurs in hyperparameter space remains uncharacterized. We map the memorization-to-generalization boundary across 384 configurations of two-hidden-layer MLPs on modular arithmetic, fitting a power-law scaling relation for generalization onset time: $T_{\mathrm{grok}} \propto H^{-0.27}\, D^{-2.04}\, \eta^{-0.50}\, \lambda^{-0.64}$ ($R^2 = 0.732$; $0.821$ with interactions). The exponent hierarchy reveals that data complexity ($D^{-2.04}$) is the dominant driver of regime transition, not model capacity ($H^{-0.27}$): doubling data accelerates generalization by ${\sim}4\times$, while doubling width yields only ${\sim}1.2\times$. A sharp phase boundary at weight decay $\lambda \gtrsim 1.0$ separates grokking from non-grokking configurations, and weight norm trajectories show monotonic compression during the transition, consistent with implicit regularization selecting low-complexity solutions. These results provide a quantitative foundation for predicting and controlling regime transitions in overparameterized networks.

Selecting LoRA rank for diffusion fine-tuning requires balancing quality and compute cost. We present a controlled study on CIFAR-10 using a DDPM U-Net with ranks {2,4,8,16,32}, fixed optimization settings, and a reproducible local-folder pytorch-fid protocol. We report FID, trainable parameters, runtime, and GPU memory, then validate trends with extended-budget DDPM runs (20 epochs; ranks 4/8/16) and a Tiny DiT backbone (10 epochs; ranks 4/8/16). Results show moderate ranks are most efficient: rank 4 achieves the best DDPM FID (124.1380), rank 8 is close (124.2136), and higher ranks provide limited gains despite larger adaptation cost. These findings support small-to-moderate ranks as practical defaults under fixed training budgets.

The Abstraction and Reasoning Corpus (ARC) benchmarks cognitive generalization, the ability to infer and apply abstract rules from limited examples. This paper presents a multi-stage rule-chaining framework that performs compositional reasoning across symbolic, structural, and conceptual levels. The framework integrates three complementary solvers: (1) a deterministic rule discovery module that induces atomic transformations through geometric, color, and object-based analysis; (2) a pattern-composition engine that reconstructs outputs via block merging, repetition, and spatial heuristics; and (3) a structural abstraction layer that infers hierarchical and nested relationships across grids. These solvers operate sequentially within a progressive fallback hierarchy, where each stage reuses prior reasoning traces to enhance interpretability and generalization. Training passed for 995 tasks out of 1000, further evaluated on 105 tasks out of 120 and solved 230 test tasks out of 240 ARC-AGI-2 tasks. The system achieved strong coverage across deterministic, compositional, and abstract categories, demonstrating an overall accuracy exceeding 95 percent. The proposed architecture bridges symbolic reasoning and pattern synthesis, providing interpretable insight into cognitive generalization. The results suggest that rule chaining and hierarchical composition can advance machine reasoning toward transparent, human-aligned abstraction without relying on task-specific tuning.

Lung cancer is one of the leading causes of death worldwide, and its early diagnosis is crucial to improving patients prognosis and quality of life. However, the process of interpreting medical images for the detection of lung cancer is complex and requires trained experts. In this context, artificial intelligence (AI) and deep learning (DL) emerge as potential tools to automate and optimize image analysis. The objective of this work is to review the most recent and relevant applications of AI and DL in the field of radiology for the detection of lung cancer. To this end, an exhaustive search was carried out in scientific databases such as PubMed,IEEEXPLORE, Scopus and Web of Science, and 96 articles published from 2015 to the present addressing the use of AI and DL in biomedical engineering were selected. Emphasis is placed on the use of convolutional neural networks (CNN) with transfer learning and Data Augmentation as promising techniques to improve the accuracy and efficiency of the image interpretation process. The results show that the use of AI and DL can offer an effective alternative for the early diagnosis of lung cancer, with high sensitivity and specificity. However, current limitations and challenges that must be addressed to guarantee its responsible and safe application in clinical practice are also identified, such as the lack of standardized data, the ex plainability of the models, patient privacy, and the ethical and social implications. It is concluded that the use of AI and DL can have a positive impact on the care of patients with lung cancer, but further research and regulation are required to ensure its quality and reliability.

We study the application of federated learning (FL) to indoor fire detection. Such fire-detection systems use edge cameras that record sensitive footage which cannot easily be collected at a central server. Existing federated solutions leave three practical obstacles unaddressed: limited uplink bandwidth, Byzantine (malicious or faulty) clients, and unconditional trust in a single, permanently fixed aggregation server. Our main contributions address all three. In particular, we provide (i) a curated indoor fire-detection dataset assembled from eight public sources; (ii) an edge-deployable detector whose model updates are compressed up to 10 times with only a small loss in balanced accuracy; and (iii) a semi-decentralized Byzantine-robust FL method that combines history-aware aggregation with a rotating coordinator, evicting stealthy attacks that per-round filters miss while removing the fixed-server single point of failure. On the held-out test set the rotating-coordinator method matches its fixed-server counterpart in accuracy and detection speed, and a physically distributed six-node cloud deployment confirms feasibility.

