In reinforcement learning, critics typically estimate absolute state values $V(s)$, estimating how good a particular situation is in isolation. However, it turns out that only differences in value are relevant for control. Motivated by this, we propose Relative Value Learning (RV), a framework that learns value differences directly via an antisymmetric function $Δ(s_i, s_j) = V(s_i) - V(s_j)$. We introduce a pairwise Bellman operator and prove it is a $γ$-contraction with a unique fixed point equal to the true value differences, derive well-posed $1$-step, $n$-step and $λ$-return targets and reconstruct generalized advantage estimation from pairwise differences to obtain an unbiased policy-gradient estimator (R-GAE). Beyond theoretical results, we integrate RV with PPO and achieve competitive performance on the Atari benchmark (49 ALE games) compared to standard PPO, indicating that relative value estimation is an effective alternative to absolute critics.


GlucoTune: A Unified Framework for Blood Glucose Preprocessing, Forecasting, and Benchmarking in Diabetes

Preprocessing blood glucose time-series data is a critical yet often overlooked step in developing data-driven methods for diabetes management, particularly for type 1 diabetes. The lack of standardized preprocessing workflows and evaluation protocols hinders reproducibility and complicates fair comparison across studies. These challenges are further exacerbated by data-sharing restrictions, as privacy and licensing constraints often prevent the redistribution of preprocessed medical datasets. To address these limitations, we present GlucoTune, a comprehensive and extensible framework for reproducible experimentation with blood glucose time-series data. The framework standardizes the entire experimental workflow, from preprocessing to model evaluation, enabling reproducible experiments directly from the original datasets. Reproducible preprocessing is achieved through configurable pipelines defined in portable YAML configuration files, ensuring consistent data handling without distributing sensitive preprocessed data. Beyond preprocessing, GlucoTune provides a unified interface for implementing, training, and evaluating blood glucose prediction models. The framework integrates public datasets through standardized wrappers and provides a curated collection of state-of-the-art blood glucose prediction and general time-series forecasting methods, while remaining readily extensible to additional datasets, preprocessing strategies, and forecasting models. To promote transparent and consistent evaluation, GlucoTune includes a benchmarking leaderboard that reports results across datasets, preprocessing configurations, and forecasting methods, enabling systematic comparison of experimental settings. We demonstrate the effectiveness of GlucoTune through comprehensive experiments and assess its usability in a user study.


TOUR: A Trajectory-Level Unlearning Benchmark for Offline Reinforcement Learning

Offline Reinforcement Learning (RL) agents are trained on fixed behavioral trajectories, which makes trajectory-level deletion important when selected data must be removed after training. Evaluating such deletion is difficult because a lower membership score can reflect trajectory removal, residual memorization visible to another attack, or policy collapse that destroys useful behavior. We introduce Trajectory-level memOrization and Unlearning in offline RL (TOUR), a benchmark that combines trajectory-level partitioning, matched non-member controls, retraining references, retained-performance anchors, and multi-attack privacy auditing. Across D4RL locomotion experiments and an exploratory AntMaze extension, TOUR shows that common deletion baselines have environment-dependent privacy-utility behavior. Retraining and fine-tuning often provide stronger retained-utility references than uniform GA+Refit, while TrajDeleter remains a useful comparator but is not uniformly stronger under the same audit. Reference-model, threshold, deviation, equivalence, action-error, representation-based, and query-limited attacks further show that a single likelihood-based membership score can overstate deletion quality. In the evaluated settings, conclusions about offline RL unlearning are therefore not stable under single-score auditing. They depend on matched non-member construction, retraining-relative calibration, attack family, retained utility, and explicit scope for diagnostic architecture or component-level evidence.


Smooth Neural Point Processes via B-Splines

Temporal point processes (TPPs) provide a general and flexible framework for modeling sequences of events in continuous time. Neural networks have been successfully employed to model TPPs in a highly expressive and data-driven way. Neural TPPs are typically trained via Maximum Likelihood Estimation (MLE) by minimizing the negative log-likelihood (NLL), which depends on both the conditional intensity function (CIF) and its integral over time, the compensator. Recent neural TPP approaches enable exact evaluation of the NLL without numerical integration. However, these methods typically model the compensator rather than the CIF directly, impose constraints on the neural network architecture, and are computationally expensive during training, as event contributions to the NLL are evaluated sequentially rather than in parallel. In this work, we propose a novel neural TPP model that directly parametrizes the CIF as a non-negative combination of B-spline basis functions, whose coefficients are predicted by a neural network. This formulation enables exact evaluation of the NLL, preserves full flexibility in the neural architecture, allows efficient parallelization during training, and naturally supports CIF smoothness regularization through the integrated squared second derivative. Experiments on both synthetic and real-world datasets show improved computational efficiency and predictive accuracy compared to the reference neural TPP baseline.


A Polynomial Architecture-Attribution Co-Design Framework for Exact Aumann-Shapley Attribution in GNNs

We study feature-level and node-level explanations for graph neural networks (GNNs) through the lens of Aumann-Shapley attribution. Path-integral methods such as Integrated Gradients provide an axiomatic formulation of attribution, but their practical use in deep GNNs typically relies on finite-sample numerical approximations to the path integral, requiring a trade-off between quadrature error and computational cost. This paper proposes APEX, a model-attribution co-design framework that makes the attribution integral exactly computable under a polynomial GNN architecture. The key component is PolyGIN, a GIN-style graph network whose message-passing, normalization, and transformation operations preserve a bounded multivariate polynomial form for scalar model scores, such as pre-softmax logits. We show that, for a PolyGIN with $L$ polynomial transformation blocks, the derivative along the attribution path has degree at most $2^L-1$. Therefore, Gauss--Legendre quadrature can evaluate the Aumann--Shapley path integral exactly, up to floating-point precision, with $2^{L-1}$ deterministic evaluation points. The resulting attributions can be computed at the feature level and then aggregated into node-level scores while preserving completeness. Experiments on synthetic and real-world graph benchmarks show that PolyGIN maintains competitive predictive performance, while the complete APEX framework achieves higher attribution fidelity than the compared baselines and substantially reduces the number of evaluations required for path integration.


Training Large Language Models for Self-Explanation Faithfulness

We propose a Reinforcement Learning (RL) method to directly optimize the faithfulness of self-explanations - the extent to which a model's generated reasoning accurately reflects its internal decision-making process. While existing work focuses on evaluating faithfulness or using inference-time prompting frameworks to improve an LLM's self-explanation's tractability, these approaches do not provide a mechanism to directly optimize a model's parameters to generate faithful self-explanations. We bridge this gap by modifying existing faithfulness metrics into an RL training objective. We investigate (1) if models can be trained to accurately detect factors that affect their decisions, and (2) whether RL can directly optimize for the disclosure of these factors thereby improving LLM self-explanations' faithfulness. We experiment with two intervention types: random-word insertions and user-bias insertions, using a per-sample reward derived from the Phi-CCT correlation metric. RL fine-tuned Llama3.1-8B and Qwen3-8B show substantial improvements on the Phi-CCT faithfulness metric, with in-distribution scores rising from near-zero to as high as 0.664, and out-of-distribution scores reaching up to 0.691 on held-out tasks such as StrategyQA. Cross-intervention generalization is weaker but more interesting: a priori we would not expect a model trained only on random word insertions to generalize to user-bias phrases, yet Llama3.1-8B shows non-zero transfer in this direction. The reverse direction and Qwen3-8B do not replicate this, indicating model-dependent and setup-dependent effects we cannot yet explain. Lastly we analyze model behavior to rule out reward gaming behaviors that often plague RL training. Ultimately, we show that models can be trained to implicitly identify influential factors and disclose them, offering a scalable path toward reducing unfaithful reasoning in LLMs.


CASC: Causal Adversarial Subspace Clustering for Multivariate Spatiotemporal Data

Deep subspace clustering plays a critical role in applications involving multivariate spatiotemporal data, such as sea ice monitoring, disease spread analysis, and tracking neuro-degeneration over time. Despite recent advances, existing methods primarily rely on geometric self-expressiveness, assume static subspace structures, and often fail to capture causal dependencies, local spatial interactions, and long-range temporal dynamics inherent in complex spatiotemporal systems. To address these limitations, we propose a novel Causal Adversarial Subspace Clustering (CASC) framework for discovering evolving latent regimes in high-dimensional spatiotemporal data. CASC integrates a U-Net-inspired deep adversarial clustering architecture with stacked FAConvLSTM layers to preserve spatial and temporal structure while learning robust latent representations. A graph attention transformer-based self-expressive network is introduced to jointly model local spatial relationships, global dependencies, and long-range temporal interactions. Furthermore, we propose two new learning objectives: (1) a Causal Subspace Preservation Loss that aligns self-expression coefficients with latent causal relationships, encouraging clusters to reflect underlying causal processes rather than simple feature similarity, and (2) a Dynamic Temporal Subspace Evolution Loss that captures evolving subspace structures and temporal regime transitions in nonstationary environments. Together, these components transform deep subspace clustering from a correlation-driven paradigm into a causal-temporal regime discovery framework.


Automatic knot selection in smooth additive models

B-spline regression constitutes a widely used framework for nonparametric modeling. The performance of this methodology depends on specifying the number and placement of changepoints, known as knots, prior to the estimation process. Such knot sequence determines the dimension of the B-spline basis used to represent the regression function and the number of coefficients to be estimated. Therefore, the knots' choice affects the model's flexibility, influencing its smoothness and goodness-of-fit. Traditionally, this problem has been addressed either by explicitly selecting knots, via knot-selection algorithms, or by regularization methods, such as P-splines, which automatically tune the regressor's smoothness. The latter have become the standard in generalized additive models (GAMs). In contrast, knot-selection techniques, frequently neglected because of computational or modeling limitations, provide certain advantages which can be valuable in some contexts. In this work, we introduce a novel explicit knot-selection technique for GAMs based on an extension of the adaptive splines (A-splines) knot selection methodology, combined with a customized Fellner-Schall scheme for tuning the associated parameters. Our approach is evaluated on various synthetic and real datasets and compared with P-splines and state-of-the-art knot-selection techniques. The results indicate comparable performance, while producing models built on a substantially smaller number of basis elements.


