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01.
arXiv (CS.AI) 2026-06-16

Using AI in engineering education: a balancing act, driven by clear purpose

作者:

arXiv:2606.16626v1 Announce Type: cross Abstract: Based on a questionnaire of 100 higher-education students, predominantly from engineering-related fields, and a critical review of recent literature, this chapter examines how students use and perceive Large Language Models (LLMs) in engineering education. Students primarily value LLMs for writing support, conceptual clarification, coding assistance, and brainstorming, while simultaneously expressing concerns about inaccuracies, bias, overreliance, academic integrity, and the burden of verification. Through an analysis of two dominant metaphors, namely LLMs as an "oracle" and as a "tutor," the chapter shows how these systems cultivate expectations of authority, expertise, and personalized learning that often exceed their actual capabilities. The chapter further argues that students' attachment to the promises of efficiency and personalized support reflects a form of "cruel optimism," where the perceived benefits of LLMs often depend on the very skills, vigilance, and expertise that students are still developing. Overall, the chapter argues for a purpose-driven and context-sensitive approach to AI integration in engineering education, emphasizing critical AI literacy, reflective assessment design, pedagogical caution, and consideration of broader ethical and environmental impacts.

02.
arXiv (CS.LG) 2026-06-11

Weighted Random Dot Product Graphs

arXiv:2505.03649v4 Announce Type: replace-cross Abstract: Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields. Networks, represented as graphs, offer a natural framework for this analysis. This paper extends the Random Dot Product Graph (RDPG) model to accommodate weighted graphs, markedly broadening the model's scope to scenarios where edges exhibit heterogeneous weight distributions. We propose a nonparametric weighted (W)RDPG model that assigns a sequence of latent positions to each node. Inner products of these nodal vectors specify the moments of their incident edge weights' distribution via moment-generating functions. In this way, and unlike prior art, the WRDPG can discriminate between weight distributions that share the same mean but differ in other higher-order moments. We derive statistical guarantees for an estimator of the nodal's latent positions adapted from the workhorse adjacency spectral embedding, establishing its consistency and asymptotic normality. We also contribute a generative framework that enables sampling of graphs that adhere to a (prescribed or data-fitted) WRDPG, facilitating, e.g., the analysis and testing of observed graph metrics using judicious reference distributions. The paper is organized to formalize the model's definition, the estimation (or nodal embedding) process and its guarantees, as well as the methodologies for generating weighted graphs, all complemented by illustrative and reproducible examples showcasing the WRDPG's effectiveness in various network analytic applications.

03.
arXiv (CS.LG) 2026-06-16

Machine Learning-Driven Chemical Reactor Network Modeling of the Sandia-D Flame

arXiv:2606.14729v1 Announce Type: cross Abstract: Turbulent combustion simulations are crucial for many scientific and engineering systems. However, the high cost to fully resolve the complex multiscale and multiphysics behavior makes direct simulation typically infeasible. The equivalent reactor network (ERN) approach attempts to improve computational efficiency by replacing a multidimensional turbulent simulation with a series of much cheaper 0-D and 1-D chemical reactors, providing a surrogate model that retains detailed chemistry at the cost of simplified flow physics. However, their development remains a challenge, often requiring either expert analysis, or automated approaches that sacrifice accuracy. In this work, we develop an automated machine-learning-assisted framework for constructing ERNs of the Sandia-D turbulent methane/air flame. Principal component analysis is first used to reduce high-dimensional thermochemical computational fluid dynamics (CFD) data to a low-dimensional latent space, where k-means clustering identifies physically interpretable flame regions used to initialize a reactor-network graph. This initialization is then refined using finite-difference gradient descent wrapped around non-differentiable Cantera reactor simulations. Across 30 RANS simulations spanning a range of pilot temperatures and inlet methane compositions, the optimized 7-reactor ERN achieves a maximum-temperature $R^2$ score of 0.7945 while preserving a $\sim6000\times$ speedup over the CFD solver. Outlet CO prediction remains more challenging, with a final $R^2$ score of $-0.4183$, but improves substantially from the unoptimized clustering initialization. These results show that unsupervised thermochemical feature extraction can provide effective physics-informed initializations for ERN construction, while gradient-based refinement can significantly improve predictive accuracy without manual reactor-network design.

