Robot swarm co-design requires optimizing not only individual robot designs and behaviors, but also the heterogeneous swarm structure: how many robot types should exist, how they specialize and cooperate, and in what proportions they are deployed. However, these structural choices are often specified in advance rather than optimized. We present SwarmCoDe, a Cooperative Co-Evolutionary Algorithm (CCEA) that incorporates swarm decomposition into the optimization process without requiring the number of species to be specified in advance. SwarmCoDe combines dynamic speciation with evolved genetic tags, partner selectivity, and relative dominance to jointly optimize robot hardware, task-planning behavior, cooperative relationships, and deployed swarm composition. Across replicated simulated foraging experiments, SwarmCoDe discovers task-dependent swarm decompositions and adapts them when task requirements change, in contrast to fixed-K CCEAs which are sensitive to their pre-defined decomposition. We further show that fabrication budgets can change the preferred swarm composition and robot designs, and that SwarmCoDe can adapt its co-design under these resource constraints. Finally, SwarmCoDe co-designs 200-agent swarms using only 50 evolutionary individuals, demonstrating deployment at four times the evolutionary population size. Together, these results demonstrate that the heterogeneous structure of a robot swarm can be incorporated as a design variable and optimized alongside the robots themselves.
Santiago Berrezueta-Guzman, Andrei Koshelev, Habiba-Loai Khalil, Stefan Wagner
Apple Vision Pro (AVP), the headset Apple introduced as its first ``spatial computer,'' built by a single, vertically integrated vendor, entered the market in February 2024 and has since accumulated a fast-growing body of primary research spanning surgery, education, accessibility, design, and human-computer interaction. In this paper, we adopt the tripartite structure of Leone's 1966 film to organize a systematic review of this literature: we cataloged the validated, working applications of AVP (the good), the persistent technical and ergonomic limitations of a still-early-generation headset (the bad), and the ethical concerns and structural harms that follow from deliberate design, marketing, and deployment choices (the ugly). The review is built from a Scopus export of 218 records mentioning AVP, which we narrowed to 104 papers (2024--2026) with a primary focus on AVP, using explicit inclusion/exclusion criteria that we report in full, alongside a PRISMA-informed flow diagram of the screening process. We find the corpus heavily skewed toward validating benefits (medicine and surgery, education, and software tooling account for over half of the included papers) and comparatively thin on documented risks or misuse, a pattern we treat as a finding in its own right rather than a limitation to be explained away. We further show that several recurring issues, namely price, simulated social presence, and the gaze-tracking privacy architecture, resist a clean separation into ``bad'' or ``ugly'' using the published evidence alone, since both readings remain compatible with the same data. We close by identifying where the evidence base most needs to grow: independent risk and ethics research, bystander- and equity-focused study designs, and disclosure that would let researchers distinguish an engineering backlog from a structural choice.
Roxanne De Maeyer, Ine Dirks, Yannick Brackenier, Simon DeKeyser, Jef Vandemeulebroucke, Vicky De Ridder
The HECKTOR 2026 challenge benchmarks machine learning for head and neck cancer, where teams delineate primary and nodal tumour volumes, perform TN staging, and predict recurrence-free survival (RFS). This report describes the submissions for the HECKTOR challenge of team nucli. As the three tasks span both dense and global information from multicentric PET/CT scans, we utilise self-supervised pre-trained encoders, training a 2D DINOv2 encoder (PET-DINOv2-MIPs) on HECKTOR 2026's PET scans. Our final test submission ensembles a DynUNet trained from scratch with a SwinUNETR whose Swin trunk was initialised from a SimMIM-pre-trained checkpoint for segmentation, reaching a mean Dice of 0.5409. For TN staging, GTVp/GTVn geometric features from the segmentation masks are fit to stage probabilities by logistic regression (LR) and fused with PET-DINOv2-MIPs deep features (PCA + LR) via a second-level LR, reaching balanced accuracies of 0.3962 (T-stage) and 0.6432 (N-stage). For the RFS prognosis task, we fine-tune the last two blocks of the PET-DINOv2-MIPs ViT-S encoder jointly with an MLP head under a CoxPH loss, concatenating clinical covariates with the imaging features, reaching a test Harrell's C-index of 0.6577 and a weighted challenge score of 0.5802. The prognosis result is comparable to the best entry of the previous edition and consistent with our internal cross-validation, while our segmentation result is well below it and limits the staging results that depend on it.