Nipping the Butterfly Effect in the Bud: Self-Output Fine-Tuning for Autoregressive Weather Prediction

Long-horizon weather forecasting is a fundamental challenge in atmospheric science, for which autoregressive Deep Learning Weather Prediction (DLWP) has emerged as the primary paradigm. Although the autoregressive pipeline is highly scalable and flexible, its prediction errors grow rapidly over long forecasting horizons. In this work, we study this error growth phenomenon from both theoretical and empirical perspectives. Our analysis reveals that the growth is driven by a feedback loop between output errors and input distribution shifts. Specifically, the autoregressive process amplifies small initial output errors, which progressively corrupt subsequent input distributions, echoing the butterfly effect in atmospheric science and ultimately deteriorating forecasting accuracy over longer horizons. Furthermore, we show that this distributional shift originates at the earliest stage of inference, with out-of-distribution signatures detectable as early as the first autoregressive step. To mitigate this issue, we propose \textbf{Self-Output Fine-Tuning (SOFT)}, a plug-and-play strategy that leverages the model's own one-step predictions to calibrate the biased input distribution encountered at the first step. Extensive experiments demonstrate that, despite its simplicity, SOFT achieves state-of-the-art performance on long-horizon forecasting tasks and substantially reduces both prediction errors and distributional discrepancy. The success of SOFT highlights the importance of reexamining the fundamental pipeline of deep learning weather prediction, representing a critical pipeline advance for atmospheric science.


Spectral Transformation for Layer-wise Global Rank Discovery in Federated LoRA for Vision Transformers

Fine-tuning Vision Transformers (ViTs) with low-rank adapters (LoRA) promises better communication efficiency under federated setup, yet existing aggregation strategies face fundamental limitations. Independently averaging these LoRA factors is mathematically inconsistent, introducing cross-term aggregation error. In contrast, approaches that preserve heterogeneous client ranks by concatenating local adapters on the server substantially increase download cost and often require merging global LoRA updates into pretrained weights on the clients, causing reinitialization lag and unstable convergence. Other approaches further increase server-side overhead by reconstructing dense weight updates or training auxiliary models to refine aggregation error. In this work, we propose SpecTraL, spectral transformation for layer-wise global rank discovery, that resolves these challenges within a unified design. SpecTraL stacks local LoRA modules from clients and performs orthonormal Householder Transformation of the stacked adapters directly in the low-rank latent space, eliminating dense reconstruction of the global update and any auxiliary refinement on the server. By leveraging the Spiked Covariance Model from Random Matrix Theory, SpecTraL analytically separates the global consensus signal from non-IID noise, discovering optimal layer-wise global ranks without manual hyperparameter tuning. To match local ranks in subsequent rounds, we introduce a padding-aware initialization framework that lets clients incorporate residual LoRA dimensions without re-merging them into the pre-trained base model. Experiments on federated fine-tuning of ViT-B/16 and ViT-L/16 over DomainNet and NICO++ demonstrate improved accuracy-communication trade-offs, reduced server computation, and elimination of hyperparameter search for rank selection. Our code is available at https://github.com/DASS-Lab-Group/SpecTraL


From Evaluation to Optimisation: Hierarchy-Aware Training Signals for CWE Prediction in Python

The original ALPHA benchmark introduced a taxonomy-aware penalty for evaluating CWE-level vulnerability prediction in Python and proposed that the penalty could theoretically also serve as a training signal. This paper provides that validation. We compare three delivery mechanisms: supervised fine-tuning, a dual-head classification loss, and reinforcement learning with a dense reward derived from the normalised penalty. We find that supervised approaches consistently regress below the zero-shot baseline under distribution shift, while GRPO succeeds. Our best policy reduces the cumulative ALPHA penalty of Qwen2.5-Coder-7B on Security Hardening and Adversarial Testing (SVEN) dataset by 27.9% under greedy decoding, and by 25.5% under sampled decoding(p = 0.005, Welch's t-test), reaching statistical parity with its 4.5x larger zero-shot teacher. We conclude that the value of a hierarchical penalty as a training signal depends largely on the directness of its delivery.


Counterfactual Explainability Framework With CycleGAN And Counterfactual-Classifier Alignnment Score for Retinal Disease Classification

Automated detection of vision impairing retina-based ocular conditions from fundus images is important for early screening, timely referral and reducing dependency on specialist-only assessment, for which neural network-based deep learning (DL) models have been widely utilized. However, explainability of the DL frameworks remains a major bottleneck for clinical adoption, particularly when model decisions are not linked to retinal regions that are clinically meaningful. To address this issue, this study presents CounterFundus, a novel CycleGAN-driven counterfactual explainability framework, integrating EfficientNet-B5-based retinal disease detection with visually interpretable disease-to-normal fundus image translation. For each pathological image, the counterfactual yielded by the CycleGAN generator represents an estimated healthy counterpart and the resultant difference map is utilized to localize disease-associated retinal changes. Unlike conventional post-hoc saliency methods, CounterFundus provides counterfactual explanations through visually plausible disease-to-normal retinal translation. Thereafter, to quantify the spatial agreement between counterfactual difference maps and classifier saliency, the Counterfactual-Classifier Alignment Score (CCAS) is introduced, embedding Spearman correlation, binary IoU and pointing accuracy into a single assessment protocol. To this end, EigenCAM-aligned evaluation demonstrates that the generated counterfactual explanations remain spatially consistent with classifier-relevant retinal evidence across all CCAS dimensions. Along with that, ablation studies further confirm that CCAS-filtered counterfactual augmentation improves the downstream classification performance in fundus images, establishing CounterFundus as a clinically-grounded, explainable artificially intelligence (XAI) framework for retinal disease detection.


Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications

Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning. Their performance, however, critically depends on the accurate estimation of the underlying spectral subspace and can deteriorate substantially in the presence of noise, outliers, or model perturbations. To address this limitation, we propose a Regularized Projection Matrix Approximation (RPMA) framework for robust estimation of rank-$K$ projection matrices. RPMA extends classical spectral projection by incorporating a regularization term, producing projection estimates that are more robust, sparse, and interpretable. We formulate the proposed model as an optimization problem on the manifold of rank-$K$ projection matrices and exploit its geometric equivalence to the Grassmann manifold. Based on this manifold characterization, we derive the first- and second-order optimality conditions, establish the local stability of the regularized leading eigenspace, and characterize the stability of the critical-point landscape under sufficiently small regularization. To efficiently solve the resulting nonconvex optimization problem, we develop a Riemannian gradient projection algorithm with backtracking line search, together with a more efficient Cayley--Sherman--Morrison--Woodbury (Cayley--SMW) gradient method that avoids repeated eigendecompositions. Extensive experiments on both synthetic and real-world datasets demonstrate that RPMA substantially improves the recovery accuracy of projection matrices and consistently outperforms conventional spectral projection methods for community detection and clustering under noisy environments.


Weight-norm Criticality: A Mechanism for Loss Spikes Induced by the Normalization and Weight Decay

Most explanations of training instability focus on \emph{learning-rate criticality}, typically characterized by the Edge of Stability, beyond which optimization becomes unstable. We argue that, in practical deep neural network training, there is an additional and often overlooked \emph{weight-norm criticality}. This criticality is induced by the interaction between normalization (which introduces scale-invariant components) and weight decay (which persistently shrinks parameter norms). As the weight decay coefficient increases, the norms of scale-invariant weights are progressively driven toward zero. Meanwhile, the sharpness of the loss landscape increases rapidly, destabilizing the optimization dynamics and resulting in abrupt loss spikes. This perspective provides a rationale for why weight penalties can improve generalization yet cannot be made arbitrarily strong: excessive decay drives scale-invariant weight norms past a critical boundary and destabilizes training. Our work provides a new mechanistic understanding of loss spikes through the lens of \emph{weight-norm criticality}. Moreover, \emph{weight-norm criticality} yields testable predictions that we validate empirically in networks with scale-invariant components, providing empirical support for the proposed mechanism.


ADABORD: a novel AdaBoost approach for ordinal classification

Ordinal Classification (OC) deals with classification tasks where the classes follow a natural order. Despite the progress in OC, many existing approaches fail to fully leverage the ordinal information, treating the problem as nominal classification and thereby losing performance potential. In this work, ADABORD, an AdaBoost framework specifically designed for ordinal classification problems, is introduced. The ordinal nature of the classes is incorporated into two key components of the well-known AdaBoost algorithm: 1) the base estimator, where decision trees with the ordinal Gini splitting criterion are proposed; 2) the error function used to update sample weights at each stage and the weights of the classifier in the final ensemble model, given by the absolute ranked probability score, a measure that accounts for both the ordering and the distance between classes. ADABORD is extensively compared against seven state-of-the-art methods on the TOC-UCO repository, the largest benchmark collection for OC to date. The experimental results, supported by statistical analysis, show that ADABORD significantly outperforms competing methods, particularly on datasets with five or more classes, where the ordinal structure becomes more pronounced. Source code, along with all experimental protocols, is publicly available to ensure reproducibility and facilitate future research in OC.


