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01.
arXiv (CS.CV) 2026-06-18

NeuMesh++: Towards Versatile and Efficient Volumetric Editing with Disentangled Neural Mesh-based Implicit Field

Recently neural implicit rendering techniques have evolved rapidly and demonstrated significant advantages in novel view synthesis and 3D scene reconstruction. However, existing neural rendering methods for editing purposes offer limited functionalities, e.g., rigid transformation and category-specific editing. In this paper, we present a novel mesh-based representation by encoding the neural radiance field with disentangled geometry, texture, and semantic codes on mesh vertices, which empowers a set of efficient and comprehensive editing functionalities, including mesh-guided geometry editing, designated texture editing with texture swapping, filling and painting operations, and semantic-guided editing. To this end, we develop several techniques including a novel local space parameterization to enhance rendering quality and training stability, a learnable modification color on vertex to improve the fidelity of texture editing, a spatial-aware optimization strategy to realize precise texture editing, and a semantic-aided region selection to ease the laborious annotation of implicit field editing. Extensive experiments and editing examples on both real and synthetic datasets demonstrate the superiority of our method on representation quality and editing ability. Project page: https://zju3dv.github.io/neumeshplusplus/

02.
arXiv (CS.LG) 2026-06-12

Scale Buys Interpolation, Structure Buys a Horizon: Certified Predictability for Equivariant World Models

作者:

arXiv:2606.13092v1 Announce Type: new Abstract: Scale buys interpolation; structure buys a certified horizon. A world model's average error says nothing about whether a particular prediction can be trusted, or for how long. For equivariant latent world models we give a computable, multi-step certificate of the predictable horizon: $T$-step rollout error is provably constant over each symmetry orbit (Theorem A) and stratified channel-by-channel by the predictor's Lyapunov spectrum, $T_j(\epsilon)\sim\log(1/\epsilon)/\lambda_j$. The horizon is two-sided – a matching lower bound makes approximate equivariance provably horizon-limited – and the certificate is exclusive to structure: orbit-constant error characterizes equivariance, so no non-equivariant model has it at any scale. Empirically, on 40-D Lorenz-96 only a $\mathbb{Z}_N$-equivariant network recovers the full Lyapunov spectrum ($R^2{=}0.98$); dense and recurrent baselines fail. Because the spectrum is faithful, the certificate acts, a priori: under a fixed sensing budget a $c\times$-inflated certificate provably needs $c\times$ the budget, and the equivariant certificate meets a budget its inflated dense counterpart cannot – with zero calibration data. The same read-out, unchanged, audits public pretrained world models training-free: TD-MPC2 checkpoints land on the certificate's own scope taxonomy – calibrated where strongly expansive (ratio 0.94-1.02), optimistic where weakly expansive, correctly abstaining where contracting – a map a deployed monitor replicates cell-by-cell, out-of-sample. Across the official 1M-317M multitask ladder, calibration does not improve with parameters. On V-JEPA 2-AC (1B, real robot data) the measured cross-check correctly overrides an over-promising tangent spectrum – the cross-validated audit, not the raw number, is the deployable object. Scale buys interpolation, not a calibrated horizon.

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

EvoMemBench: Benchmarking Agent Memory from a Self-Evolving Perspective

Recent benchmarks for Large Language Model (LLM) agents mainly evaluate reasoning, planning, and execution. However, memory is also essential for agents, as it enables them to store, update, and retrieve information over time. This ability remains under-evaluated, largely because existing benchmarks do not provide a systematic way to assess memory mechanisms. In this paper, we study agent memory from a self-evolving perspective and introduce EvoMemBench, a unified benchmark organized along two axes: memory scope (in-episode vs. cross-episode) and memory content (knowledge-oriented vs. execution-oriented). We compare 15 representative memory methods with strong long-context baselines under a standardized protocol. Results show that current memory systems are still far from a general solution: long-context baselines remain highly competitive, memory helps most when the current context is insufficient or tasks are difficult, and no single memory form works consistently across all settings. Retrieval-based methods remain strong for knowledge-intensive settings, whereas procedural and long-term memory methods are more effective for execution-oriented tasks when their stored experience matches the task structure. We hope EvoMemBench facilitates future research on more effective memory systems for LLM-based agents. Our code is available at https://github.com/DSAIL-Memory/EvoMemBench.