With the help of secure hardware such as trusted execution environments (TEEs), private data can be uploaded and computed in untrusted cloud clusters, so that an adversary controlling the cloud can only see the data in encrypted form. However, the communication pattern between the processors may still reveal sensitive information about the data, so it is important to develop parallel algorithms in the BSP model whose communication pattern is independent of the input data, a property known as \textit{communication obliviousness}. In this paper, we study such algorithms for three fundamental problems: permutation, sorting, and 0-1 sorting. For the first two problems, we prove a tight (up to lower-order terms) communication complexity of $(2-2/p)n\pm o(n)$. Here, $p$ is the number of processors and $n$ is the input size, assuming $2\le p$ and $p=o(n^{1/3})$. Our lower bound holds regardless of the number of rounds and local memory size, while for balanced permutation and sorting the upper bound is achieved in a constant number of rounds with load at most $n/p+o(n/p)$. For 0-1 sorting, we also derive a tight communication complexity of $C_{\mathrm{cut}}(p) \cdot n \pm o(n)$, where $C_{\mathrm{cut}}(p)$ is the optimal value of a linear program parameterized by $p$. Although there appears to be no closed-form for $C_{\mathrm{cut}}(p)$, we show that it is strictly smaller than $2-2/p$ for all $p\ge 3$, thus separating 0-1 sorting from general sorting in terms of their communication complexity.
Targeted protein degradation (TPD) represents a fundamental shift in drug discovery, moving beyond traditional target inhibition toward the event-driven removal of disease-causing proteins. A prominent strategy for TPD is the use of proteolysis-targeting chimeras (PROTACs), heterobifunctional molecules that selectively route a protein of interest (POI) to the ubiquitin-proteasome system for degradation. While PROTAC design still relies heavily on trial-and-error synthesis and experimental testing, deep generative models offer a promising means to explore PROTAC chemical space in silico and generate novel molecules. However, many existing generative methods formulate PROTAC design primarily as a linker-generation problem, with POI-binding (warhead) and E3-ligase-binding components fixed in advance. This restricts exploration of the full PROTAC chemical space and often leaves the POI implicit through the predefined warhead, rather than using protein-level information as an explicit conditioning signal during generation. To address these limitations, we propose TACFormer: a transformer-based generative model for target-aware de novo PROTAC design. The model conditions a GPT-style molecular decoder on pretrained ESM-2 representations of POI sequences, allowing POI-level information to steer full-molecule generation. Our results show that TACFormer generates highly novel and chemically diverse PROTACs while showing consistent POI-dependent shifts in generated chemical space. In particular, molecules generated under specific target conditions preferentially populate chemical neighborhoods associated with POIs in the held-out dataset, while extrapolating to novel chemotypes. By natively integrating biological context into the generative process, TACFormer moves PROTAC design toward a more biology-informed exploration of degrader chemical space.
Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target contact laws, with only a few asperities in unit cells. The predicted designs are validated against high-fidelity Boundary Element Method (BEM) simulations. By front-loading computational costs during training, the neural surrogate yields near-instantaneous design inference, bypassing the bottlenecks of traditional multi-start optimization. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for the high-throughput discovery and real-time control of functional tribological surfaces.
Super-telephoto imaging on mobile phones suffers from complex, device-dependent degradations that are poorly captured by conventional handcrafted pipelines. Collecting large-scale aligned training pairs across different phones and diverse scenes, however, is both costly and difficult to scale. We therefore study whether device-specific degradations can be learned from only a small number of physical captures and transferred for training a unified super-resolution (SR) model. Our key idea is to factor degradation learning into two learnable components: one captures the device-specific imaging characteristics under well-resolved conditions, while the other captures the additional information loss and artifacts that arise in super-telephoto imaging. We build a paired benchmark across three phone brands (Huawei, Apple, and vivo) by photographing the same content at two display sizes and zoom settings. The larger displayed image is captured at the phone's maximum optical zoom setting, while the smaller image is photographed directly at the phone's highest native zoom setting through the phone's native imaging pipeline. The benchmark contains 519 training and 60 held-out pairs. We use the benchmark to learn device-specific degradation, then apply it to external images to synthesize thousands of additional pairs to train our UniTele SR model. Relative to the pretrained Qwen and FLUX backbones before adaptation, the full UniTele training recipe substantially improves paired restoration fidelity and perceptual similarity on the held-out benchmark and yields markedly more stable and visually faithful restorations.
Raffaele Giancotti, Francesca Santucci, Amama Anjum, Monique de Villa, Rupsa Mitra, Soham Biren Katlariwala, Vishala Mishra, Leo Anthony Celi
Failures of deployed clinical artificial intelligence (AI) systems have often originated in how their training data were generated. Whether the programs that train the health AI workforce teach practitioners to examine data provenance is unknown. We conducted a cross-sectional analysis of the publicly advertised curricula of health AI education programs at U.S. universities, identified through a structured multisource web search between April and July 2026. Two investigators coded coverage of data provenance (structural, dataset limitations, or data management only), ethics, and sustainability; collaborative structure; technical prerequisites; and the disciplinary background and gender of named instructors. The primary outcome was provenance coverage at the structural or dataset-limitations level. Of 43 candidate entries, 36 programs at 25 institutional units in 21 universities were included. Ethics was covered by 29 programs (80.6%; 95% confidence interval [CI], 65.0 to 90.2), data provenance by 8 (22.2%; 95% CI, 11.7 to 38.1), and structural provenance by 6 (16.7%; 95% CI, 7.9 to 31.9). None of the seven master's degree programs met the primary outcome, and no program addressed sustainability. Eighteen programs included team-based work, but only 5 assembled teams across clinical and technical backgrounds. Of 92 named instructors, 76.1% came from computational disciplines and 3.3% from the social sciences or humanities; among the 51 whose gender could be determined, 66.7% were men. U.S. health AI education programs widely taught ethics but rarely taught how clinical data are produced. None addressed the environmental cost of computation, and most instructors came from computational disciplines.