The Weight of Silence: A Causal Case for Weights Over the Scratchpad in Latent Chess Reasoning

Latent, or silent, reasoning lets language models carry out intermediate computation in continuous vector space instead of words, and is widely assumed to function as an internal scratchpad the model actively consults during inference. Whether that assumption survives reinforcement learning has not been tested directly: existing causal analyses of latent reasoning are confined to math and logic tasks, and compare a model's reliance on its thoughts within a single checkpoint, never before and after an RL stage. We train a chess-playing model through a staged latent-reasoning curriculum followed by reinforcement learning, and find legality climbs monotonically to 61% (from a 48% pre-RL baseline) while checkmate confabulation is eliminated entirely. To locate this gain, we run a six-condition causal intervention suite on the same model before and after RL: substituting or adding matched noise to the latent thought vectors leaves performance unchanged, ablating them causes only mild degradation, and only exact-zero vectors cause collapse. This robustness gap is itself the finding: under exact-zero corruption, legality collapses to 1% pre-RL versus 9% post-RL, a gap that survives correction for testing across the full battery; milder conditions trend similarly without independently reaching significance. RL appears to add robustness to disruption, not reliance on thought content. These results push back against the field's default assumption that latent thoughts function as an actively consulted inference-time scratchpad, and instead indicate latent reasoning's principal effect here is shaping the model's parameters during training. We also demonstrate a working RL gain in chess, a domain outside the math and logic settings where multiple groups report the same latent-reasoning-plus-RL recipe failing to improve accuracy over SFT.


Best-of-Evidence: Best-of-N Selection under Partial Verification

BoN improves model outputs by sampling several candidates and selecting one with a proxy score, but it assumes that complete candidates can be evaluated reliably. Many vision-language tasks instead provide only partial verification: a finding, span, value, region, or relation may be checkable even when no dependable whole-response verifier exists. Moreover, the same claim may recur across candidates with opposing stances, allowing one observation to support part of the pool and contradict another. We introduce Best-of-Evidence (BoE), an inference-time selection framework that keeps the BoN candidate pool fixed, represents reusable claims with a signed candidate--factor graph, and allocates a limited budget to evidence actions that can change the final choice. BoE formalizes selection under partial verification and provides a practical score-based controller, with the zero-budget case recovering the underlying BoN decision. Theoretically, we show that residual evidence capacity limits any evidence-driven improvement and that shared factor queries can achieve an O(log K) versus Θ(K) query separation in a factor-code model. Common-ledger experiments on four medical VQA settings show that BoE can improve fixed-pool selection and rescue some BoN failures when evidence is reliable, contrastive, and decision-relevant, while also revealing the channel-quality and candidate-generation limits that prevent universal gains.


An Analytically Trained Variational Surrogate for Quantum Phase Estimation on NISQ Hardware

Quantum Phase Estimation (QPE) is a foundational algorithm for molecular ground-state energy estimation, but its deep circuit requirements make direct hardware execution impractical on Noisy Intermediate-Scale Quantum (NISQ) devices. We present an analytically grounded variational surrogate framework in which a shallow Variational Quantum Circuit (VQC) is trained to reproduce the QPE measurement distribution without any quantum circuit simulation. The training target is computed entirely classically via the Dirichlet kernel, evaluated directly from the Full Configuration Interaction (FCI) ground-state energy, the ancilla qubit count, and the time evolution parameter, eliminating the exponentially scaling simulation bottleneck of prior surrogate approaches. We apply this framework to the hydrogen molecule (H$_2$) with a symmetry-tapered Hamiltonian, conducting a four-stage experimental investigation on IBM Quantum hardware. Stage 1 compares linear and full entangler topologies for the $R_Y$-$R_Z$-$CZ$ ansatz, with and without XpXm Dynamical Decoupling (DD), across four distributional metrics (Hellinger distance, fidelity error, total variation distance, Jensen-Shannon divergence), identifying the linear entangler as optimal. Stage 2 varies VQC layers ($p=1$ to $5$) for the linear-entangler ansatz, identifying single-layer depth as optimal under hardware noise. Stage 3 applies this configuration to the reduced $R_Y$-$CZ$ ansatz, comparing ideal and noisy simulator-trained parameters. A supplementary noise analysis at $p \in \{8,64\}$ characterizes the depth-dependent interplay between circuit depth and DD effectiveness. The framework enables faithful QPE mimicry using a linearly scaling VQC, recovering the ground-state energy within the chemical accuracy threshold (1 kcal/mol), constituting a scalable, hardware-efficient paradigm for QPE-based molecular energy estimation on NISQ devices.


Three-Pronged Spectral Control for Federated Parameter Efficient Fine Tuning

Federated parameter-efficient fine-tuning (PEFT) enables communication-efficient adaptation of large pretrained models on decentralized edge data, but it remains fragile under non-IID client heterogeneity. In low-rank adaptation (LoRA), different clients may learn locally useful but spectrally misaligned update subspaces, causing high-variance aggregation and poor global transfer. We propose TRISHUL, a spectral-control framework for robust federated PEFT. TRISHUL follows the FL no-raw-data-sharing setting but does not itself provide formal privacy guarantees. TRISHUL uses shared frozen multi-head low-rank bases to obtain algebraically exact aggregation of compact core updates, applies nuclear norm proximal shrinkage to suppress client-specific high-rank spectral components before upload, and allocates adaptation heads non-uniformly across layers using a concave water filling budget rule derived from pretrained layer capacity. Because shrinkage is performed only on small core matrices, TRISHUL adds negligible computation and no extra per-round communication over the underlying multi-head PEFT protocol. Across vision and language benchmarks, including CIFAR-100, SVHN, 20 Newsgroups, MRQA, and GLUE with LLaMA3.2-1B, TRISHUL improves convergence, stability, and final performance over federated LoRA baselines, with greater gains under stronger heterogeneity.


RadioTrace: Transmitter-Aware Diffusion for Radio Map Estimation without Deployment-Time Fine-Tuning

Radio map (RM) estimation aims to reconstruct the spatial distribution of wireless signal characteristics, such as received signal strength (RSS), from sparse measurements, a task that is critical for spectrum management, interference mitigation, and localization in modern wireless networks. Traditional approaches, including interpolation and deep learning, either struggle to capture complex propagation effects or require large-scale retraining for each new sampling pattern, which limits their generalization. More recently, prior-based methods have combined pre-trained generative models with measurements to reduce the need for deployment-time model fine-tuning, but they typically treat the prior as a simple regularizer and lack explicit transmitter-aware integration. In this paper, we propose RadioTrace, a novel RM estimation framework without deployment-time fine-tuning that tightly integrates sparse RSS measurements with a frozen pre-trained diffusion prior. RadioTrace incorporates transmitter (Tx) location estimation directly into the denoising loop, iteratively refining Tx coordinates based on reconstruction quality to guide the generative process. To further enhance robustness, we introduce a propagation-guided K-means initialization that mitigates poor local minima in the Tx update and provides a geometry-consistent starting point. Moreover, we provide a stochastic stability analysis for the Tx-coordinate refinement component, showing that the Tx update remains stable under perturbations induced by diffusion sampling and Tx-map relaxation. Extensive experiments demonstrate that RadioTrace achieves competitive performance with state-of-the-art learning-based methods under random sampling, and maintains strong reconstruction quality under restricted-area sampling, highlighting its adaptability, robustness, and practical relevance.


Multi-turn RL with Structural and Performance Aware Rewards for CUDA Kernel Generation

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful technique to enhance the reasoning capacity of LLMs for optimized code generation. However, existing RLVR approaches primarily rely on outcome-based signals such as correctness and speedup, overlooking performance-critical structural properties of programs that are essential for generating optimized code. In this work, we propose CudaPerf, a reflective RL framework that incorporates both verifiable execution rewards and structural code-aware rewards derived from parallelization features (e.g., memory coalescing, occupancy, Arithmatic Intensity, and synchronization patterns). CudaPerf operates in two stages: (1) an offline pairwise ranking module that learns to distinguish strong and weak program candidates via contrastive comparisons, and (2) an online RL training phase that jointly optimizes for correctness, performance, and structural efficiency through a unified reward signal. To further enhance learning, CudaPerf utilizes iterative refinement using execution feedback enabling progressive improvement of generated candidates. We also introduce a dataset comprising 2.9k C to CUDA and 1k PyTorch to CUDA programs, each paired with diverse input configurations and multiple CUDA implementations encompassing diverse optimization strategies. CudaPerf is evaluated across multiple benchmarks comprising both C to CUDA and PyTorch to CUDA transformations. Empirical findings suggest that CudaPerf significantly outperforms strong baselines, including Qwen-3-32B (for C to CUDA) and CUDA Agent (for PyTorch to CUDA) by achieving up to 5X & 3.32X improvements in speedup, and 17% & 7% improvements in correctness, respectively.


HierarchicalDAEW: Domain-Aware Edge-Weighted Graph Convolution with Evidential Uncertainty for Multi-Section Spatial Gene Expression Prediction from H&E Histology

Spatial transcriptomics assays remain costly and technically demanding, restricting transcriptome-wide profiling to specialist settings and preventing routine clinical deployment. Predicting spatially resolved gene expression from H&E histology could close this gap, yet current methods largely ignore the underlying tissue architecture and rarely quantify how their predictions can be trusted. We introduce HierarchicalDAEW, a dual-graph architecture that addresses both gaps. On the spot graph, a Domain-Aware Edge-Weighted convolutional operator learns separate projections for inter-domain, intra-domain, and boundary edges derived from Leiden clustering, allowing the model to treat tissue heterogeneity as an explicit structural signal rather than an implicit one. A second gene-level graph then fuses protein-protein interaction priors from STRING-DB with tissue-specific co-expression through learned attention gating, propagating predictions from a landmark gene set to a broader gene panel. Reliability is handled through evidential uncertainty estimation, which produces far better calibrated confidence intervals than Monte Carlo dropout under identical conditions. Across six human Visium sections spanning breast, colorectal, prostate, and cerebellar tissue, and against thirteen published baselines, HierarchicalDAEW achieves the strongest correlation with ground-truth expression, with gains that hold up under multi-seed reproducibility checks and negative controls that rule out positional shortcuts. Ablations further confirm that both the domain-aware edge typing and the hierarchical depth are necessary to this improvement, and calibrated uncertainty estimates identify low-confidence predictions for pathologist review before clinical action.