04.
arXiv (CS.CV) 2026-06-24

S1-Omni-Image: A Unified Model for Scientific Image Understanding, Generation, and Editing

We present S1-Omni-Image, an open-weight unified multimodal model for scientific image understanding, generation, and editing. Unlike general-purpose image generation models, scientific image tasks require not only high-fidelity synthesis, but also robust understanding of scientific semantics, structural relations, domain knowledge, and task intent. To this end, S1-Omni-Image builds on the scientific multimodal reasoning backbone S1-VL-32B and couples its understanding capability with an image generation module under a unified think-before-generate paradigm. Given a user instruction, the model first produces a task-oriented reasoning trace, a textual answer, and a task special token; their hidden states are then injected into the generation module to condition image generation or editing. S1-Omni-Image supports scientific image understanding, generation, and editing in a unified framework. For generation, it focuses on scientific illustrations and text rendering, including logical diagrams, relational comparisons, data charts, and realistic scientific visualizations. For editing, it casts segmentation and other domain-specific vision tasks as native image editing problems, enabling multi-turn illustration editing, medical and geographic image segmentation, medical image translation, and scientific image super-resolution. We construct SciGenEdit, a 314K-sample training dataset, and release the model weights, inference code, and SciGenEdit-10K. Experiments show that S1-Omni-Image substantially improves scientific image generation and editing while preserving the scientific image understanding capability inherited from S1-VL-32B. It outperforms open-source models on GenExam and TechImage-Bench, achieves state-of-the-art results on four editing benchmarks including MSD, cigRockSEM, SynthRAD2025, and IXI, and maintains stable performance on scientific image understanding evaluations.

05.
arXiv (CS.CL) 2026-06-11

VietMed-MCQ: A Consistency-Filtered Data Synthesis Framework for Vietnamese Traditional Medicine Evaluation

Large Language Models (LLMs) have demonstrated remarkable proficiency in general medical domains. However, their performance significantly degrades in specialized, culturally specific domains such as Vietnamese Traditional Medicine (VTM), primarily due to the scarcity of high-quality, structured benchmarks. In this paper, we introduce VietMed-MCQ, a novel multiple-choice question dataset generated via a Retrieval-Augmented Generation (RAG) pipeline with an automated consistency check mechanism. Unlike previous synthetic datasets, our framework incorporates a dual-model validation approach to ensure reasoning consistency through independent answer verification, though the substring-based evidence checking has known limitations. The complete dataset of 3,190 questions spans three difficulty levels and underwent validation by one medical expert and four students, achieving 94.2 percent approval with substantial inter-rater agreement (Fleiss' kappa = 0.82). We benchmark seven open-source models on VietMed-MCQ. Results reveal that general-purpose models with strong Chinese priors outperform Vietnamese-centric models, highlighting cross-lingual conceptual transfer, while all models still struggle with complex diagnostic reasoning. Our code and dataset are publicly available to foster research in low-resource medical domains.

06.
arXiv (CS.LG) 2026-06-19

Adversarial Dependence Minimization

arXiv:2502.03227v2 Announce Type: replace Abstract: Minimally redundant representations are typically learned by minimizing feature covariance. However, covariance-based methods fail to eliminate all dependencies/redundancies, as linearly uncorrelated variables can still exhibit nonlinear relationships. To address this, we introduce ADM, a differentiable algorithm that minimizes statistical dependence between feature dimensions through an adversarial game: auxiliary networks identify dependencies, while the encoder removes them. We prove that mutual independence is achieved at the global optimum, empirically verify convergence, and study three potential applications: extending PCA to nonlinear decorrelation, improving generalization in image classification, and preventing dimensional collapse in self-supervised learning. By promoting statistically independent representations, ADM paves the way for learning more robust, compressed, and generalizable representations across diverse applications.