Nhan Trong Luu, Duong Trung Luu, Thang Cong Truong
Spiking neural networks (SNNs) promise event-driven, low-power inference, but on vision tasks they still acquire rotation invariance only through data augmentation. Group-equivariant CNNs build such symmetries into the architecture, yet a faithful spiking analogue is missing: a leaky integrate-and-fire (LIF) neuron placed after a $G$-equivariant convolution can break equivariance through its membrane recurrence. We give a necessary and sufficient condition for this not to happen. The layer is equivariant at every time step if and only if the neuron parameters $(β, v_{\mathrm{th}})$ are constant along the joint orbits of the group action on the (group, space) index. We solve it in closed form, and it covers any elementwise stateful neuron. Its sufficiency half specialises a known result for equivariant recurrent networks; its necessity half rules out the heterogeneous per-neuron parameters common in SNNs. The per-channel parameterisation that satisfies it, Group-Coupled LIF (GC-LIF), is combined with $p4$ and $p4m$-equivariant convolutions and a spike-rate group max-pool into SGE-Net. On MNIST, KMNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100, evaluating each checkpoint on the clean test set and all its group-transformed copies, SGE-Net trained without rotations is invariant under $C_4$ and $D_4$ and outperforms a plain SNN trained with rotations in nine of ten dataset-group pairs, whereas non-equivariant baselines lose up to $72$ percentage points in the worst case. Operator-level tests confirm the theory before and after training, and an analytical estimate places SGE-Net at $1.7\times$ the arithmetic energy of a standard CNN and $2.3\times$ below its ANN counterpart at eight time steps.
Wind Farm Layout Optimization places turbines to maximize the expected energy under a wind rose, each turbine lowering the wind downwind. In the EndoWake model the wind field is a variable, propagated by linear inequalities, and layouts are certified by branch-and-check. On a ladder of grids it certifies the $10\times10$ grid and leaves the larger grids open after one hour. We tighten the relaxation by a convexification computed rather than derived: every pattern of turbines inside a small tile of the grid is enumerated once with its power and enters the master as a column. The device is valid because the wind field is antitone, and exact, for the cubic power curve, with a Benders cut at integer layouts. Reduced-cost fixing and propagation between overlapping tiles shrink the master before the tree search, and the tree repeats the fixing at every improving incumbent. The incumbent comes from a tile heuristic or an LP dive. On the same computer as the branch-and-check, the $12\times12$ and $14\times14$ grids close in 48 and 395 seconds. The $16\times16$ grid is certified on five seeds from random starts, one job per seed, the heuristic on a GPU, in 1413 seconds under the uniform rose and 6484 seconds under a non-uniform one. Times are medians. A pre-specified test set of 36 unseen instances with forbidden cells confirms the advantage in the axial setting. Certified means closed at the solver's gap of $10^{-4}$: the optimum lies within it plus a residual of at most 0.00042%.
Haotian Lyu, Haoyu Wang, Ru Wang, Feng Ji, Ziwen Li, Jiaxian Guo, Mingming Gong
Label-free test-time reinforcement learning adapts vision--language models using rewards derived from their own predictions. However, misinterpreted visual evidence and sensitivity to textual formulation can produce a consistent but incorrect consensus that majority voting reinforces. Cross-view aggregation can expose such errors, but image and text transformations may themselves degrade task-relevant evidence to different extents. We introduce \method, a reliability-aware harmonic consensus framework for multimodal test-time reinforcement learning. \method constructs a $2\times2$ grid combining original and perturbed images with direct-solving and reframing modes, selects pseudo-labels through weighted harmonic aggregation, and adapts modality-level weights using batch-averaged, temporally smoothed shifts in pseudo-label confidence as a heuristic reliability signal. We formulate consensus as a weighted $χ^2$-barycenter problem whose unique minimizer is the normalized weighted harmonic aggregate, without requiring correct-answer invariance. An exact support--dispersion decomposition characterizes when harmonic aggregation preserves or corrects arithmetic rankings, while a sensitivity analysis establishes how modality reweighting changes pairwise ranking margins, informing interpretation of the heuristic updates. Across six benchmarks and three Qwen3-VL model scales, \method outperforms TTRV in 16 of 18 benchmark--model settings on adaptation instances and 17 of 18 settings on held-out instances under matched estimation and optimization rollout counts. These results demonstrate improved target-task adaptation and transfer to unseen instances without further updates.