Information-Theoretically Secure Aggregation for Lightweight Federated Learning: Resilient to Dropouts and Adversaries

On-device federated learning (FL) enables privacy-preserving and personalized model training on resource-constrained devices such as smartphones and IoT nodes. To reduce communication cost, sign-based methods (e.g., signSGD) transmit one-bit gradients. However, exposing gradient signs makes them vulnerable to inference attacks, while existing secure aggregation schemes are often incompatible with such methods or incur significant computational and communication overhead. We propose a lightweight and information-theoretically secure aggregation framework tailored for sign-based FL. The framework securely computes the majority vote (MV) polynomial through single-round secure multiplication, ensuring end-to-end information-theoretic security under the honest-majority assumption while revealing only the final aggregated sign to the server. To enhance efficiency and scalability, we introduce two key techniques. First, inverse-form exponent reduction halves the effective MV polynomial degree, reducing both communication and computation costs. Second, we propose single-round secure multiplication, achieving linear offline complexity and storage with only a single online communication. Together, these techniques reduce online communication by up to 99.5% and latency by up to 85.7% compared to conventional approaches. Also, by leveraging inherent MDS-code-based decoding, the framework achieves robustness against both dropouts and adversarial behaviors, yielding accuracy gains of up to 20.65% and 10.74%, respectively. Overall, the proposed framework establishes a practical foundation for large-scale, low-latency, and information-theoretically secure aggregation in sign-based FL.


TwistedMerge: Certified Higher-Order Diagnostics and Abstention for Model Merging

Model merging combines independently trained or fine-tuned models, but pairwise alignability does not imply globally consistent alignment. We formulate merging as a finite descent problem in which checkpoints are local objects, alignment maps are transitions, and cycle products are residuals. TwistedMerge is a conservative certification pipeline that separates fixed-chart averaging, synchronization-removable gauge inconsistency, a certified central obstruction on a specified comparison complex, and nonabelian holonomy. A residual is promoted to a cohomology class only after inverse-consistency, coefficient-identification, centrality, and closure tests; otherwise the method abstains and returns an ordinary or synchronized fallback. We prove a constant-edge no-go result, frozen-complex three-way and predeclared-family error-control theorems, and a refinement test for comparison-complex sensitivity. A planted neural alignment defect is removed by cycle-consistent synchronization, showing that a nonzero cycle score alone is not a higher obstruction. Controlled central systems recover the predicted non-coboundary and projective-rank behavior, while noisy estimates move from certification to abstention without false lifts on the tested controls. A trained low-rank-adapter audit shows that naive factor averaging depends on the chosen GLr representative, whereas global factor synchronization and dense-delta SVD are stable. On natural checkpoint collections, cycle residuals do not predict merge degradation and no natural central or period-index class is certified. The results position descent theory as a falsifiable certification and abstention framework.


Machine Learning for Charge State Characterization of Isolated Double Quantum Dots

Scaling semiconductor quantum dot arrays toward fault-tolerant quantum computing requires efficient tuneup of spin qubits, a process that depends on the analysis of charge stability maps (CSMs) and remains largely manual. While machine learning has been widely applied to CSM analysis in reservoir-coupled devices, automated tuning in the increasingly important isolated-mode regime has received limited attention. In isolated-mode CSMs, charge transitions appear as near-vertical lines, making them well suited to compact, task-specific models. We present two convolutional neural networks with fewer than one million parameters, trained on CSMs collected from 32 silicon metal-oxide-semiconductor (SiMOS) double-quantum-dot devices measured at approximately 1 K using an automated cryogenic probing system. Sixteen devices were used for training and sixteen were held out to evaluate cross-device generalization against hand-labeled ground truth. CSMClassifier identifies charge instability and sensor artifacts, achieving 94% macro-averaged accuracy across three quality classes on 2,407 held-out images. ChargeLineNet localizes charge-transition lines and determines electron occupancy, achieving 95.3% exact line-count accuracy on 1,131 held-out images. Combined into a single pipeline, the models correctly determine electron occupancy for 93.8% of clean held-out images. Pre-training on synthetic images substantially improves label efficiency. Fine-tuning the pre-trained model on limited experimental data maintains over 90% accuracy, whereas training from scratch degrades significantly under the same conditions. Together, the two models occupy only 6.5 MB and process images in less than 60 ms on standard laboratory hardware, demonstrating a practical path toward scalable, automated characterization and tuneup of quantum-dot devices.


Position Bias is Hidden Behind Ceiling Effects: A Permutation Diagnostic for LLM Benchmarks

Position bias in multiple-choice LLM evaluation is widely cited as a confound in capability comparisons, but published measurements rely on single answer-order shuffles whose results confound the bias signal with content-level noise and sampling stochasticity. I introduce inspect_permute, an open-source extension to the inspect_ai evaluation framework that runs exhaustive answer-order permutations per question and reports the chi-squared / Cramer V signature of position bias with bootstrap confidence intervals. I apply the tool across four vendors (gpt-4o-mini, claude-haiku-4-5, gemini-2.5-flash, grok-3) on five MMLU subjects, 24,000 API calls under temperature-0 generation, with falsifier predictions pre-registered via a public SHA-256 hash before half the data was observed. Position bias turns out to be statistically detectable only within a roughly 60-95% base-accuracy Goldilocks zone. Below it, processing-load dominance swamps subject-specific signal; above it, ceiling effects compress the variance below the chi-squared test resolution. Detectable cells separate into two mechanism types: monotone A-to-D decrease (processing_load, in low-tier models) and non-monotone D-drop (content_ambiguity, in a narrow capability band). Standard MMLU places every frontier-tier model above the detection band, so absence of signal there should be read as not measurable, not unbiased. Together with the ceiling-effect characterisation in arXiv:2606.26185, this work brackets the detectable region of position-bias measurement and makes the field central question askable in a verifiable form. Package, data, preregistration under MIT.


Probabilistic Residual Learning for Online Recommendations

Modern recommender systems are typically based on deep learning (DL) models, where a dense encoder learns representations of users and items. As a result, these systems often suffer from the black-box nature and computational complexity of the underlying models, making it difficult to systematically enhance their recommendation capabilities. To address this problem, we propose Probabilistic Residual Learning (PRL), a causal Bayesian recommendation model that models the residual between ground-truth and base predictions, enabling targeted refinement of existing systems. Specifically, PRL (1) probabilistically groups users for localized residual modeling, (2) models domain-level confounders that influence user and item representations, and (3) aggregates cluster-specific residual predictions over the confounders using do-calculus. Experiments demonstrate that our plug-and-play PRL is compatible with various base deep learning recommender systems, improving their performance while automatically discovering meaningful user clusters.


Multilevel Graph Wavelet Compressed Sensing with Scale-Aware Neural Recovery

Scientific machine learning methods such as neural operators and physics-informed neural networks have advanced engineering applications and inverse problems, but their training typically requires large volumes of simulated data. This makes data preparation and model training expensive. We propose Graph Wavelet Compressed Sensing (GWCS), a learning-based framework for offline compression of graph signals by representing them as sparse, interpretable wavelet-domain representations using the spectral graph wavelet transform. The framework combines a nonparametric multilevel importance sampler, which retains high-energy wavelet coefficients within each scale for a given compression ratio, with a scale-aware graph neural network that reconstructs the signal from the sparse coefficients. We evaluate the proposed framework on synthetic approximately band-limited graph signals over random graphs and four PDE simulation datasets over meshes, which include Turbulent Radiative Layer, Viscoelastic Instability, Kolmogorov Flow, and Dynamic Stall. We compare against graph signal sampling methods and graph autoencoder baselines. Results demonstrate that the framework achieves high reconstruction fidelity and substantial data compression compared to existing benchmarks.


Offline RL with Hierarchical Action Chunking

Offline goal-conditioned reinforcement learning (RL) holds the promise of learning general-purpose policies from static datasets. However, scaling these methods to long-horizon tasks remains a challenge due to the curse of horizon, where value estimation errors can compound through long chains of bootstrapped Bellman backups. Existing hierarchical approaches mitigate this by decomposing tasks into subgoals, yet they often rely on low-level controllers that suffer from myopic execution and biased value estimates. In this work, we propose Hierarchical Implicit Q-Chunking (HiQC), an offline goal-conditioned RL algorithm that combines high-level latent planning with low-level action chunking. By conditioning the low-level critic on temporally extended action sequences, HiQC enables unbiased k-step value backups, compressing the horizon at both the planning and execution levels. We theoretically demonstrate that this dual decomposition results in a tighter bound on value error under a bounded per-backup error model compared to standard hierarchy or flat chunking alone. Empirically, HiQC achieves the highest aggregate performance among the compared methods on the OGBench suite, with its largest gains on long-horizon navigation tasks such as humanoid-giant.


Beyond Heavy Log Curation: Perplexity-Based APT Detection via Unsupervised, Context-Augmented Language Models

Advanced Persistent Threats (APTs) remain difficult to detect because only a small fraction of events in large-scale logs are attack-related, and investigation is expensive and hard to scale. Prior machine-learning approaches can reduce analyst workload, but they often rely on heavily curated training data and sophisticated preprocessing pipelines. Building and maintaining such pipelines require substantial domain expertise and engineering cost. Motivated by insights from a study of a strong APT detection baseline, we propose CAPTAIN (Context-Augmented Perplexity-based Threat Activity log detectIoN), a perplexity-based detector that leverages general, pre-trained language models with minimal, domain-agnostic preprocessing, enabling robust scoring of long, minimally processed log entries. CAPTAIN encodes recent history with an encoder model and a Q-Former-style bridge, then injects the compact context tokens into the decoder input so that perplexity reflects temporal context. To improve stability, CAPTAIN additionally applies smoothing filters to the perplexity time series. Across APT-oriented benchmarks, CAPTAIN competes with strong existing baselines and remains robust under substantially less curated inputs, that reduces the development and operational cost of advanced log preprocessing.