07.
arXiv (math.PR) 2026-06-17

Diffuse Interface Energies with Microscopic Heterogeneities II: Rare Events

arXiv:2606.17968v1 Announce Type: cross Abstract: We analyze Allen-Cahn functionals with stationary ergodic coefficients in the regime where the length scale $\delta$ of the heterogeneities is much smaller (microscopic) than the interface width $\epsilon$ (mesoscopic). In a companion paper, we show that if the ratio $\epsilon^{-1} \delta$ vanishes fast enough as $\epsilon \to 0$, then the functionals converge to an effective surface energy where the energy density is determined by homogenization effects originating at microscopic scales. Here we prove that if the ratio $\epsilon^{-1} \delta $ vanishes too slowly, the limit of the functional may actually be smaller than this homogenized energy. We refer to this as the rare events regime. In the case of the random checkerboard in dimension one, we use large deviations techniques to give a complete description of the rare events regime, showing that the limiting energy depends in a nontrivial way on the limit of $\epsilon^{-1} \delta | \log \epsilon |$. We further construct, in any dimension, examples of random media in which rare events become relevant at algebraic scales $\delta \approx \epsilon^{1 + \alpha}$ for an arbitrary $\alpha > 0$, as well as almost periodic examples in which atypical configurations play the same role as rare events.

08.
medRxiv (Medicine) 2026-06-11

Allostatic Load in Endometrial Cancer Disparities

Background: Endometrial cancer incidence and mortality are increasing, particularly among Black women and for aggressive subtypes. Allostatic load (AL), a composite measure of physiologic dysregulation across metabolic, cardiovascular, and immune systems, varies by racial category and tumor subtype in other cancers. Endometrial cancer is strongly associated with obesity, and it is unknown whether AL scores maintain sufficient heterogeneity to evaluate differences across subgroups or with clinical outcomes. Objective: To describe the performance of AL scoring in endometrial cancer patients and examine associations with tumor characteristics (grade/histology) and survival outcomes. Methods: We evaluated AL among 398 participants newly diagnosed with endometrial cancer. AL score was calculated by assigning 1 point for each ''high-risk'' value (by clinical reference range or distribution-based) for 15 biologic variables for vital signs, anthropometrics, blood-based biomarkers, and medical comorbidities. Results: Distribution-based thresholds for variables were used to preserve heterogeneity in this obesity-dominant context. Overall, 68.7% of Black women had high AL compared to White (56.7%), Hispanic (56.7%), and other race (32.3%) women. Decision tree analyses revealed grade-dependent associations between AL and survival. For women with low-grade tumors, higher AL was associated with poorer overall survival. For high-grade tumors, intermediate AL ([≥]4,

09.
arXiv (CS.CV) 2026-06-16

Unified Multimodal Model for Brain MRI Imputation and Understanding

Multimodal large language models (MLLMs) hold great potential for medicine, as they inherit knowledge from LLM and allow multiple data modalities to be integrated, analysed and interpreted in natural language. However, the field of medical MLLMs is constrained by non-trivial challenges, notably the scarcity of high-quality training data and the frequent occurrence of missing data in the real-world clinical setting. Here, we propose a novel unified multimodal model, UniBrain, for brain magnetic resonance image (MRI) analysis. To address potential missing brain MRI modalities, we employ a unified training strategy to perform joint imaging modality imputation and brain image understanding. During training, an interleaved and description-enriched data flow is constructed to train the model in an autoregressive manner, enabling medical reasoning with generated multimodal data. A self-alignment strategy is introduced to leverage dense image embeddings to learn fine-grained anatomical features without requiring detailed image captions. Furthermore, we propose a dynamic hidden state mechanism to alleviate the exposure bias during long-context multimodal inference. Extensive experiments on multi-disease brain MRI dataset demonstrate that UniBrain achieves high performance for brain image imputation, understanding, and disease diagnosis under various extents of modality incompleteness.

10.
arXiv (CS.LG) 2026-06-18

Unlocking air traffic flow prediction through microscopic aircraft-state modeling

arXiv:2605.10083v2 Announce Type: replace Abstract: Short-term air traffic flow prediction in terminal airspace is essential for proactive air traffic management. Existing approaches predominantly model traffic flow as aggregated time series. However, traffic dynamics are governed by aircraft states and their interactions in continuous airspace. Such aggregation obscures fine-grained information, including aircraft kinematics, boundary interactions, and control intent. Here we present AeroSense, a state-to-flow modeling paradigm that predicts future traffic flow directly from instantaneous airspace situations represented as dynamic sets of aircraft states derived from ADS-B trajectories. By establishing an end-to-end mapping from microscopic aircraft states to future regional traffic flow, AeroSense preserves aircraft-level dynamics while naturally accommodating varying traffic density without relying on historical look-back windows. Experiments on a large-scale real-world dataset show that AeroSense exhibits admirable predictive accuracy and robustness over aggregation-based forecasting approaches, particularly during high-density traffic periods. These findings suggest that aircraft-state situation modeling provides a promising alternative to conventional time-series forecasting in air traffic flow management.