An identifying code of a graph is a dominating set $C$ such that the sets $N[v]\cap C$ are pairwise distinct. The minimum density of an identifying code has been studied extensively for several infinite grids. It is known to be $1/4$ for the triangular grid and $7/20$ for the square grid, whereas for the hexagonal grid the problem is still open, between $5/12$ and $53/126$. These three grids are the regular members of the family of the eleven Archimedean grids. In this paper, we start a systematic study of identifying codes in this family. We determine the minimum density for five of the nine Archimedean grids for which it was not known: it is $2/3$ for the truncated hexagonal grid, $3/7$ for the truncated square grid, and $1/3$ for the trihexagonal (kagome) grid, the elongated triangular grid and the snub hexagonal grid. All lower bounds are proved by the discharging method. For the three remaining non-regular Archimedean grids, we also obtain some bounds: the minimum density lies between $3/7$ and $13/30$ for the truncated trihexagonal grid, between $1/3$ and $11/30$ for the rhombitrihexagonal grid, and between $2/7$ and $9/28$ for the snub square grid. As a by-product, we prove that every identifying code of a cubic graph with the slow growth property in which every vertex lies on exactly one triangle (resp. $4$-cycle) has density at least $2/3$ (resp. $3/7$).
We study multidimensional online generalized assignment under nonstationary arrivals, motivated by resource allocation for large language model agent services. Providers may commit model and tool allowances to agent tasks upon admission, reserving budgets for their internal execution loops. Each request is rejected or accepted with an irrevocable assignment to one compatible server, earning reward and consuming a vector of its nonreplenishing budgets. Arrivals are independent with known, potentially time-varying type distributions. Scalar reductions can discard feasible combinations of requests with complementary resource requirements. To maximize expected reward, we develop Vector-Aware Best-Fit, which combines linear-programming-guided candidate routing with calibrated acceptance while retaining vector feasibility. Relative to the expected clairvoyant offline optimum, its guarantee improves on scalar reduction in the multidimensional case and has the best possible inverse-dimensional order. With an appropriate acceptance parameter, the proposed policy attains the optimal competitive ratio on all-heavy instances, where every feasible assignment consumes more than half of at least one resource budget. We further develop two heuristics that retain its performance guarantee. Computational results show that the heuristics perform well against benchmarks in most tested settings, especially when capacity is scarce relative to demand.
Eli A. Underwood, Nicolas Rondan, Angel V. Peterchev, J. Matias Di Martino
Aligning a partial, real-world 3D face scan to a canonical representation requires solving two coupled problems at once: estimating the rigid pose that brings the scan into a common frame, and completing the facial shape in regions the scan never observed. Existing pipelines typically decouple these steps, running a generic point-cloud registration front end followed by a separate non-rigid fitting or deformation stage. Building on the GeoTransformer superpoint-matching architecture, we propose a single network that predicts both a rigid pose and a shape-complete point cloud in one forward pass: a cross-attention regressor, conditioned on transformer point features and predicted coarse correspondences, maps a partial scan to per-patch coefficients of a 3D morphable face model learned offline from a corpus of 8,000 identities. The resulting morphed template is then used, in the same forward pass, as the target for fine-grained Sinkhorn matching and rigid pose estimation, supervised purely by geometric alignment to ground-truth morphed geometry, so no hand-labeled coefficients are required. Against six classical and learned non-rigid registration baselines on held-out identities, our method leads the strongest ones by 3-4 times on per-vertex error and baselines that collapse the head onto the visible region by more than an order of magnitude, and is simultaneously the most accurate and fastest method on ground-truth-free scans from two independent real-scan datasets, NoW and NPHM. Code will be made publicly available.
Password-based authentication remains challenging for many users, especially for those who face usability and accessibility issues. The burden of maintaining security can cause user fatigue, frustration and non-engagement. To address these issues, we conducted a pilot study to assess ECG-based biometric authentication as a passwordless alternative and to gather adult participants' perspectives on this approach. The research consisted of a survey study, an authentication prototype and a follow-up usability experience questionnaire. Our approach combined an online survey of 337 adults examining authentication practices and perceptions, with a separate usability evaluation in which 49 participants interacted with a simulated ECG-authentication and password interface in a health-care application prototype, then completed a post-test usability test questionnaire. The survey examined how adults across age groups use and perceive various authentication techniques, their experiences with biometrics, their views on security and convenience, and their willingness to adopt ECG authentication. In parallel, the usability prototype and questionnaire captured participants' responses after hands-on interaction with an ECG authentication prototype.