Computational RNA structure pipelines generate many candidate conformations for the same sequence. Reliable evaluation therefore requires more than recognising plausible geometry, it requires determining whether that geometry is compatible with the sequence. We introduce SIRGE, a sequence-informed geometric evaluator that conditions structural representations on nucleotide embeddings from a pretrained RNA language model. Early results show that SIRGE outperforms established evaluators in Kendall–$\tau$ alignment, Top-1 selection, and Top-3 ranking. Controlled comparisons further show that sequence conditioning corrects errors made by an otherwise matched geometric model and improves target-level rank structure. These findings provide initial evidence that pretrained sequence representations supply ranking information that complements geometric reasoning.

Natural load-bearing patterns such as leaf venation, trabecular bone, and spider webs achieve high stiffness per unit mass, yet classical topology optimizers rarely reach such geometries, and few let engineers express structural design intent through natural language. This work treats a frozen text-to-image diffusion model as a training-free source of design knowledge and distills it into the physics loop of density-based topology optimization via score distillation sampling, so that a text prompt becomes an explicit, machine-interpretable representation of engineer intent. The prompt-induced generative gradient and the finite element sensitivity are combined at every iteration, letting physics decide which prompt-induced features survive. In 245 primary SDS runs spanning four geometric domains and two physics regimes, 38 of 49 prompt–domain combinations achieved statistically significant compliance reductions (up to $-31.5\%$ mechanical and $-23.0\%$ thermoelastic), outperforming gradient-based baselines. Cross-domain morphological analysis identifies a recurring structural signature of improvement: in most domains the generative prior suppresses dead-end branches in the rib skeleton, with endpoint–compliance correlation $r = +0.56$ to $+0.99$. A Heaviside projection with $\beta$-continuation resolves a pronounced intermediate-density tendency in this diffusion–physics coupling ($42.6\%$ to $<3\%$), and an automated skeleton-based pipeline converts optimized density fields into \rev{candidate geometry ready for computer-aided design. By retargeting the generative prior across domains, loading conditions, and physics objectives through a change of text prompt, with each new problem's physics setup specified separately, the framework uses a pretrained generative model as a reusable, training-free prior for engineering design.

Machine-learning systems are built almost exclusively on a few large Python-orchestrated frameworks, and they inherit those stacks' engineering costs: environments of hundreds of version-coupled packages, separate export toolchains for deployment, and the split between the language research is written in and the language products ship in. We report on the construction and verification of numbat, a machine-learning stack written in one general-purpose language (Zig) with no third-party runtime dependencies. The stack spans tensor computation, automatic differentiation, neural-network modules, mixed precision, multi-GPU training, data loading and monitoring; an SDK exposes it behind a stable, additively versioned C ABI of over 1,400 entry points, with bindings for six languages; and its clinical domain planes encode regulatory requirements as executable acceptance gates rather than documentation. Verifying such a stack is the harder half of building it: a defective training run rarely fails, it converges quietly to a slightly worse model. We treat a widely used reference implementation as an executable specification and verify against it at five levels, from operator gradient checks to an automated trajectory gate against a same-machine reference run - the arrangement our companion study formalizes as a trajectory-level differential oracle. The protocol surfaced ten silent recipe divergences, which we catalog with mechanisms and symptoms. As the acceptance test, we train a 25.9M-parameter detector of the YOLOv8m class from random initialization on COCO 2017 for the full 500-epoch schedule: the exported weights score 0.4956 mAP50-95 under the official protocol, scored by the reference stack's own validator (published endpoint 0.502), with single-GPU step time at parity on identical hardware. Weights, per-epoch metrics and the full run manifest are released.

A false data injection attack (FDIA) can change the estimated grid state while evading a residual-based bad data detector (BDD). Existing blind attacks learn a low-rank measurement subspace, but this algebraic view does not state the physical grid constraints that make an attack stealthy or the minimum information needed to recover the complete attack space. Under the connected direct-current (DC) branch-flow model, we show that the residual-sensitive subspace of the noiseless orthogonal test is exactly the weighted cycle space. Its orthogonal complement is therefore the complete stealthy attack space, making weighted cycle-space knowledge both necessary and sufficient for complete blind FDIA. This space identifies the topology only up to 2-isomorphism and the relative cycle-edge parameters only up to one scale per biconnected component; bridge parameters are neither identified nor required. We then formulate a computationally unconstrained benchmark and a tractable measurement-only reconstruction method. Experiments on IEEE systems compare BDD bypass rate at a 95% nominal-acceptance threshold against state impact. As a compact alternating-current (AC) extension, we characterize feasible branch P/Q measurements by a cycle manifold and demonstrate topology-assisted manifold fitting and measurement generation on a graphics processing unit (GPU). In the lossless fixed-voltage small-angle limit, the normal space of the active-power slice reduces to the DC weighted cycle space.