11.
arXiv (CS.CV) 2026-06-16

KeepLoRA++: Continual Learning with Layer-Scaled Residual Gradient Adaptation

Continual learning for pre-trained vision-language models requires balancing three competing objectives: retaining pre-trained knowledge, preserving knowledge from a sequence of learned tasks, and maintaining the plasticity to acquire new knowledge. This paper presents KeepLoRA++, balancing these objectives through a unified dual-dimensional knowledge retention mechanism. We analyze knowledge distribution of Transformer architecture from both inter-layer and intra-layer perspectives. The inter-layer perspective examines how retention is distributed across layers, while the intra-layer perspective focuses on the parameter space within each layer. Our analysis reveals a structural property: general transferable knowledge is mainly encoded in the shallow layers and the principal subspace of the parameters, while task-specific adaptations are localized in the deep layers and the residual subspace. Motivated by this insight, KeepLoRA++ introduces a layer-scaled residual gradient adaptation method. New tasks are learned by restricting LoRA parameter updates to the residual subspace, combined with a shallow-to-deep layer scaling, to prevent interference with previously acquired capabilities. Specifically, the gradient of a new task is projected onto a subspace orthogonal to both the principal subspace of the pre-trained model and the dominant directions of previous task features, while simultaneously assigning smaller update magnitudes to shallow layers and larger ones to deeper layers. Our theoretical analysis and empirical evaluations confirm that KeepLoRA++ successfully balances these three competing objectives, consistently outperforming representative baselines across image classification, visual question answering, and video understanding tasks.

12.
arXiv (math.PR) 2026-06-16

Purely unrectifiable sets, fractal percolation and graphs of functions

arXiv:2606.15745v1 Announce Type: cross Abstract: This paper contains a survey of some of the results of the author related to unrectifiablity and is an extended version of the author's talk given at the Second Winter School Geometric Measure Theory Rectifiability vs. Pure Unrectifiability in Hanghzou, China. These results include irregular/purely unrectifiable $1$-sets on the graphs of continuous functions like the Takagi, the Weierstrass-Cellerier and the typical (in the sense of Baire) continuous function. It is also discussed that there exists $ {\alpha}_{0}\alpha_0$. The background of the $1$-unrectifiability is discussed in more detail.

13.
arXiv (CS.AI) 2026-06-15

Regional Climate Model Emulation with Diffusion Approaches: What is the Added Value of Generative Machine Learning?

arXiv:2606.14570v1 Announce Type: cross Abstract: Emulators provide a cost-effective alternative to regional climate models (RCMs) by capturing their dynamical downscaling function. They link large-scale predictors simulated by global climate models (GCMs) to RCM-simulated high-resolution fields of the target variable, here precipitation. Machine learning methods, typically deep learning, are cheaper than running RCMs in computation time and energy. Among them, generative models are appealing because they can simulate ensembles of local high-resolution fields consistent with the predictors. This ensemble, which we call the uncertainty envelope, remains to be properly assessed for added value. Here, we make three contributions. First, we introduce ParamDiffusion, a new two-stage diffusion-based framework, and compare it with a state-of-the-art diffusion approach. Second, we expand standard validation through a comprehensive framework aligned with climate-science needs, examining specific precipitation events, including extremes. Third, within this framework, we assess the added value of diffusion approaches relative to deterministic methods. We intercompare four deep-learning models: a deterministic model designed to capture the precipitation tail; a parametric probabilistic model based on it; a recently proposed diffusion approach; and ParamDiffusion, which couples the parametric model with a diffusion model. Our results show that diffusion-based approaches reproduce climatological precipitation statistics with high skill, including distributional tails and spatially compounded extremes, while generating spatially detailed fields. However, none of the assessed models consistently accounts for the most extreme RCM-simulated events within its uncertainty envelope. Diffusion models are therefore promising for probabilistic RCM emulation, but progress is still required before they can reliably represent high-impact precipitation extremes.