Nizar Khalfet, Francisco A. Monteiro, Ioannis Krikidis
This paper investigates a quantum relay-assisted free-space optical (FSO) communication system in which a decode-and-forward relay is powered by time-switching optical energy harvesting and forwards the decoded information using displaced squeezed signaling (DSS). To obtain a physically con sistent description of turbulence-induced loss for non-classical signaling, each hop is modeled as a pure-loss bosonic chan nel whose random transmissivity follows a truncated Gamma Gamma law, i.e., the Gamma-Gamma irradiance conditioned on the physically admissible range of a transmittance. Under this channel, coherent states remain pure, whereas squeezed states are mapped to mixed Gaussian states. Under Helstrom-optimal detection, the average error of the coherent hop is derived in exact Laplace-series form. For the DSS hop, we derive the output states, a closed-form Gaussian fidelity with rigorous two sided bounds on the Helstrom error, and prove the existence of a loss-aware optimal photon partition. Furthermore, we prove that optimized squeezing preserves both the turbulence-induced diversity order and the leading asymptotic constant of coherent relaying, so that its benefit is a finite-photon-budget effect, and that an interior throughput-optimal harvesting fraction exists. A covariance-preserving benchmark with an exact series representation yields an analytical upper bound on the achievable throughput whose absolute gap vanishes as the relay photon budget grows. Numerical results based on the exact mixed-state Helstrom error quantify the benefit of squeezing and the regime in which it is useful.
Understanding the loss-landscape geometry near a minimum is key to explaining the implicit bias of gradient-based methods in non-convex optimization problems such as deep neural network training and deep matrix factorization. A central quantity for characterizing this geometry is the maximum eigenvalue of the Hessian of the loss. Currently, its precise role has been obfuscated because no exact expressions for this sharpness measure were known in general settings. In this paper, we present the first exact expression for the maximum eigenvalue of the Hessian of the squared-error loss at any minimizer in deep matrix factorization problems, resolving an open question posed by Mulayoff and Michaeli [2020]. This expression reveals a fundamental property of the loss landscape in deep matrix factorization: It is sufficient, but not necessary, for flatness that, across all layers, the product of the spectral norms of the left and right intermediate factors equals a constant determined by the depth and the spectral norm of the target matrix. Most notably, in both depth-2 matrix factorization and deep overparameterized scalar factorization, we show that this condition is both necessary and sufficient for flatness, which implies that flat minima are spectral-norm balanced and not necessarily balanced in depth-2 matrix factorization. To complement our theory, we provide empirical verification, relying on our exact expression, of an escape phenomenon during gradient-based training near a minimizer of a deep matrix factorization problem.
Large language models pass most functional-correctness benchmarks, but passing tests says little about whether their code is readable, efficient or secure. Many techniques claim to improve these qualities, yet their evidence is scattered, usually covers one quality dimension and is rarely compared at an equal compute budget. We contribute a systematic review and a controlled re-evaluation. A systematic literature review of 628 primary studies (July 2021 to October 2026), with disclosed, author-reviewed LLM assistance, organizes the techniques by stage, signal source and quality target. Most studies measure only the dimension they target, gains often come with unchanged or unreported correctness, single automated quality signals are gamed, and compute, variance and contamination are rarely reported. A controlled re-evaluation runs ten techniques on four models at matched budgets on correctness, maintainability, efficiency and security benchmarks, extends it to thirteen current models and repository-level tasks, and compares 66 highlighted techniques head-to-head on Gemma 4 31B. At one call, quality prompting raises analyzer issue counts and leaves complexity and judge scores almost unchanged. At matched budgets, best-of-n sampling with an analyzer-weighted ranker matches or beats prompting, planning, self-refinement, a reviewer agent and retrieval on measures the ranker does not optimize, while an analyzer feedback loop and fine-tuning beat it only on analyzer issue counts. Large correctness losses on HumanEval+, a likely contaminated benchmark near its ceiling, do not appear on contests held after the models' training cutoffs. In the head-to-head, 1 of 66 techniques beats best-of-n on its primary target beyond the 95% interval, a rate consistent with chance. Gains should be reported against a budget-matched sampling baseline and on measures independent of the technique's own signal.
We (the author and the AI systems that did the heavy lifting) show that the quantum query complexity of minimizing a convex function over a convex subset of $\mathbb{R}^n$ with evaluation and membership queries is $\tildeΩ(n)$, nearly matching the best known upper bound. In particular, we show this even for quadratic minimization, which is equivalent to inverting an $n \times n$ real matrix using matrix-vector queries. We also show linear or nearly linear lower bounds on the quantum query complexity of computing the trace, the sign of the determinant, and the magnitude of the determinant of a real matrix in the matrix-vector query model. We use a novel quantum lower bound technique, the determinantal witness method, based on identifying a witness whose Fourier transform vanishes on low-rank matrices and that correlates well with the function being computed.