Robust Asynchronous Q-Learning under Reward and State Corruption via Batching

Motivated by reinforcement learning in harsh environments, we consider the problem of learning an optimal policy subject to adversarially corrupted feedback. Specifically, at each time-step, an adversary can perturb both the reward and state observations of the learner following the Huber contamination model. To defend against such data corruption, we propose {\texttt{BR-Async-Q}}: a novel, epoch-based, robust \(Q\)-learning algorithm built upon two key ideas: (i) partitioning the online data stream into batches to reduce variance, and (ii) constructing robust estimates of the Bellman optimality operator using such batched data. We prove a high-probability $\ell_\infty$ error bound for {\texttt{BR-Async-Q}} that matches that for vanilla \(Q\)-learning, up to a small additive term that scales with the fraction of corrupted samples. To our knowledge, this provides the first robustness guarantee for asynchronous \(Q\)-learning subject to both reward and state corruption. Furthermore, when only rewards are corrupted, the dependence of our algorithm's bound on the corruption fraction is minimax optimal.


New Complexity-Theoretic Frontiers of Tractability for Neural Network Training

In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions. Indeed, while there has been a number of very recent results that establish ever-tighter lower bounds for the problem under linear and ReLU activation functions, less progress has been made towards the identification of novel polynomial-time tractable network architectures. In this article we obtain novel algorithmic upper bounds for training linear- and ReLU-activated neural networks to optimality which push the boundaries of tractability for these problems beyond the previous state of the art. In particular, for ReLU networks we establish the polynomial-time tractability of all architectures where hidden neurons have an out-degree of $1$, improving upon the previous algorithm of Arora, Basu, Mianjy and Mukherjee. On the other hand, for networks with linear activation functions we identify the first non-trivial polynomial-time solvable class of networks by obtaining an algorithm that can optimally train network architectures satisfying a novel data throughput condition.


The Geometry of Personality: Activation Steering with Jungian Cognitive Functions

Activation steering enables control and interpretation of LLMs, yet existing work primarily models personality through static trait frameworks such as the Big Five. We investigate whether personality can instead be represented and controlled as a set of cognitive processes using the eight Jungian Cognitive Functions. To this end, we introduce a framework comprising a Jungian evaluation protocol and a dataset of over 2,100 role-playing character narrations.   Activation steering vector extraction and evaluation experiments on Llama-3.1-8B demonstrate effective monotonic control over all eight cognitive functions through activation steering. Beyond controllability, our analysis reveals that: 1. personality information is concentrated in middle transformer layers; 2. steering vectors exhibit structured geometric relationships consistent with distinctions between rational and irrational functions; 3. effective multi-dimensional steering directions cannot be recovered as linear combinations of single-function directions. These findings provide new insights into the representation of personality in LLM activation space and establish a framework for studying interpretable, effective, and multi-dimensional personality control.


External Clustering Validation by the Homogeneity-Parsimony Trade-off

Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to related proposals. Extending the information-theoretic framework beyond Shannon entropies, we furthermore derive set-matching and pair-based counterparts of the homogeneity and parsimony scores. These unify commonly used evaluation criteria and show that, in the pair-based setting, the homogeneity-parsimony trade-off recovers the receiver operating characteristic of binary classifiers. We demonstrate the framework's utility for feature selection and algorithm comparison, illustrating how considering scores jointly can clarify clustering operating points and identify Pareto-optimal solutions.


Memoir: Should a Model Write to Its Memory While It Thinks?

Memoir combines per-sample fast memory, shared slow parameters, variable-depth latent recurrence, and a future-latent energy objective. We test its riskiest coupling: each pondering iteration may rewrite the fast tier that the same iteration reads. On procedural associative recall with key interference, we compare a coupled arm against an otherwise identical read-only pondering arm. Both arms contain 81,738 parameters, including 76,362 trainable parameters, and use matched declared forward multiply-accumulate counts, data, optimizer, schedule, and seeds. After 240 training steps across 12 seeds, coupled recall is 0.5203 with a 95 percent interval of [0.4522, 0.5883], while read-only recall is 0.6557 with [0.5953, 0.7160]. The arms are paired per seed, and the read-only lead of 0.1354 gives a paired t of 3.23 on 11 degrees of freedom with a 95 percent interval of [0.0431, 0.2277] on the difference, winning on 10 of 12 seeds. After 960 steps across 8 seeds, both arms reach 1.0000, so the measured effect is a learning-speed penalty at a fixed budget, not a demonstrated capability penalty. That longer control is ceiling limited, leaving convergence on a non-saturating task unmeasured. A predicted failure in which memory rewriting corrupts the energy signal did not occur: the energy margin grew and held. Kernel restructuring also reduced delta-rule forward time from 0.907 ms to 0.351 ms on the stated device. Code and evidence are available at https://github.com/RightNow-AI/Memoir


Synthetic minority data is redundant or invalid: a data-dependent validity theory and a de-biased test

For two decades, the standard remedy for class-imbalanced learning has been to fabricate synthetic minority examples, and the standard evidence of their validity has been a check that cannot fail: synthetic points are scored against the very data that generated them. We de-bias the check. Validity becomes a population quantity -- the probability that a synthetic point truly belongs to the minority class -- with a consistent estimator that scores synthetic points against withheld real data. Where held-out ground truth is available, the classical test underestimates true invalidity in 96-99% of method-by-imbalance-ratio cells, while the de-biased estimator tracks it closely. We prove validity is a property of the data, not the method: class overlap sets an invalidity floor no faithful generator escapes, making oversampling redundant where classes separate and invalid where they overlap. Across 91 methods, three classifiers, and datasets spanning medicine and finance -- including a generator engineered to pass the classical check -- none clears both bars: gains over the best trivial baseline are noise-thin (median below 0.01 F1, a decision threshold's reach), and most damage calibration. We release the audit as a pip-installable test and flip the burden of proof: synthetic minority data must now demonstrate, on the data at hand, both validity and information gain.


Toward Mechanistic Interpretability of an AI Foundation Model Fine-Tuned for Atmospheric Chemistry

Weather forecasting foundation models (FMs) are increasingly fine-tuned to predict air quality, offering fast global pollution forecasts at lower computational cost than conventional chemical transport models. These FMs are typically trained on reanalysis data and generate forecasts through autoregressive rollout. They do not explicitly represent governing physical or chemical processes. Therefore, high forecast skill does not reveal whether a model has learned physical mechanisms or exploits statistical regularities in its training data. Here, we present the first study of what a FM fine-tuned for atmospheric chemistry has learned by examining Microsoft's Aurora model. We impose controlled chemical perturbations on its forecasts and test them against known photochemical relationships. We then examine the internal representations that generate these forecasts. We find that Aurora captures a first-order ozone response to reactive nitrogen but does not enforce the chemical constraints that a process-based model encodes. It generates chemically inconsistent combinations of related species and relaxes localized emission features such as wildfire plumes toward background. Internally, its representations remain largely organized around the meteorology inherited during pretraining, with little structure specific to chemistry. Using sparse autoencoders, we identify internal components that causally control the chemical forecast but do not map cleanly onto individual atmospheric processes. This work provides a framework for testing whether AI forecasting systems learn atmospheric chemistry from reanalysis data. As these models are increasingly positioned to inform environmental policy decisions, we argue that composition forecasts should also be judged by their internal mechanisms rather than by benchmark skill alone.


Emergent Compositional Skills in Mixture-of-Experts VLAs

We consider the problem of learning compositional robot policies end-to-end from expert demonstrations, without any pre-specified notion of task decomposition or hierarchy. We ask whether a VLA trained with a simplified Mixture-of-Experts (MoE) action head can emergently learn to decompose tasks into reusable, interpretable primitives. We find that learned experts are heavily reused across tasks and consistently correspond to qualitatively distinct low-level behaviors, suggesting that the router implicitly learns to perform high-level sequencing while experts serve as compositional primitives. Our MoE matches the task performance of a monolithic baseline while demonstrating meaningful expert specialization, a step toward modular, interpretable robot policies that emerge from data alone.


Memory-Computation Tradeoffs in Semi Amortized Parametric Optimization

Learning-enabled decision systems often use offline data or computation to reduce online compute cost. Despite the empirical success of such approaches, there is limited general understanding of how much offline information is needed to achieve a desired accuracy under a fixed online computation budget. We study this question through the lens of amortized parametric optimization: an offline phase stores a finite memory of solved problem instances, and an online phase produces a solution to a new instance by retrieving a warm start and applying $K$ steps of projected gradient descent. We analyze this setup for smooth convex parametric optimization over a compact domain, using a nonparametric predictor built from the stored offline solutions. For $μ$-strongly convex objectives, we establish matching upper and lower bounds on the memory required to guarantee $\varepsilon$-accuracy under a fixed online iteration budget $K$. For convex objectives satisfying a $β$-growth condition ($β>2$), we obtain near-matching bounds and identify a phase transition in $K$ beyond which additional memory provides no benefit. We further provide a general proof framework that (i) explicitly quantifies the memory cost of acceleration---how much offline memory is required to achieve a prescribed speedup over the unaided online optimizer---and (ii) identifies two key quantities driving this cost: the convergence rate of the online optimizer and the Lipschitz sensitivity of the solution map to the problem parameter. Experiments on parameterized ridge regression confirm the predicted memory--computation--accuracy tradeoffs.