14.
arXiv (CS.CL) 2026-06-25

Story Operators: Decomposing the Original $\to$ Sequel Transformation in Embedding Space

I treat a book as a point in a sentence-embedding space and a literary transformation as an operation on points. Given an original novel and its sequel, I ask what it takes, geometrically, to turn the first into the second. Using all-mpnet-base-v2 paragraph embeddings drawn from a precomputed index of the PG19 corpus, I form the displacement $d=\bar{x}_seq-\bar{x}_orig$ and greedily decompose it along a content basis obtained by PCA over the two books' own paragraphs. Each component is an interpretable axis anchored by real passages at its poles. Across thirteen verified author pairs from Project Gutenberg, the decomposition reveals a small taxonomy of sequels: formulaic (a tiny, low-rank change: Doyle's Holmes collections, $\|d\|=0.12$), concentrated (one dominant axis: Alcott's Little Women $\to$ Little Men, 75% on a single move), and compositional (many small axes: Twain, Burroughs's Barsoom, Nesbit). For the canonical case, Tom Sawyer $\to$ Huckleberry Finn, the dominant recovered axis is structural – the collapse of sheltering domesticity into a picaresque road – rather than the famous surface themes of vernacular voice or slavery, which ride later, smaller axes; and the transformation routes through adventure-journey space rather than diluting toward generic realism. I corroborate the recovered geometry against Twain's documented authorial intent (his 1875–76 letters to Howells), which names the first-person picaresque move years in advance, and I quantify, with an explicit representation caveat, how much of the realized transformation his stated intentions span. All computations are reproducible from the released scripts and data.

15.
arXiv (CS.AI) 2026-06-16

HoloRec: Holistic Encoding and Interleaved Reasoning for Generative Recommendation

arXiv:2606.15331v1 Announce Type: cross Abstract: Generative recommendation models that formulate the task as sequence generation overcome the objective fragmentation problem of traditional cascade architectures, yet existing approaches still suffer from flat semantic representations lacking hierarchical structure for multi-step reasoning and an externally constructed chain-of-thought (CoT) that requires expensive annotations and remains disconnected from the generation objective. We propose HoloRec, an endogenous chain-of-thought recommendation mechanism that unifies representation, reasoning, and generation by constructing a hierarchical semantic encoding matrix via multi-granularity nested residual quantization optimized by a holistic reconstruction loss. HoloRec supports two inference modes: a non-thinking mode that uses lightweight multi-granularity supervised alignment for fast prediction, and a thinking mode that employs an interleaved reasoning scheme to generate CoT steps on the fly, directly embedding reasoning into the generation process without external data. Experiments on multiple public recommendation datasets demonstrate that HoloRec consistently outperforms baselines, with especially significant gains in sparse scenarios, and the thinking mode achieves better accuracy than the non-thinking mode with only modest inference overhead.

16.
arXiv (quant-ph) 2026-06-12

Quantum-Driven Neuromorphic Computing for Million-Qubit-Scale Workloads

arXiv:2606.12968v1 Announce Type: new Abstract: We introduce Apollo, a 10000 node p-qubit neuromorphic processor fabricated in 16 nm mixed signal CMOS and operating fully at room temperature with a typical analog core power envelope of about 0.5 W. Its fundamental element, the p-qubit, is a bistable stochastic unit whose continuous time state fluctuations are driven by integrated quantum entropy units that inject true quantum derived randomness. This enables ultrafast stochastic transitions at low energy while preserving a classical state representation. Apollo combines these p-qubits with a high degree Hyperion 256 interconnect topology, allowing efficient embedding of dense Ising and QUBO problems with substantially reduced minor embedding overhead compared with sparse annealing platforms. We show that, through the Suzuki Trotter correspondence, the equilibrium statistics and annealing dynamics of the p-qubit network reproduce key properties of transverse field quantum annealing without cryogenic cooling, long lived coherence, or microwave control. Beyond device level validation, Apollo is evaluated on a three dimensional spin glass benchmark previously used to study quantum advantage in superconducting annealers. Across 300 disorder realizations, Apollo reaches substantially lower ground state energies than reported cryogenic quantum annealing hardware, while remaining distinct from classical simulated annealing and simulated quantum annealing. A 350 nm release candidate device experimentally validates the core p-qubit dynamics, thermodynamic sampling correctness, and continuous time annealing behavior. These results establish Apollo as a room temperature, industrially scalable platform for quantum driven energy based optimization, probabilistic inference, generative modeling, and hybrid classical quantum workflows.