John S. McAlister, Nina H. Fefferman, Tadele A. Mengesha
Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to coordinate action with one another through myopic best response or other replicator dynamics, the resulting dynamical system can exhibit many rich behaviors. Here we seek to understand these coordination dynamics in the non-atomic setting by use of a nonlinear, nonlocal diffusion equation framework. For this class of nonlocal equations, we prove existence and uniqueness for the initial value problem in the free boundary case and, with certain conditions on the underlying game theory, we go further and prove a maximum principle, weak regularity results, and a characterization of asymptotic behavior. Additionally, with the help of several numerical results, we present several modeling results, characterizing stationary solutions both rigorously and through numerical experiments.
Mohammad Sadegh Akhondzadeh, Soroush H. Zargarbashi, Aleksandar Bojchevski
Even though current safety-aligned language models are able to refuse harmful requests, their guard can still be bypassed by adversarial perturbations. As in other domains, adversarial training is considered a standard defense. However, due to the autoregressive nature of language generation, supervised finetuning on template refusals does not necessarily teach the model to refuse. Evidence of this is that the adversarially trained model still complies when the attacker injects a compliant prefill. We propose Adversarial Self-Distillation (ASD), which extends a model's own safe behavior to the space of adversarial perturbations. The teacher (the model itself given the clean prompt) can refuse the harmful request by default, or with the help of an additional instruction in its context. ASD distills this knowledge to the student (which is the same model under attack) at the prefixes that the student visits (due to on-policy sampling). These potentially include compliant openings. ASD achieves lower attack success than state-of-the-art defenses with little loss in multiple-choice accuracy, and it becomes able to recover a refusal even after a compliant opening.
Synthetic medical tabular data generation has become essential for developing and validating computer-based medical systems (CBMSs) when real clinical data is restricted due to privacy, ethical, or data availability limitations. Existing probabilistic and deep generative models often lack interpretability and fail to preserve clinically meaningful dependencies, limiting their suitability for safety-critical applications. This paper proposes a novel application of Fuzzy Cognitive Maps (FCMs) in a framework for synthetic medical tabular data generation with explicit causality and privacy preservation. Clinical features are described using linguistically interpretable fuzzy sets, and inter-feature dependencies are encoded as FCM edge weights computed from fuzzy set intersections. Synthetic patient records are generated by propagating randomly initialized linguistic activation vectors through the FCM until convergence, followed by defuzzification to produce clinically coherent numerical values. The approach natively handles mixed data types, and domain constraints common in health records. Experimental evaluation on UCI medical benchmark datasets demonstrates competitive performance under a Train-on-Synthetic-Test-on-Real (TSTR) protocol. The proposed method achieves accuracy of up to 0.81 and AUROC of up to 0.90 on the Heart Disease dataset, matching or exceeding TVAE and Gaussian Copula baselines while running exclusively on CPU. Fidelity metrics including KS Complement (up to 0.91) and Correlation Similarity (up to 0.95) confirm strong statistical coherence, and DCR Baseline Protection scores consistently exceed those of TVAE, confirming adequate privacy guarantees. These results demonstrate that causally grounded, interpretable fuzzy modeling offers a computationally efficient and transparent alternative to deep generative models for trustworthy synthetic data generation in CBMSs.
Zhuoyuan Hao, Zhuo Li, Wu Li, Fangming Liu, Min Zhang, Jing Li
Recent work improves reasoning in large reasoning models (LRMs) by test-time scaling through self-consistency and parallel thinking, adding generic "thinking tokens", or presenting the question twice, as in re-reading (RE2). However, these approaches either inject task-agnostic tokens or mandate heuristics that do not explain, and often ignore, the spontaneous repetition that many LRMs exhibit at the head of their long chain-of-thought (CoT). In this work, we analyze and harness the model's tendency to restate the question, dubbed Echo of Prompt (EOP), as a front-loaded, compute-shaping mechanism, which can be viewed as self-generated prompt repetition inside the reasoning trace rather than in the input. Specifically, we formalize its probabilistic cost by casting echo removal as rejection-based conditioning, and define the Echo Likelihood Gap $Δ\mathcal{L}$ as a computable proxy linking early repetition to likelihood gains and downstream accuracy. We find that (1) in a causal intervention, reinserting an echo into failed GSM8K traces raises exact match by 7.9-10.4 points for two reasoning models but not for a non-reasoning base model; and (2) in length- and suffix-controlled likelihood analyses and layer-wise attention studies conducted to show that EOP's benefits go beyond verbosity, EOP increases answer to answer-prefix attention in middle layers, consistent with an attention refocusing mechanism. Building on these findings, we develop Echo-Distilled SFT (ED-SFT) to instill an "echo-then-reason" pattern through supervised finetuning, and training-free Echoic Prompting (EP) to re-ground the model mid-trace. We evaluate on GSM8K, MathQA, Hendrycks-MATH, AIME24, and MATH-500 under identical decoding settings and budgets, and find consistent gains over baselines, including thinking-token insertion. Our code is publicly released at https://github.com/hhh2210/echoes-as-anchors.