04.
arXiv (math.PR) 2026-06-16

On stability of outliers from the circular law

arXiv:2606.16609v1 Announce Type: new Abstract: This work investigates the stability of outliers from the circular law, via the convergence of their associated diagonal overlaps between eigenvectors - also known as the squared eigenvalue condition numbers. We consider and compare two paradigmatic cases, namely: 1) the Complex Ginibre Ensemble conditioned on the existence of an outlier, and 2) the outlier induced by a rank-one Hermitian perturbation of a Complex Ginibre matrix. In both cases, we prove almost sure convergence towards a specific constant that only depends on the radius of the outlier and its status - either conditioned or induced. These results can be generalized to other complex integrable ensembles with the same techniques, and complement our understanding of eigenvalue stability in non-Hermitian ensembles.

05.
arXiv (quant-ph) 2026-06-17

Vorticity Induced by Non-frontal Collisions of Quantum Droplets

arXiv:2606.17498v1 Announce Type: cross Abstract: The rotational dynamics induced by the non-frontal binary collisions of quantum droplets composed of ultracold alkali atoms are analyzed. A theoretical study is presented within the extended Gross-Pitaevskii equation framework, using experimentally feasible conditions. Numerical experiments elucidate a rich landscape of possible topological excitations in the system that are robust towards measurements. The collision of heteronuclear quantum droplets composed of $^{41}$K and $^{87}$Rb atoms in the incompressible regime, gives rise to dynamical instabilities that spontaneously generate topological defects: vortex rings, dislocation lines, and vortices in one species. Their presence depends on the Weber number and the impact parameter. An experimental proposal for vortex detection in both real and Fourier space using interaction ramps is described.

06.
arXiv (CS.AI) 2026-06-12

TokaMark: A Comprehensive Benchmark for MAST Tokamak Plasma Models

arXiv:2602.10132v3 Announce Type: replace-cross Abstract: Development and operation of commercially viable fusion energy reactors such as tokamaks require accurate predictions of plasma dynamics from sparse, noisy, and incomplete sensors readings. The complexity of the underlying physics and the heterogeneity of experimental data pose formidable challenges for conventional numerical methods, and highlight the promise of modern data-native approaches. A major obstacle in realizing this potential is, however, the lack of curated, openly available datasets and standardized benchmarks. Existing fusion datasets are scarce, fragmented across institutions, facility-specific, and inconsistently annotated, which limits reproducibility and prevents a fair and scalable comparison of AI approaches. In this paper, we introduce TokaMark, a structured benchmark to evaluate AI models on real experimental data collected from the Mega Ampere Spherical Tokamak (MAST). TokaMark provides a comprehensive suite of tools designed to unify access to multi-modal fusion data and standardize evaluation protocols. The benchmark includes a curated list of 14 tasks spanning a range of physical mechanisms, exploiting a variety of diagnostics and covering multiple operational use cases. A baseline model is provided to facilitate transparent comparison and validation within a unified framework. By establishing a unified benchmark, TokaMark aims to accelerate progress in data-driven AI-based plasma modeling, contributing to the broader goal of achieving sustainable and stable fusion energy. The dataset, benchmark, documentation, and tooling are open-sourced under https://github.com/UKAEA-IBM-STFC-Fusion-FMs/tokamark_baseline.