17.
Nature (Science) 2026-06-10

SIRT7 regulates dosage compensation and safeguards the female X chromosome

Sirtuins are deacetylases implicated in stress responses and longevity in mammals1,2. Although their differential impact on disease for the two sexes has been noted3–7, the underlying reasons are unclear. Here, using Sirt7 as a model in mice, we examine the mechanisms leading to sex differences and find that Sirt7−/− female mice have decreased fitness throughout their lifespan. Notably, SIRT7 preferentially localizes to the sex chromosomes. In female individuals, SIRT7 loss affects X-chromosome inactivation, the first arm of dosage compensation that equalizes X-linked gene expression between males and females8–10. Xist is overexpressed and gene silencing becomes more efficient. However, SIRT7 loss has greatest impact on the active X (Xa) chromosome. The Xa chromosome becomes hyperacetylated at Lys36 of histone H3, structurally disorganized, prone to DNA damage and overexpressed. Increased Xa-chromosome expression leads to genome imbalance and augmented X-chromosome upregulation—the second arm of dosage compensation that balances X-chromosome versus autosomal gene expression. These data reveal an essential crosstalk between sirtuins and the sex chromosomes, with SIRT7 safeguarding X-chromosome integrity and dosage balance with autosomes. We propose that the sex bias in SIRT7 biology can be explained in part by unequal effects on the sex chromosomes. SIRT7 safeguards X-chromosome integrity and dosage balance with autosomes.

18.
arXiv (CS.CL) 2026-06-16

Whose hotel does the AI recommend? An algorithm audit of reputation signals in LLM-assisted hotel selection

Travelers increasingly ask large language model (LLM) assistants which hotel to book, making these systems gatekeepers of property visibility – yet what moves their recommendations is undocumented. We conduct a pre-specified algorithm audit using a randomized choice-based conjoint: across personas, prompt templates, and twelve open-weight and proprietary models, assistants choose among five hotels whose guest rating, review volume and recency, management response, chain affiliation, price, eco-certification, and list position are independently randomized. We estimate the average marginal component effect of each signal on the probability of recommendation. Guest rating and price dominate (a top rating raises selection by 31.6 percentage points; a high price lowers it by 30.0), reproducing human valence-and-price primacy but over-weighting eco-certification and ignoring management response. List position – a content-free artifact – shifts recommendations causally, worth about \$12 per night. Stated reasons track revealed weights imperfectly. The findings ground generative engine optimization and the accountability of AI infomediaries in causal evidence.

19.
arXiv (quant-ph) 2026-06-16

VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians

arXiv:2606.15061v1 Announce Type: new Abstract: Quantum Phase Estimation (QPE) is the quantum algorithmic workhorse for computing ground state energies of quantum Hamiltonians with quantum computers. Ground state energy calculation of physical systems is perhaps the most promising use case for quantum computing in terms of scientific and commercial value with a plausible path to outperformance of classical alternatives. This path, however, hinges on the availability of initial states for QPE with significant overlap with the true ground state. Using extensive (classical) numerical computations, we study whether the NISQ-era algorithm VQE (Variational Quantum Eigensolver) could be used to efficiently prepare high-overlap states of disordered fully-connected anisotropic Heisenberg spin glass quantum Hamiltonians with up to $15$ qubits. We find that (i) – consistent with widely held, but rarely numerically illustrated beliefs – VQE is generally unable to efficiently converge to the ground state for our Hamiltonians, which is a well-known issue with VQE due to a variety of factors including vanishing gradients and local minima; (ii) low energy states do not necessarily have large ground-state overlap, but there is typically a correlation between the two measures; (iii) adding more than three layers to the VQE ansatz neither improves overlap nor the energies found; and (iv) the best-found overlap scaling as a function of the Hamiltonian system size is not strongly exponentially decreasing, suggesting potential for VQE to be a heuristic state preparation algorithm for QPE.