First-derivative edge detectors such as Sobel, Prewitt, Roberts and Scharr measure absolute grey-level differences. We revisit the log-gradient magnitude, a relative-gradient edge operator, and motivate it by analogy with the superderivative, a multiplicative derivative in which the independent variable is perturbed multiplicatively rather than additively. In one and two dimensions the logarithm of the superderivative is a radial logarithmic derivative; its local, origin-free, isotropic analogue is the magnitude of the logarithmic gradient. The resulting operator measures relative rather than absolute change, giving an edge-strength map that is invariant under global intensity rescaling. We present the theory, show how the operator can be implemented in two steps---a classical gradient kernel plus a pointwise division---and compare it with standard first-derivative filters on synthetic images with ground-truth edges and on the official BSDS500 benchmark. We also study a parametric family that interpolates between the absolute gradient and the log-gradient; empirically, the best members are small intermediate exponents, which edge the classical kernels by a small but statistically detectable margin in the per-image metric and, with the same Gaussian smoothing as the single-$σ$ Canny, match it in ODS and lead it in OIS and AP, while the tuned Canny remains ahead in ODS. The single-threshold margin over the kernels does not replicate on the held-out test split, and the fully relative endpoint is never the best member, its ranking depending on the edge-map normalisation. The contribution is the construction and the invariance it buys, not a new state of the art.
Can a Watershed transform, the classical tool of morphological segmentation, be placed at the end of a deep network and trained through? The Power Watershed (PW) is the limit of the seeded Random Walker (RW) as p grows to infinity with edge weights raised to the power p. At every finite p the RW solves a sparse positive-definite linear system and is exactly differentiable with respect to the edge weights and the unaries through one adjoint solve; its multi-label form costs one right-hand side per label, and its limit is the PW. We study this family as the last layer of a segmentation network, the watershed layer (WS layer). A conditioning study measures how the solve, the gradient and the distance to the limit evolve with p, and the implicit gradient is checked against unrolling. On synthetic data with correct edge costs the WS layer transforms a soft prediction into an exact boundary. On nuclei segmentation (PanNuke), a binary WS layer is level with a thresholded U-Net. With the instances as labels, the WS layer turns the U-Net into an instance segmenter whose number of labels is set per image by the markers rather than by the output layout, and the network is trained through that partition: instance F1 score rises from 0.656 to 0.795 over a U-Net with connected components, level with the same network followed by a tuned marker watershed. At the training temperature the partition is a watershed of the learned costs, and the finite temperature lets the solve hedge, discounting weak markers and sharing contested pixels. The hedging puts the WS layer 0.015--0.020 F1 ahead of the baseline when trained on a tenth of the data, at the price of having to deploy the finite-p solve rather than its exact limit at inference. Code and the full experimental record are released.
The diagonals of a regular pentagon dissect it into eleven pieces and draw a pentagram; the dodecahedron dissected by the twelve face planes of its inner core gives Kramer's seven "elementary cells" of 1982. We define the stellation dissection of a golden regular polytope in any dimension as the dissection of the convex hull of its final regular stellation by the facet hyperplanes of the core, show that the core has phi^(-d) of the inradius of the hull for d = 2, 3, 4, and carry the dissection out for the first time on the 120-cell. The foundation is the arithmetic of the golden ring Z[phi], the ring of integers of Q(sqrt 5): vertices and hyperplanes live in Z[phi]^d, every orientation test is the exact sign of an element of Z[phi], decided with integers, and the pieces are named by sign vectors. We develop this foundation from scratch (conjugation, norm, units, the primes sqrt 5, 2, 3, the exact sign test, the lattice x -> (x, conj x), the vertex modules of the dodecahedron and the 120-cell, the icosian ring) and let it carry the geometry. The definition bifurcates in dimension four: the star cut at depth phi^(-4), a unit, has 2,455,201 cells in 338 orbits of H4; the hereditary cut at depth 1 - phi^(-4) = sqrt 5 / phi^2, a unit times the ramified prime, induces the three-dimensional dissection on every facet and has 8,161 cells in 8 orbits. New here: all vertices of the dodecahedral and of the hereditary dissection lie in the vertex module of the polytope being cut, whereas the star cut needs the denominators 2, 3 and 5; the seven kinds of pieces of the dodecahedron are exactly the I_h-orbits of sign vectors, with stellation layer equal to the number of plus signs. We catalogue the four-dimensional pieces and treat the circumscribed disc, ball and 4-ball. Every number quoted is recomputed exactly by a script whose output is reproduced in an appendix.