07.
arXiv (CS.LG) 2026-06-16

Generative Modeling on Metric Graphs via Neural Optimal Transport

arXiv:2606.16273v1 Announce Type: cross Abstract: We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target measures on a metric graph, our method embeds the graph into a smooth ambient space, solves an entropic Kantorovich problem via a neural semidual parameterization, and projects generated samples back onto the original graph. We study two embedded geometries: an extrinsic Euclidean realization and the intrinsic tropical Abel–Jacobi embedding into the Jacobian torus. In both cases, the resulting generator is graph-supported by construction. We prove that, in the joint limit of increasing neural expressivity, the learned generator converges weakly to a valid transport coupling between the original graph measures. Empirically, across a range of geometrically distinct graphs, our method matches or improves upon heuristic transport baselines based on discrete graph OT, while scaling more favorably. Finally, we demonstrate scalability on real-world urban mobility data by training our model on one million Uber pickup locations in Manhattan, New York City.

08.
arXiv (CS.AI) 2026-06-12

Evaluation Sovereignty in Metadata-Driven Classification: A Multi-Track Framework for Weakly Supervised Information Systems

arXiv:2606.13436v1 Announce Type: new Abstract: Evaluation in machine learning is typically treated as a neutral measurement process. However, in operational information systems, evaluation outcomes are often conditioned by the processes used to generate labels. This paper does not seek to improve classification performance. Instead, it examines the validity of performance measurement under differing label-authority regimes. This issue is particularly relevant in large-scale metadata-driven systems, where labels are often incomplete, inconsistent, or weakly supervised. We introduce evaluation sovereignty, defined as the degree to which performance metrics are independent of label authority and supervision regime, and propose a multi-track evaluation framework that systematically varies training and evaluation label sources. Using hierarchical multi-label classification on large-scale scientific metadata, we demonstrate that models exhibiting strong performance under operational ("silver") evaluation degrade substantially under independent ("gold") evaluation, particularly for fine-grained classification. For example, Micro-F1 decreases from approximately 0.54 to 0.03. Notably, ranking-based metrics remain above baseline, revealing a divergence between latent model signal and classification validity. These findings suggest that commonly reported performance metrics may reflect alignment with labeling processes rather than true predictive capability. We therefore reconceptualize evaluation validity as a system-level property shaped by label governance and provide a practical methodology for auditing intelligent systems operating under weak supervision.

10.
arXiv (quant-ph) 2026-06-11

Tensor-Network-Based Distributed Quantum Dynamics on Independent Quantum Computers

arXiv:2606.11579v1 Announce Type: new Abstract: We present an approach based on tensor networks for distributed quantum computing simulation of chemical wavepacket dynamics in a continuous variable representation. The central idea is that the tensor-network representation of the multidimensional time-evolution operator naturally induces an elevated Hilbert space where the dynamics decomposes into a set of independent lower-dimensional propagations. This transformation converts an entangled quantum evolution into a set of parallel computational tasks that can be executed asynchronously across heterogeneous quantum and classical computing architectures. The resulting formalism establishes a direct connection between tensor-network decompositions, uniformly controlled quantum circuits, and asynchronous distributed quantum computing. The approach is developed with a goal towards hybrid quantum/classical implementation, and is appropriate for a general heterogeneous mixture of quantum hardware systems. The experimental realization of the asynchronously distributed quantum processes that arise from the tensor-network decomposition are carried out on the Sandia National Laboratories' trapped-ion quantum computer, where the circuits are compiled using native partial-entangling $XX(\theta)$ gates, reducing the expected two-qubit gate infidelity by more than 30\% relative to conventional fully entangling decompositions. We demonstrate the methodology by quantum computing the vibrational spectra of a small protonated water cluster that shows critical quantum nuclear behavior. Such water cluster systems have been found to be challenging for experimental action spectroscopy and for theory, and here, for the first time, we provide results for vibrational spectroscopy that are in agreement with the respective classical results to within 4cm$^{-1}$, thus allowing for the potential for spectroscopic accuracy from quantum computations.