20.
arXiv (CS.LG) 2026-06-16

Transformers Learn the Mestre-Nagao Heuristic

arXiv:2606.15036v1 Announce Type: new Abstract: We train a two-layer transformer encoder to classify rational elliptic curves $E/\mathbb{Q}$ of conductor $\leq 10000$ as either rank 0 or rank 1 from the first 128 normalized Frobenius traces. We achieve >99% accuracy on both classes, and accuracy is essentially unchanged on test curves with no isogeny or quadratic-twist relative in the training set. We then apply techniques from mechanistic interpretability such as attention analysis, linear probing, activation patching, logit attribution, and neuron-level circuit analysis to reverse-engineer the algorithm the (centroid in function space) model learned. We find that a sparse circuit of 20 out of 512 layer-1 MLP neurons is sufficient for rank prediction under a linear probe with an AUROC of 0.992 at plateau, implementing a push-pull detector architecture of rank-0 and rank-1 detectors with a one-sided readout. However, we notice that the model has sub-optimal readout problems indicating a mismatch in rank-order between the readout pathway and the discriminative circuit. Critically, the learned input weights of the top discriminating neuron match the Mestre-Nagao sum heuristic weights $\log(p)/(p\cdot \log{B})$ with a Spearman coefficient $r = 0.997$ and Pearson coefficient $r = 0.952$: the model has learnt a result from analytic number theory from the Frobenius trace data alone. We additionally find that all 50 independently trained models concentrate CLS attention on prime positions at 2-50$\times$ the rate of composite positions. The CLS embedding encodes $\log{L(E,1)}$ with $R^2 = 0.962\pm 0.011$ across the 50 models (after controlling for the conductor). Activation patching analysis reveals that attention weights are dissociated from causal information flow. Additionally, the 50 solutions from training are near-identical in function space (with pairwise agreement $>$98.8%) despite large weight space barriers.

21.
arXiv (CS.CL) 2026-06-25

Why Do Accumulated Transformations Extrapolate?

PaTH Attention showed that replacing RoPE's position-indexed rotations with accumulated data-dependent Householder reflections yields strong length extrapolation, though performance degrades at extreme context lengths. We ask whether this depends on Householder-specific structure or reflects a general property of accumulated transformations along source-to-query paths. We study a simpler variant keeping RoPE's block-diagonal SO(2) rotations but replacing position-indexed angles with accumulated token-dependent ones. It shows the same pattern: improved extrapolation then degradation at long contexts. We prove the result extends to accumulated orthogonal transformations satisfying certain regularity conditions: their products become incoherent after finitely many steps, suppressing attention to distant tokens. Accumulated rotations of queries and keys create a finite mixing window independent of context length; per-token suppression learned in training transfers unchanged to any evaluation length, and high-dimensional concentration produces a score gap suppressing far tokens while near-route transport preserves the target signal. Conversely, a lower bound shows accumulated rotations must eventually degrade: as the far set grows, no rotations preserve the near signal without explicit far-mass control. For SO(2) rotations, rotating values too makes residual far contributions combine incoherently, extending the range. Controlled experiments support these predictions: random accumulated rotations substantially improve extrapolation over RoPE, learned token-dependent rotations maintain near-training-length perplexity far beyond the training context, and rotating values helps over queries and keys alone. Rotation-only models still degrade at extreme lengths, while ALiBi stays length-stable, consistent with the need for far-mass control.

22.
arXiv (quant-ph) 2026-06-25

Quantum Detectability in Invisibility Cloaks

arXiv:2606.25666v1 Announce Type: new Abstract: Classical invisibility cloaks are designed to suppress selected scattering signatures and thereby make an object appear absent to external electromagnetic probes. However, the suppression of a classical scattering observable does not, by itself, establish that all information about the concealed object has been removed from the detected quantum state of light. Here we formulate the detectability of classically cloaked objects as a quantum-state distinguishability problem. Treating a linear passive cloak as an effective Gaussian quantum channel acting on the accessible detected modes, we show that local quantum undetectability requires the detected first and second moments to be independent of the hidden-object parameter. In this framework, quantum Fisher information provides an operational criterion for whether the concealed parameter remains estimable from the detected output state. We derive displacement- and covariance-level detectability conditions and show that a nonzero parameter imprint surviving in the detected Gaussian state leads to a nonzero accessible quantum Fisher information. To connect the criterion with a physical cloaking model, we analyze a regularized cylindrical transformation-optical cloak in the Born limit and compare the scaling of the classical scattering response with the derivative-based quantum sensitivity. The analysis shows that reducing a scattering amplitude is not equivalent to eliminating local quantum-state sensitivity. Loss, environmental noise, and finite numerical aperture degrade the accessible information, but quantum undetectability is reached only when the parameter imprint is removed from the detected state or projected entirely outside the accessible subspace. These results provide a Gaussian-channel framework for assessing when classical cloaking does, and does not, imply quantum-state undetectability.