Given an arrangement of $\{1,\dots,n^2\}$ in an $n\times n$ grid, we lift each cell to $\mathbb{R}^3$ by centring its grid coordinates $(x,y)$ at the origin and taking its centred entry $z = s_{ij} - (n^2+1)/2$ as a vertical height. The convex hull of these $n^2$ points is the gem of the arrangement, whose lower and upper boundaries are the regular subdivisions of the grid induced by $\pm z$. While random arrangements and generic linear magic squares have gems whose vertex counts grow with $n$, our main theorem shows that the classical Siamese (de la Loubère) magic square of every odd order $n\ge5$ has $f$-vector $(12,26,16)$, isometry group $\{\pm\mathrm{id}\}$, and only the twelve vertices forced by the boundary of the grid. The proof shears the lift onto five horizontal terraces and reduces the hull calculation to a finite table of polynomials in $m=(n-1)/2$; the same method gives $f$-vector $(12,24,14)$ for the base-$n$ digit-exchanged square. Along any family of linear squares with fixed steps the $f$-vector is eventually periodic in $n$, whereas over all linear magic squares of prime order $n$ the maximum vertex count grows as $Θ(\ln n)$. Whenever the heights have vanishing first moments, a short principal-axes argument shows that the point set has a non-trivial isometry if and only if the arrangement is self-complementary up to dihedral symmetry. An exact census of the $880$ magic squares of order four yields $616$ congruence classes and $352$ combinatorial types of gems, and shows that while vertex and facet counts are nearly insensitive to the magic line-sum conditions, the volume and solid centroid shift systematically.
Underdamped Langevin dynamics (ULD) is a widely-used sampler for Gibbs distributions $π\propto e^{-V}$, and is often empirically effective in high dimensions. However, existing non-asymptotic convergence guarantees for discretized ULD typically scale polynomially with the ambient dimension $d$, leading to vacuous bounds when $d$ is large. The main known dimension-free result concerns the randomized midpoint discretization in Wasserstein-2 distance (Liu et al.,2023), while dimension-independent guarantees for ULD discretizations in KL divergence have remained open. We close this gap by proving the first dimension-free KL divergence bounds for discretized ULD. Our analysis refines the KL local error framework (Altschuler et al., 2025) to a dimension-free setting and yields bounds that depend on $\mathrm{tr}(\mathbf{H})$, where $\mathbf{H}$ upper bounds the Hessian of $V$, rather than on $d$. As a consequence, we obtain improved iteration complexity for underdamped Langevin Monte Carlo relative to overdamped Langevin methods in regimes where $\mathrm{tr}(\mathbf{H})\ll d$.
Language models increasingly create 3D content through code, with practical workflows often relying on editing existing programs rather than regenerating them, for speed and precise control. Such edits require understanding what a program builds and foreseeing how a change reshapes it, yet prior benchmarks mostly evaluate generation or simple edits against a reference. In this paper, we introduce 3DCodeEdit, a benchmark of 2,592 instruction-guided editing tasks over 108 Blender programs that construct objects entirely in code. Its edits range from parameter to structural changes, style redesign, and scene composition, and are judged from renders against human-reviewed checklists. Across 17 models, the average success rate is only 37%, and even the strongest models complete fewer than 60% of structural and style edits. As models become more capable, their failures shift to geometric foresight, where the code runs but builds the wrong shape. We therefore study whether multi-turn feedback can compensate for this missing foresight. Feedback from a separate reviewer model that describes how the renders differ from the request helps most, more than maximum reasoning effort or an agent harness, and can let a 27B model surpass the single-shot rate of a 2.8T-parameter model.
For each time $t$, the regression function $m_t(x)=E[Y_t\mid X_t=x]$ of an outcome on contemporaneous covariates can be regarded as a field on covariate space. When the covariates of units move as a diffusion and each unit's outcome has its own dynamics, we show that $m_t$ satisfies a second-order evolution equation whose diffusion term is $\frac12\mathrm{tr}(Σ\nabla^2 m_t)$, the Hessian of the regression function weighted by the covariance $Σ$ of covariate increments, whose transport term is the drift of the time-reversed covariate process, and whose source term is the conditional mean rate of change of the outcome; this yields a Feynman-Kac representation along reversed covariate paths. We relate this Hessian to quadratic regression (under Gaussian design the best quadratic approximation has Hessian $E[\nabla^2 m(X)]$) and to kernel smoothing bias. For bistable replicator dynamics on covariate space, travelling fronts are exactly logistic in $(x,t)$, so one logistic regression identifies the diffusion-reaction ratio and the invading strategy. We then ask whether spread in covariate space reflects fluctuating unit characteristics or imitation among similar units. Imitation acts through exactly the same operator as covariate fluctuation, so the two are observationally equivalent in the regression field; panel data separate them because they identify $Σ$ directly. The two cannot be separated on a travelling front, and we propose a split-sample instrumental-variables test that works on seeded, non-front profiles, with size and power evaluated in agent-based experiments.