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

Discriminative Span as a Predictor of Synthetic Data Utility via Classifier Reconstruction

In many real-world computer vision applications, including medical imaging and industrial inspection, binary classification tasks are characterized by a severe scarcity of positive samples. A widely adopted solution is to generate synthetic positive data using image-to-image transformations applied to negative samples. However, a fundamental challenge remains: how can we reliably assess whether such synthetic data will improve downstream model performance? In this work, we propose a geometry-driven metric that predicts the utility of synthetic data without requiring model training. Our approach operates in the embedding space of a pre-trained foundation model and represents the dataset through difference vectors between samples. We evaluate whether the weight vector of a linear classifier can be expressed within the subspace spanned by these variations by measuring the relative projection error. Intuitively, if the variations induced by synthetic data capture task-relevant directions, their span can approximate the classifier, resulting in low projection error. Conversely, poor synthetic data fails to span these directions, leading to higher error. Across multiple datasets and architectures, we show that this metric exhibits strong correlation with downstream classification performance of CNNs trained on mixtures of real negative and synthetic positive data. These findings suggest that the proposed metric serves as a practical and informative tool for evaluating synthetic data quality in data-scarce settings.

12.
arXiv (CS.CL) 2026-06-15

Sub-Token Routing for KV Cache Compression

Transformer inference often requires a large KV cache, especially for long-context language modeling and multimodal generation. Existing compression methods usually reduce cache cost by selecting, evicting, quantizing, or compressing cached tokens, or by reducing the visual-token sequence before language-model inference. We introduce sub-token routing, a KV-compression method that adds a finer control axis inside retained tokens. It splits each retained value vector into groups and keeps only selected groups, while leaving query and key states unchanged. The method is designed to work after token-level reduction. First, a token-reduction method determines which tokens are retained. Then, sub-token routing compresses the value states inside those retained tokens. Experiments under matched KV budgets show that adding sub-token routing improves token-level reduction performance in both LLM and VLM settings, including Quest on LLaMA-2-7B and Qwen2.5-7B, and FastV/VisionZip across LLaVA and Qwen-VL models. The gains are larger at smaller KV budgets, suggesting that value-group routing is especially useful when further token removal becomes costly. Overall, token-level reduction and sub-token routing provide complementary ways to reduce KV cost.

13.
arXiv (quant-ph) 2026-06-11

Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian

arXiv:2506.03453v3 Announce Type: replace Abstract: Global control provides a promising route to implementing multi-qubit gates without individual qubit addressing. This is especially appealing for permutation-invariant (PI) gates, whose symmetry is often broken when they are compiled into individually addressed one- and two-qubit gates. Important examples include SWAP, $\sqrt{iSWAP}$, and the n-qubit controlled-Z gate, which is equivalent, up to two single-qubit Hadamard gates, to the multi-qubit Toffoli gate. Motivated by this global-control perspective, we show that all PI unitaries on an arbitrary number of qubits can be realized using the Tavis-Cummings (TC) interaction, the multi-qubit version of the Jaynes-Cummings interaction, together with global uniform z and x fields. Here, the $n$ qubits are identically coupled to a single bosonic mode (oscillator), which is initialized in and returned to its vacuum state. A corollary is that all PI states, including GHZ and Dicke states, can be prepared using the same global control. For the case n=2 qubits, which is particularly important in quantum computing, we also find explicit pulse sequences for implementing all PI qubit unitaries that conserve angular momentum in the z direction, using only the TC interaction and global z fields. This includes controlled-Z, SWAP, and $\sqrt{iSWAP}$.