23.
arXiv (CS.CL) 2026-06-11

Agreement in Representation Space for Open-Ended Self-Consistency

Self-consistency improves LLM reasoning by sampling multiple outputs and selecting the most consistent answer, but existing formulations largely rely on exact matching and therefore remain limited to tasks with categorical outputs. In this work, we study self-consistency in open-ended generation tasks such as code synthesis and text summarization. We hypothesize that consistency can be understood as a geometric property of the generation space, where semantically compatible generations concentrate in similar regions of representation space. To study this hypothesis, we introduce Embedding-Based Agreement (EBA), a simple training-free operationalization that estimates agreement by clustering sampled generations in embedding space. Through experiments on mathematical reasoning, code generation, and summarization, we show that agreement in representation space provides a robust and scalable signal of self-consistency for open-ended tasks. In particular, EBA consistently outperforms random selection and exhibits more stable scaling behavior than recent selection approaches based on LLM evaluation or uncertainty estimation. We further show that these agreement signals remain stable across model families and embedding spaces, even with native hidden representations. Finally, our analysis shows that the geometric location occupied by sampled generations is strongly correlated with generation quality: generations concentrated near central regions of representation space tend to correspond to more reliable outputs, whereas peripheral generations are substantially less accurate. Overall, our findings support viewing self-consistency as a property of the geometric organization of sampled generations rather than exact symbolic overlap.

24.
arXiv (CS.AI) 2026-06-16

RaBiT: Residual-Aware Binarization Training for Accurate and Efficient LLMs

arXiv:2602.05367v3 Announce Type: replace Abstract: Efficient deployment of large language models (LLMs) requires extreme quantization, forcing a critical trade-off between low-bit efficiency and performance. Residual binarization enables hardware-friendly, matmul-free inference by stacking binary ($\pm$1) layers, but is plagued by pathological feature co-adaptation. We identify a key failure mode, which we term inter-path adaptation: during quantization-aware training (QAT), parallel residual binary paths learn redundant features, degrading the error-compensation structure and limiting the expressive capacity of the model. While prior work relies on heuristic workarounds (e.g., path freezing) that constrain the solution space, we propose RaBiT, a novel quantization framework that resolves co-adaptation by algorithmically enforcing a residual hierarchy. Its core mechanism sequentially derives each binary path from a single shared full-precision weight, which ensures that every path corrects the error of the preceding one. This process is stabilized by a robust initialization that prioritizes functional preservation over mere weight approximation. RaBiT redefines the 2-bit accuracy-efficiency frontier: it achieves state-of-the-art performance, rivals even hardware-intensive Vector Quantization (VQ) methods, and delivers a $4.49\times$ inference speed-up over full-precision models on an RTX 4090. Code is available at https://github.com/SamsungLabs/RaBiT.

25.
arXiv (CS.CV) 2026-06-12

Skeleton Sparsification and Densification Scale-Spaces

The Hamilton-Jacobi skeleton, also known as the medial axis, is a powerful shape descriptor that represents binary objects in terms of the centres of maximal inscribed discs. Despite its broad applicability, the medial axis suffers from sensitivity to noise: Minor boundary variations can lead to disproportionately large and undesirable expansions of the skeleton. Classical pruning methods mitigate this shortcoming by systematically removing extraneous skeletal branches. This sequential simplification of skeletons resembles the principle of sparsification scale-spaces that embed images into a family of reconstructions from increasingly sparse pixel representations. We combine both worlds by introducing skeletonisation scale-spaces: They leverage sparsification of the medial axis to achieve hierarchical simplification of shapes. Unlike conventional pruning, our framework inherently satisfies key scale-space properties such as hierarchical architecture, controllable simplification, and equivariance to geometric transformations. We provide a rigorous theoretical foundation in both continuous and discrete formulations and extend the concept further with densification. By growing the skeleton successively instead of shrinking it, we allow inverse progression from coarse to fine scales. Densification scale-spaces can even reach beyond the original skeleton to produce overcomplete shape representations with relevancy for practical applications. Through proof-of-concept experiments, we demonstrate the effectiveness of our framework for practical tasks including robust skeletonisation, shape compression, and stiffness enhancement for additive manufacturing.