Are Diversity Metrics Measuring Diversity? A Capability-Controlled Audit of Majority-Vote Gain in LLM Ensembles

Majority voting over LLMs is widely assumed to benefit from diversity, and diversity measures are used to choose which models to combine. We ask whether five such measures track diversity or mainly re-express capability, auditing them as predictors of majority-vote gain over the best member across 31,900 subsets of 30 LLMs on MMLU-Pro (29 on TruthfulQA) under explicit capability controls. Three findings emerge. First, latent complementarity is ubiquitous: oracle gain is positive in 100% of subsets, yet simple voting beats the strongest member in only 9.98% of all canonical size-3 subsets (18.71% with held-out best selection); the pooled size-2-4 rate is 1.27%, partly reflecting deterministic even-size voting behavior. Second, a joint-correctness proxy (strict diversity) is nearly collinear with one minus mean accuracy (size-3 Spearman rho = +0.991 / +0.988); raw diversity-gain associations are strongly capability-entangled and, with one exception, unstable under control. Third, three linear contingency-table statistics are algebraically non-separable; after capability control, the empirically stable remainder is a modest residual pairwise co-failure association in which more shared error corresponds to lower gain. This direction is robust, but its magnitude is configuration-dependent. Joint rawspace linear regressions treating strict diversity, disagreement, and double-fault as independent predictors are rank-deficient by construction.


GaugeQuant: Online Learning of Quantization-Optimal Bases from LLM Symmetries

Transformers are known to have internal continuous symmetries that leave outputs invariant, while modifying quantization. GaugeQuant leverages this in-training by introducing a LogSumExp term to the loss that breaks the symmetries, thus selecting a basis that minimizes activation outliers. A stop-gradient operator ensures that only rotation matrices are updated, yielding the language modeling objective completely unaltered. Our requires no specific calibration data, no quantization simulation, and adds negligible training overhead. With the LLaMA-2 7B model under W4A4 quantization with group size 128, perplexity drops from 8.22 to 6.73, competing with post-training methods that require frozen models and calibration datasets. Under W4A16, perplexity drops from 11.16 to 5.45. Code is available at https://github.com/MPedraBento/gauge-quant.


Self-Supervised Bio-Inspired Robotic Trajectory Planning with Obstacle Avoidance

Trajectory planning is a fundamental problem in robotics, requiring the generation of collision-free and efficient trajectories in a potentially complex environment. While sampling-based planners remain the dominant approach, they are often computationally expensive, particularly in high-dimensional spaces and obstacle-rich environments. Methods based on model learning offer a promising alternative, enabling efficient planning through a bounded number of forward passes through a neural trajectory planner, but commonly suffer from low sample efficiency or limited generalisation due to their reliance on exploration or expert demonstrations. This follow-up work tests our neuro-inspired self-supervised learning framework for trajectory planning that leverages forward and inverse models as the internal supervisory mechanism in an environment that contains an obstacle. Experimental results demonstrate the feasibility of the approach while revealing a tendency of our planner to exploit the learning signal provided by the forward and inverse models. To address this issue, additional training regimes and mitigation strategies are proposed and evaluated.


Adaptive Confidence-weighted Expansion for Trustworthy Multi-Omics Multimodal Fusion

Multimodal learning is a robust approach to improve predictive performance in applications such as medical prognosis. However, the clinical applicability of models that use multimodal learning is hampered by their poor performance under noisy or uninformative data streams. Present fusion approaches often lack robust mechanisms for the dynamic assessment of data quality and for the provision of a trustable confidence score on the final prediction. This dissuades their deployment in safety-critical settings. To address these limitations, we introduce Adaptive Confidence-weighted Expansion (ACE), a novel framework to enhance the trustworthiness of multimodal fusion models. ACE first enhances the multimodal space by generating new, complementary modalities from intra-modality correlations. It then employs a dual-level confidence mechanism that (1) adaptively reweighs all modalities by their reliability before fusion and (2) estimates a global trust score over the fused, final decision. To evaluate ACE, we used four challenging multi-omics datasets (BRCA, KIPAN, LGG, and ROSMAP). ACE significantly outperforms existing state-of-the-art algorithms in both classification performance and confidence calibration. Our framework provides a more stable and robust data fusion method that facilitates the use of multimodal learning in addressing high-stakes problems.


In large-scale machine learning, distributed training commonly involves multiple workers evaluating the gradients of the model on different dataset partitions. A common challenge is the presence of straggling workers, which may significantly slow down training. Traditional gradient coding (GC) addresses this by duplicating dataset partitions across workers, allowing for the replacement of missing gradients from stragglers. However, GC requires workers to evaluate gradients on multiple dataset partitions in each step, potentially increasing overall training time. In this paper, we propose to pipeline GC, such that gradient evaluation is segmented across multiple steps and each worker evaluates gradients on just a single dataset partition per step. We develop the pipelined version for fractional repetition (FR) and cyclic repetition (CR), two representative dataset placement schemes in GC, and prove convergence guarantees for both. Through extensive simulations and experiments on cloud infrastructure, our schemes not only significantly reduce training time but also accelerate convergence compared to GC and other baselines.


Cardinality-Decomposed Loss: Matching Training Objectives to Relation Structure in Heterogeneous Recommendation Graphs

Graph Neural Networks trained on heterogenous bipartite graphs form a common basis in recommendation systems. These graphs often express relations that vary in cardinality, for example, user-item preferences are one-to-many and user-attribute features are one-to-one. Traditionally, a unique loss function is applied for all of the network components which is often Bayesian Personalized Ranking (BPR). While BPR works well for the recommendation task, we find that it causes attribute embeddings to collapse to near-random geometry -- a silent failure that leaves standard ranking metrics largely unaffected and therefore invisible to conventional evaluation. This in turn pollutes user node embeddings, which are shaped by both edge types simultaneously, hurting downstream tasks like personalization, segmentation, etc. Here we propose a Cardinality-Decomposed Loss (CDL) that combines both Cross Entropy (CE) and BPR to enable the model to collectively optimize for relations across cardinalities. We confirm this CE-BPR conflict by showing the two losses compete in the shared encoder's parameter space. We evaluate CDL on five datasets spanning two structural configurations -- one-to-one attributes on user nodes (MovieLens-1M, Last.fm-360K, PayPal Audience Factory, BookCrossing) and on item nodes (Yelp) -- and find that CDL consistently improves discriminability in attribute embeddings. We also show that ranking (NDCG) improves when attributes carry meaningful preference signal, but conflicts with it when the correlation is weak. We use a lambda parameter to navigate this trade-off, and a lambda-sweep reveals that dataset behavior is governed by two graph properties -- semantic alignment and topology leakage. Semantic alignment measures whether the attribute predicts preferences, while topology leakage measures whether the graph's connectivity already encodes it.


As LLMs become more capable, they are increasingly deployed as collaborative agents, taking on user-delegated tasks through iterative interaction. Yet genuine interaction is inherently dynamic: users rarely specify their intent upfront, instead disclosing, revising, and reshaping it as the conversation unfolds. Despite this, LLMs are still predominantly evaluated or trained in single-turn, fully-specified settings, leaving open a fundamental question: how well do LLMs track and act on user intent as it evolves over the course of a conversation? To study this, we introduce a framework that transforms static, single-turn tasks into dynamic multi-turn conversations in which the user's intent evolves across turns--incrementally revealed, revised, and at times redirected mid-conversation--while preserving each task's original evaluation protocol, enabling existing benchmarks to be reused as controlled testbeds without new annotation. Across multiple tasks, we surface a consistent phenomenon: strong static-setting performance does not transfer to the evolving-intent setting, with substantial drops across model families. Our findings point to a fundamental gap: today's LLMs do not yet faithfully track and act on the user's evolving intent, a capability invisible to static evaluation yet critical for future collaborative agents.


Leaky Language Models: Stealing Architecture and Inference Optimizations via Per-Token Timing

This work presents LeakyLMs, a set of attacks that leak proprietary model, architecture, and deployment information from production language models. LeakyLMs is the first to demonstrate that key model and deployment details can be inferred using only token generation timing, even when interacting through remote APIs. LeakyLMs introduces two core attacks. The first attack targets inference optimizations and deployment strategies. For example, our attack detects whether a provider uses speculative decoding, a widely deployed inference-time optimization, and further identifies the context length of the draft model used in the pipeline. Our measurements show that Google Gemini Flash 2.5 uses speculative decoding with a draft context window of approximately 128K tokens. The second attack recovers key architectural properties, including the number of transformer layers, hidden dimension size, and number of attention heads. To achieve this, LeakyLMs builds a detailed and accurate model of token-generation timing on modern NVIDIA GPUs, characterizing how latency scales with model configuration and hardware parameters. The attack then performs a search over the architecture space using this timing model. In experiments with Llama models, the near-correct architectural configuration appears in the top-10 guesses more than 90% of the time.


Perspective Latents as an Architectural Condition for Causal Emergence in Active Inference Agents

A recent line of work measures causal emergence in reinforcement learning agents through Integrated Information Decomposition, reporting that $Φ_r$ grows with training and tracks reward improvement. For active inference, this raises the question of how reward-free predictive organization relates to such information-theoretic signatures. I test this within an active inference agent whose architecture separates a fast perception latent $z$ from a slow global latent $g$, where $g$ is driven by prediction error and structurally decoupled from policy gradients. In a reward-free environmental regime-switching protocol, $Φ_r$ concentrates in $g$; its aggregate magnitude is largely architectural and decreases with training. The substantive effect of learning becomes legible only at the atom-compositional level: decoupling flips sign from negative to positive and becomes regime-invariant under environmental change, while downward causation carries the regime-dependent adjustment. These results identify $g$ as the architectural locus of $Φ_r$-relevant temporal organization in an active inference agent, and argue against reading scalar $Φ_r$ as a direct index of learned integration.


CEDAR: Causal Edge Discovery for Autoregressive Processes

We propose CEDAR (Causal Edge Discovery for Autoregressive Processes), a constraint-based method for lagged causal edge discovery in sparse autoregressive time series. CEDAR screens candidate cross-variable lags using AR(1)-residualized, U-centered distance correlation, then applies two targeted conditional-independence tests per significant cross-variable lag candidate and accepts at most one lag per ordered pair. A stable MCI pruning step removes indirect edges, and optional deterministic C-nodes adjust for specified trend-like nonstationarity. In sparse regimes where few lags survive screening, CEDAR requires $O(d^2)$ CI tests after screening while retaining edge-level interpretability. CEDAR is most effective when data are scarce and variables exhibit lag-1 self-dynamics; methods with richer conditioning sets become preferable as $T$ grows or when higher-order autoregressive or simultaneous multi-lag effects are common.