14.
PLOS Computational Biology 2026-06-15

Fung-AI: An AI/ML-driven pipeline for antifungal peptide discovery

by Daniel S. Berman, Libby M. Lewis, Tom D. Curtis, Olivia N. Tiburzi, Daniel F. Q. Smith, Arturo Casadevall, Laura J. Dunphy Emerging fungal pathogens represent a concerning threat to both global health and food security. In this study, we aimed to address our rising vulnerability to fungal pathogens through the development of the Fung-AI pipeline: an AI/ML-driven approach for antifungal discovery. A generative adversarial network (GAN) was trained to generate novel candidate antifungal peptide sequences. Next, in silico antifungal and hemolytic classifiers were built to further prioritize AI-generated peptides for experimental validation. From a pool of ~10,000 candidates, thirteen peptides were selected for testing over two-stages of experimentation. Five peptides were found to display mild antifungal activity against the wheat pathogen, Fusarium graminearum, with minimal inhibitory concentrations (MICs) ranging from 250 µg/mL to 500 µg/mL. Four of the five peptides also showed activity against the human pathogen, Candida albicans (MIC: 500 µg/mL). Two of our AI-generated antifungal peptides additionally demonstrated low cytotoxicity in HepG2 human liver carcinoma cells (LC50 > 704.2 µg/mL) indicating that they may be useful as scaffolds for future optimization for therapeutic applications. None of our peptides were found to considerably inhibit the emerging pathogen C. auris, suggesting the need for pathogen-specific down-selection of candidate peptides. Overall, we present a proof-of-principle, generative-AI-based approach for the rapid design of de novo antifungal peptides.

15.
arXiv (CS.CL) 2026-06-15

BayLing-Duplex: Native Full-Duplex Speech Dialogue with a Single Autoregressive LLM

Real-time, full-duplex speech interaction is a key feature of next-generation spoken chatbots, allowing the model to listen and speak at the same time and to handle natural phenomena such as overlap, hesitation, and barge-in. Existing speech language models (SpeechLMs) such as LLaMA-Omni and GLM-4-Voice are still turn-based and rely on an external Voice Activity Detection (VAD) module to mark the end of the user's turn, which fundamentally limits their interactive ability. In this paper, we introduce BayLing-Duplex, a native full-duplex SpeechLM where a single autoregressive LLM decides when to listen, when to speak, and when to stop, with no auxiliary turn-taking module. The design adds only a few special tokens to the standard vocabulary, so it transfers across LLMs and reuses existing training and serving stacks with no architectural adaptation. Starting from the public GLM-4-Voice checkpoint and using only 400K full-duplex samples for fine-tuning followed by a lightweight DPO stage, BayLing-Duplex reaches 92% turn-taking success and 100% interruption success on InstructS2S-Eval, while improving the speech-response score from 2.17 to 3.39 over Moshi. BayLing-Duplex also matches or surpasses its turn-based counterpart on Llama Questions, Web Questions, and Alpaca-Eval, showing that simultaneous listen-and-speak modeling does not sacrifice response quality.

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

PERRY: Policy Evaluation with Confidence Intervals using Auxiliary Data

arXiv:2507.20068v2 Announce Type: replace Abstract: Off-policy evaluation (OPE) methods estimate the value of a new reinforcement learning (RL) policy prior to deployment. Recent advances have shown that leveraging auxiliary datasets, such as those synthesized by generative models, can improve the accuracy of OPE methods. Unfortunately, such auxiliary datasets may also be biased, and existing methods for using data augmentation within OPE lack principled uncertainty quantification. In high stakes domains like healthcare, reliable uncertainty estimates are important for ensuring safe and informed deployment of RL policies. In this work, we propose two methods to construct valid confidence intervals for OPE with data augmentation. The first provides a confidence interval over $V^{\pi}(s)$, the policy value conditioned on an initial state $s$. To do so we introduce a new conformal prediction method suitable for Markov Decision Processes (MDPs) with continuous state spaces, extending prior work to higher-dimensional settings. Second, we consider the more common task of estimating the average policy performance over all initial states, $V^{\pi}$; we introduce a method that draws on ideas from doubly robust estimation and prediction powered inference. Across simulators spanning inventory management, robotics, healthcare, and a real healthcare dataset from MIMIC-IV, we find that our methods can effectively leverage auxiliary data and consistently produce confidence intervals that cover the ground truth policy values, unlike previously proposed methods. Our work enables a future in which OPE can provide rigorous uncertainty estimates for high-stakes domains.