Machine learning explanations reveal model behavior beyond predictions, creating attack surfaces for model confidentiality and data privacy. We systematize 25 studies that exploit explanations for model extraction, membership inference, and model inversion, treating attribute inference as partial inversion. Existing work is often labeled only black- or white-box, obscuring substantial differences in what explanation signal reaches an adversary. We therefore separate model knowledge from explanation acquisition and identify five paths: target-released, attacker-derived, secondary disclosure, privileged access, and released global artifacts. Across these paths, explanations reduce extraction cost, expose membership signals through explanation statistics, recourse distance, and explanation-guided robustness, and support spatial or algebraic reconstruction of private inputs. We compare system and threat models, explanation signals, auxiliary knowledge, target models, modalities, query budgets, evaluation metrics, reported performance, and defenses. Our analysis shows that no explanation family is uniformly unsafe and no defense is uniformly effective. Risk depends on which signal is exposed, how it is acquired, which asset is targeted, and what the attacker already knows. We argue that explanation privacy should therefore be evaluated as an end-to-end disclosure problem, with defenses matched to the acquisition path and protected asset.

We present a simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic (or something close) in the presence of nuisance parameters, based only on a sample generator from the distribution of interest. We show that the statistic is near-pivotal in the sense of minimum average KL-divergence of its $p$-values versus uniform and we argue that it can be expected to have good power when the dimension of the statistic equals the dimension of the parameter. It is able to incorporate prior knowledge about group invariances such as translation and scale. It can discover the one-sample $t$-test almost exactly, outperforms the Welch test in terms of worst-case size over a constrained variance-ratio range and achieves good calibration on partial biserial correlations, while showing higher power (and being much faster) on small-to-moderate samples than profile likelihood-ratio techniques.

We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and a unique optimal arm. For each suboptimal arm $i$, let $\Delta_i=\mu_*-\mu_i$ be its gap from the optimal mean, and write $H=\sum_{i\ne *}\Delta_i^{-2}$. Let $p_r$ be the fraction of $H$ contributed by arms with $2^{-(r+1)}<\Delta_i\le2^{-r}$, and let $\mathrm{Ent}(I)=\sum_{r:p_r>0} p_r\log(1/p_r)$. Among all algorithms that identify the optimal arm with probability at least $1-\delta$ on every Gaussian instance, the optimal expected number of samples on a given instance, averaged over all permutations of the arm labels, is within absolute constant factors of $H(\log(1/\delta)+\mathrm{Ent}(I))$. Moreover, there is an algorithm, independent of the instance, whose expected number of samples is bounded by a constant multiple of this quantity plus $g^{-2}\log\log(e^e/g)$, where $g=\min_{i\ne *}\Delta_i$ is the gap to the closest competitor.

Language generation in the limit asks for valid unseen elements from every exhaustive positive presentation of an unknown infinite language. We characterize this task for arbitrary families over a countable universe. Generation is possible exactly when each target can be assigned a finite positive witness so that the targets activated by any finite sample have an infinite common intersection. The necessary direction follows from a universal normalization: a search through unconfirmed histories converts any successful generator into one depending only on the observed set. We then ask how large compatible witnesses must be. Positive separation width records the smallest uniform size bound, with two further levels for unbounded finite witnesses and the absence of any compatible finite-witness assignment. Every level occurs. Countable families admit singleton witnesses, explicit families realize every finite width, and a union of two families with infinite common cores requires unbounded finite witnesses. Finally, countable-support and finite-profile obstructions explain why local combinatorial data cannot determine generation in the limit. The characterization and full width hierarchy are checked in Lean, including the simplified normalization and a direct diagonal capture lemma. The accompanying Lean development is maintained at https://github.com/xiaoyulics/language-generation-characterization

We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknown state on $\mathbb{C}^d$ of rank at most $r$ to trace norm error $\varepsilon$ with constant success probability requires, and is achievable with, $$\Theta\left(\frac{dr}{\varepsilon^2}\mathop{\mathrm{max}}\left\{1,\frac{r}{\sqrt{t}}\right\}\right)$$ samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive. Thus joint measurements on at most $t$ samples improve the complexity of algorithms making single-sample measurements by at most a factor $\sqrt{t}$. Further, measuring order $r^2$ samples jointly is necessary and sufficient to attain the unrestricted collective rate. For the lower bound, we vary the support of a state with fixed uniform spectrum and bound the Fisher information trace of every joint measurement on $t$ samples. The adaptive Fisher chain rule and the van Trees inequality then give the trace norm lower bound. For the upper bound, we construct and analyze a nonadaptive tomography protocol based on a Gaussian joint measurement. An explicit second moment identity and a conditional Gaussian law outside the state's support give a rank-dependent error analysis, yielding the matching rate.