Attribution Markets: A Fisher-Market Formulation for Fractional Credit Assignment Between Planned Tasks and Performed Actions

Personal and organizational planning systems maintain two records that drift apart: what was planned (a task's effort budget) and what was done (a logged action's duration and description). Existing systems bridge them with an exclusive, all-or-nothing link that strands genuinely related but unlinked effort and reports false stalls on active goals. We formulate the bridge as a quasi-linear Fisher market: planned tasks are budget-constrained buyers, performed actions are divisible goods, and a fused text/structural/temporal signal sets each buyer's valuation. Two market instruments - a seller reserve price and a buyer cash option - yield conservation, a hard budget cap, and a provable junk filter as theorems. We extend the market with a concave completion utility discounting progress as a task nears its plan; standard convergence theory for the market's algorithm does not transfer here, resolved by a satiation-threshold fixed point with existence (Brouwer) and local uniqueness under an explicit diagonal-dominance condition, validated empirically on random and adversarial instances. A de-circularized, multi-seed benchmark - observed affinity corrupted independently of the scored ground truth - surfaces a genuine weak spot: the market's sharp, zero-entropy equilibrium is more sensitive to affinity noise than entropy-regularized optimal transport's permanently smoothed one. We resolve this with a one-parameter entropy-regularized generalization unifying the two, plus a noise-adaptive rule for its regularization strength. We report full reproducibility parameters, discuss limitations candidly, and relate the result to multi-touch attribution, optimal transport, and online Fisher-market algorithms.


Explanation-Based Runtime Verification for Trustworthy ML-driven Optical Networks

Machine learning (ML) models are increasingly integrated into optical network automation frameworks to support tasks such as failure management, performance monitoring and resource allocation. In these environments, ML-driven predictions may be directly coupled with control-plane actions where incorrect decisions can immediately impact service quality, resource efficiency, and network stability. As automation levels increase, ensuring the reliability of individual decisions at deployment time becomes a critical requirement. Explainable artificial intelligence (XAI) techniques have emerged to improve transparency by highlighting the factors influencing ML predictions. In addition to identifying influential features, they provide insights into the underlying reasoning process of the model, revealing how different input variables contribute to the final outcome and how feature interactions shape the decision boundary. In this work, we introduce explanation-based runtime verification, an approach that exploits model explanations to assess the soundness of individual ML decisions before they are executed in the network control loop. The proposed approach evaluates explanation coherence and physics grounding consistency at runtime, enabling the system to defer or reject decisions flagged as uncertain. We demonstrate the effectiveness of our approach on a representative use case of lightpath quality of transmission classification. Experimental results show that explanation-based verification can intercept a significant fraction of erroneous decisions while preserving high automation rate.


End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers

We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.


Cross-Domain Generalization in Optical Networks via Joint Contrastive and Classification Learning

The robustness of machine learning techniques across heterogeneous network domains remains an open challenge in optical networks. Models trained on data from a specific topology or operational configuration often exhibit degraded performance when deployed in unseen networks. In this work, we address this challenge by proposing a representation learning technique aimed at capturing task-relevant relationships that remain stable across domains. The proposed technique is based on a novel joint contrastive and classification learning approach in which representation learning and task optimization are performed simultaneously, allowing both objectives to shape the latent space. Experimental results on a representative use case, namely, lightpath quality of transmission estimation, demonstrate the effectiveness of our approach compared to baseline approaches, and highlight its capacity for rapid adaptation, providing excellent performance even with limited fine-tuning.


Writhe-Based Polymer Link Classification Using Machine Learning

Unique and rapid classification of knots and links is an open mathematical problem that is relevant to a range of (bio)physical systems, including polymer melts, DNA, and proteins. In this paper, we explore a data-driven approach to the classification problem of link topology. Extending the framework introduced in Ref. 1 (Sleiman et al, 2024 Soft Matter, 20(1), pp.71-78), we show that a feedforward neural network trained on the writhe density matrix classifies thermally equilibrated configurations of the first six prime links with 97% accuracy. We demonstrate that this accuracy remains high across a range of temperatures and lengths of link components, while rapidly deteriorating with the addition of topology-altering Gaussian noise; a result consistent with the writhe density matrix containing features sensitive to topology. Our results show that neural networks based on the writhe density matrix efficiently classify two-component links, establishing machine learning as a promising tool for rapid classification of more complex link topologies, e.g. Borromean rings and multi-component links, as the computational cost of exact numerical calculation of topological invariants becomes prohibitive.


Adaptive Multi-Horizon Reinforcement Learning

Effective decision-making in complex and changing environments requires balancing short-term and long-term consequences. In reinforcement learning (RL), this trade-off is typically controlled through a fixed discount factor, which imposes a single exponentially discounted temporal horizon. However, biological agents exhibit flexible and adaptive temporal discounting, suggesting that effective planning requires multiple timescales. Here, we propose a multi-horizon approach that adaptively selects and combines temporal horizons, enabling robust adaptation to changes in reward structure without manual discount-factor tuning. This flexibility makes the method particularly suitable for continual learning scenarios involving task switches and varying environmental configurations. Empirically, we demonstrate that our approach identifies effective discount factors across a range of MiniGrid environments, including continual settings composed of three sequentially changing tasks. These results suggest that adaptive temporal discounting can improve parameter efficiency and enhance adaptability in both artificial and biologically inspired learning systems.


SalesLoop: Reinforcement Learning from Performance Feedback for Sales Lead Ranking

Lead ranking in Customer Relationship Management (CRM) systems faces a persistent challenge: models achieving high offline accuracy often underperform in production. We identify three fundamental gaps responsible for this disconnect: offline-online metric mismatch, pointwise-listwise objective misalignment, and temporal distribution drift. To address these gaps, we propose SalesLoop, a reinforcement learning framework that establishes a closed feedback loop between model predictions and real-world business outcomes. Our approach introduces (1) a performance-aware reward that encodes conversion outcomes weighted by ranking position and conversion velocity, and (2) Discriminative GRPO, a listwise optimization objective that adapts Group Relative Policy Optimization to discriminative ranking models.   SalesLoop improves NDCG@K by +7.9\% and P@K by +15.8\% over the strongest static baseline. A 160-day production A/B test at a New Energy Vehicle manufacturer, spanning 16.5M leads and 280 sales specialists across two provincial markets, validates statistically significant cumulative lift of +4.7\% ($p=0.047$) and +8.7\% ($p=0.002$). In production, the ranking backbone achieves Top-10\% recall of 44.1\% and surfaces high-intent leads at $2.3\times$ the conversion rate of specialist baselines.


The Frankl--Tokushige product conjectures for $r$-cross-intersecting families

We settle the uniform and biased product conjectures of Frankl and Tokushige for $r$-cross-intersecting families. Let $r\geq2$, let $0\leq k_i\leq(r-1)n/r$, and let $\mathcal{F}_i\subseteq\binom{[n]}{k_i}$ be $r$-cross-intersecting. We prove the sharp inequality $$\prod_{i=1}^r\frac{|\mathcal{F}_i|}{\binom{n}{k_i}}\leq \prod_{i=1}^r\frac{k_i}{n},$$ with equality attained by the corresponding levels of a common $1$-star. As a consequence, we obtain the analogous $p_i$-biased measure theorem for $0\leq p_i\leq(r-1)/r$, $$ \prod_{i=1}^rμ_{p_i}(\mathcal{F}_i)\leq \prod_{i=1}^r p_i.$$The main difficulty is that unequal parameters do not determine a single common target level; instead, the target levels $\ell_1,\ldots,\ell_r$ must satisfy $\sum_{i=1}^r \ell_i=(r-1)n$. We overcome this asymmetry in three steps. An ordered-partition coupling gives a sharp additive inequality for every such choice of target levels. A star-calibrated upper-shadow inequality relates the density of a family on its original level to the density of its upper shadow on a suitably chosen target level; it is proved by induction on $n$, with the induction step reduced to a two-point inequality. Finally, an analytic inequality shows that the resulting asymmetric additive estimate implies the required product bound. Perhaps surprisingly, the coupling captures all the combinatorial information of cross-intersection, reducing the remainder of the proof to an analytic argument.


Tight Hamilton Cycles in Linearly Quasirandom 3-Graphs

We study tight Hamilton cycles in linearly quasirandom 3-graphs. An $n$-vertex 3-graph $H$ is $(p,μ)$-dense if $e_H(X,Y,Z)\ge p|X||Y||Z|-μn^3$ for all $X,Y,Z\subseteq V(H)$. Ara{ú}jo, Piga and Schacht asked whether $p,α>1/4$ together with $δ_2(H)\geαn$ force a tight Hamilton cycle. We give a negative answer: for every $\varepsilon,μ>0$ and all sufficiently large $n$, there exists an $n$-vertex $(p_0-\varepsilon,μ)$-dense 3-graph $H$ with $δ_2(H)\ge(p_0-\varepsilon)n$ and no tight Hamilton cycle, where $p_0:=\max_{0\le x\le1}\min\{x^3,1-x\}\approx0.317672$.   For every $p>1/3$, we determine the asymptotically sharp minimum-codegree threshold. Writing \[   δ_0(p)=   \left(\frac{1-\sqrt{(4p-1)/3}}{2}\right)^2, \] we prove that every sufficiently large $(p,μ)$-dense 3-graph $H$ with $δ_2(H)\geαn$ contains a tight Hamilton cycle whenever $α>δ_0(p)$ and $μ$ is sufficiently small. A matching construction shows that this threshold is best possible. The proof uses absorption together with a new fixed-length connecting lemma based on a regular slice, a directed pair-state graph, and a finite scalar lemma.


Arithmetic progressions in a random set on a budget

A restricted-budget version of the random graph process, introduced by Frieze, Krivelevich, and Michaeli in 2025, studies the construction of structures by an online player who can purchase only a limited number of random edges. In this paper, we transfer this framework from random graphs to random subsets of integers, focusing on the construction of $k$-term arithmetic progressions. A player, Builder, is presented with a sequence of $t$ integers drawn uniformly at random from $[n]$. As the elements are revealed one by one, Builder must immediately and irrevocably decide whether to select the current integer, subject to a maximum budget of $b$ selected elements in total. We establish the optimal thresholds for this process, proving that for $t = ω(n^{1-2/k})$, a budget of $b = Θ((n/t)^{\frac{k-2}{2}})$ is both necessary and sufficient for Builder to successfully construct a $k$-term arithmetic progression with high probability.


A new recursive construction for large sets of Kirkman triple systems

We give a recursive construction of an LKTS(7q + 2) from an LKTS(q + 2) and an auxiliary permutation structure on an abelian group of order q, which we call a cubic orthomorphism. We prove that cubic orthomorphisms exist whenever q is a product of prime powers congruent to 1 modulo 6. The construction yields, in particular, LKTSs of orders 93, 177, 219, 261, and 303.


Improved lower bounds for the Shannon capacity of odd cycles

The Shannon capacity $Θ(G)$ of a graph $G$ quantifies the maximum rate at which information can be transmitted with zero error over a noisy channel. It is lower bounded by $α(G^d)^{1/d}$ for any $d$, where $α(G^d)$ is the independence number of the $d$-th strong power of $G$. We construct independent sets of size $134753$ in $C_7^{10}$, $21909$ in $C_{11}^{6}$, and $62530$ in $C_{13}^{6}$, improving the best known lower bounds for the Shannon capacity of these graphs to $Θ(C_7)\geq 134753^{1/10}>3.258020$, $Θ(C_{11})\geq 21909^{1/6}>5.289773$, and $Θ(C_{13})\geq 62530^{1/6}>6.300109$. We also improve the best known lower bounds on the independence numbers of several individual strong powers of odd cycles that do not improve the Shannon capacity lower bound. The constructions were discovered through iterative interactions with a Large Language Model (LLM), illustrating the potential of LLMs for finding explicit combinatorial constructions.


Interval Garside groups arising from involutions in finite reflection groups

We identify and study the interval Garside groups arising from the restriction of the absolute order on a Coxeter group to a lattice $[1,w]_T$, where $w$ is an involution. Those involutions $w$ for which $[1,w]_T$ is a lattice were previously classified by the second author; every such involution lies in the center of the parabolic subgroup generated by $[1,w]_T$. Except in type $B_n$, the obtained groups are isomorphic to (decomposable) right-angled Artin groups. We also investigate the situation for some finite complex reflection groups, mostly in rank two, taking for $w$ a (not necessarily involutive) central element.


Chromatic symmetric functions of claw-free graphs are not Schur positive

Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize chromatic polynomials of graphs. In 1995, Stanley introduced these symmetric functions and conjectured that they are Schur positive for claw-free graphs. We give examples of a line graphs, which are thus claw-free, whose chromatic symmetric function have a negative coefficient in its Schur expansion. We also give a counterexample to the 2018 conjecture of Monical that Schur positive chromatic symmetric functions have saturated Newton polytope when expanded in any finite number of variables. Both of these examples were found using ChatGPT-5.6 Sol Pro.


Adjacency-degree algebras and spectral determination of graphs

McKay proved that the spectra of all polynomial functions of the adjacency matrix $A$ and the diagonal degree matrix $D$ determine a tree. We prove a principal version of this theorem. Let $\mathcal A(G)=\langle I,A_G,D_G\rangle$ and let $M_G=\mathcal A(G)\mathbf1$ be the cyclic module generated by the all-ones vector. For connected graphs the ideal $\mathcal A(G)J\mathcal A(G)$, where $J=\mathbf1\mathbf1^T$, acts on $M_G$ as the full endomorphism algebra. We show that every forest satisfies $M_G=U_G$, the automorphism-orbit module, and that the induced algebra on the orbit quotient of a tree is a full matrix algebra. It follows that the scalar moments $\mathbf1^Tw(A_T,D_T)\mathbf1$ determine every tree. For general graphs these moments are degree-decorated caterpillar homomorphism counts. The resulting moment-rigidity class lies inside the amenable, compact, refinable hierarchy of color refinement, and its first small-order failures are ten-vertex integral switchings invisible to $M_G$.


A (3, 6)-fullerene is a cubic planar graph whose faces all have 3 or 6 sides. We give an exact enumeration of (3, 6)-fullerenes with V vertices and each of five possible symmetry types: *332, 332, 2*2, *222, and 222, in orbifold notation. We use this enumeration, together with some constructions, to resolve three conjectures about the existence of (3, 6)-fullerenes with 2*2$, *222, and 222 symmetry for given numbers of vertices.


Fat minors are the metric analog of graph minors that are tailored to the analysis of metric (edge-weighted) graphs and, more generally, metric spaces having a suitable notion of shortest paths. Despite a large interest in this notion, not much is known about the structure of metric graphs excluding a fixed fat minor.   We prove that if a metric graph $G$ excludes a fixed graph $H$ as a $δ$-fat minor, for some $δ>0$, then $G$ enjoys the metric analog of flatness (aka uniform quasi-wideness) - a structural property from the field of Sparsity. In essence, our flatness result says that for any $α\geq β$ large enough compared to $δ$, in every large enough set $A$ in $G$ one can find a sizable subset $B$ that becomes $α$-scattered after removing a bounded number of balls of radius $β$. We call this property drill-flatness. Notably, the proof only relies on excluding shallow fat minors: every branch set has radius at most $2α$.   As a corollary, we prove that metric graphs that exclude a fixed $δ$-fat minor have bounded $\varepsilon$-scatter dimension if we consider only $\varepsilon$-scatters at distances large enough compared to $δ$. By combining this with the results of Abbasi et al. [FOCS 2023], we infer that the $k$-Center problem on instances excluding $H$ as a $δ$-fat minor admits an approximation algorithm that finds a solution of cost at most $(1+\varepsilon)\cdot\mathsf{OPT}+{\cal O}(δ/\varepsilon^2)$ in time ${\cal O}_{H,\varepsilon}(n^{{\cal O}(1)})$. This is one of the first algorithmic results for general fat-minor-free metrics.   We also study drill-flatness in hereditary classes of (unweighted) graphs, where we obtain a characterization equating drill-flatness with excluding shallow induced minors. This is an induced analog of the equivalence between flatness and nowhere denseness - one of central results of Sparsity.


A lower bound on the growth rate of $(132,213)$-avoiding cyclic permutations

We construct a new reduction process which takes a $(132,213)$-avoiding permutation to a shorter one that is cyclic if and only if the original was. Iterating it determines whether a given $(132,213)$-avoiding permutation is cyclic. Reversing it gives four moves that build every cyclic $(132,213)$-avoiding permutation, uniquely, from $1$ if $n$ is odd, and $21$ if $n$ is even. Our main application is the first non-trivial lower bound for the growth rate of $\mathcal{C}_n(132,213)$, the cyclic permutations of length $n$ avoiding $132$ and $213$. We also give several other consequences of the reduction, including a bijection between the odd and even size classes and an exact enumeration for those permutations with a restricted number of layers.


Homotopy types of intervals in corank-three higher Bruhat orders

We prove Reiner's conjecture for higher Bruhat orders in corank 3: the facial intervals of B(n,n-3) are precisely the spherical intervals, and all other intervals are contractible.


Selection-structure generalizations of the Borsuk-Ulam theorem

We prove Borsuk-Ulam-type results governed by selection structures. Selection structures extend the matroidal framework for colorful theorems in discrete geometry and include non-matroidal examples such as chessboard complexes.   Motivated by Frick and Wellner's Radon-type strengthening of Fan's theorem and its colorful variants, we prove selection-structure analogues whose conclusions are determined by Radon partitions. We also prove a prime-power selection-structure covering version of Volovikov's theorem, governed by Tverberg partitions. We include applications to fair partitions, including selection-structure versions of the ham sandwich and necklace splitting theorems.


A six-neuron counterexample to the target-free clique conjecture

The target-free clique conjecture asserts that the supports of stable fixed points of a nondegenerate combinatorial threshold-linear network (CTLN) are exactly its target-free cliques: bidirected cliques for which no outside vertex receives an edge from every clique vertex. We give an explicit six-neuron counterexample. For every sufficiently small $\varepsilon>0$, the CTLN defined by one fixed graph at $δ=29\varepsilon/25$ is nondegenerate and has a stable fixed point with nonclique full support. Its values of $q=δ(1-\varepsilon)/\varepsilon$ tend to $29/25$. In the complementary direction, for any CTLN on $n\geq3$ vertices, we prove that in the parameter range \[   q\geq n-2-\frac{n-3}{2}\varepsilon, \] no nonclique support can satisfy both the fixed-point positivity and linear stability conditions. Consequently, throughout this range, every nondegenerate CTLN has exactly its target-free cliques as supports of stable fixed points. In particular, this holds when $\varepsilon\leqδ/(δ+n-2)$.


A Weighted Sum Formula for Double Eisenstein Series

We prove a weighted sum formula for double Eisenstein series. Its corresponding identity for the generating series of multiple divisor sums was conjectured by the author in his master's thesis. The double Eisenstein series identity follows from the restricted double-shuffle relations proved by the author and Tasaka, while the proof of the divisor-sum identity is combinatorial and uses generating series.


Frieze patterns and aperiodic tilings of the plane

This short note provides two examples of aperiodic frieze patterns of the plane, supported on the rhombic Penrose tiling and the Godrèche--Lançon--Billard tiling. That is, we provide a decoration of their vertices with positive integers which satisfy the diamond rule, in analogy to the usual (in)finite frieze patterns as defined by Conway and Coxeter.