17.
arXiv (math.PR) 2026-06-12

Explosion and non-explosion in pure birth Crump–Mode–Jagers branching processes

arXiv:2601.06850v2 Announce Type: replace Abstract: In this short note, we provide an explicit sufficient condition for non-explosion of Crump–Mode–Jagers branching processes with pure birth reproduction. It shows that the standard sufficient condition for explosion, namely the convergence of the series of reciprocals of the birth rates, is – at least for rate sequences without excessive oscillations – remarkably close to being necessary. At the same time, it is not necessary in full generality: we construct a counterexample which also yields a general preferential attachment tree without fitness with an infinite path and no vertices of infinite degree, thereby answering an open question previously raised in the literature.

18.
arXiv (CS.CV) 2026-06-12

SmartFont: Dynamic Condition Allocation for Few-Shot Font Generation

Few-shot font generation simultaneously requires global structural completeness and fine-grained local style fidelity. Existing methods usually either rely on global content-style modeling, which is robust but imperfectly disentangled, or emphasize component/local modeling, which captures fine details but relies heavily on local priors and reference coverage. We argue that the key challenge is not merely to learn purer conditions, but to organize complementary yet biased global and local conditions through multi-level allocation during generation. To this end, we propose SmartFont, a diffusion-based few-shot font generation framework that combines global content-style generation with weakly supervised local corrective experts. The local branch performs semantic-spatial allocation by learning expert-wise local concepts and semantically meaningful spatial maps under weak component supervision, enabling fine-grained correction without requiring explicit component-conditioned inference. On top of this, a denoising-state condition allocation module adaptively weights global content, global style, and local corrective feature across timesteps and injection blocks. Extensive experiments show that SmartFont achieves better global-local balance, improves glyph quality and local detail fidelity.

19.
arXiv (CS.LG) 2026-06-12

Circuit Synchronization Precedes Generalization: Causal Evidence from Fourier Structure in Grokking Transformers

arXiv:2606.12966v1 Announce Type: new Abstract: Grokking – where a transformer on modular arithmetic suddenly transitions from near-chance to near-perfect validation accuracy – is attributed to a Fourier circuit, but its timing, causal structure, and controllability remain poorly understood. We introduce the Frequency Synchronization Degree (FSD), a normalised, permutation-tested metric for Fourier circuit synchronisation requiring no prior circuit knowledge. Across nine modular addition configurations (primes p in {53, 71, 97, 113, 131}, three seeds), FSD synchronises 500-3,000 steps before grokking (mean lead +1,722 steps; all nine positive, sign-test p~0.004), and precedes a restricted-logit loss baseline (Nanda et al.'s excluded loss) in all nine cases, making it the earliest available predictor. We provide direct causal evidence that the inter-phase gap is a regularisation phenomenon: forking training at the FSD-ceiling step and varying weight decay lambda produces strictly monotone earlier grokking, with Delta_t proportional to 1/lambda. This law replicates across three primes (p in {53,97,131}; R^2=1.00 and R^2=0.99 for two clean cases), captured as Delta_t ~ C/lambda, consistent with (1/lambda)*log(||W_mem||/tau). Architecture ablations show an attention-only model groks with a strong FSD precursor; an MLP-only model never groks; a single-layer model's FSD lags, confirming the precursor is a multi-block circuit property.

20.
arXiv (quant-ph) 2026-06-16

Lattice surgery for near-term experimental logical qubit entanglement creation in planar architectures

arXiv:2606.15190v1 Announce Type: new Abstract: In the era of early fault-tolerant quantum computing, basic demonstrations of entanglement operations between a few logical qubits are at the frontier of recent developments in quantum computing. In this work, we describe in detail, at both the logical and physical qubit levels, a logical teleportation protocol between two surface code logical qubits based on lattice surgery. We address several aspects of the teleportation protocol pertinent to superconducting qubit architectures. We explore the modularity constraints in the number and location of stabilizer readouts and compare variants of the teleportation protocol in this regard. Additionally, we investigate potential performance improvements related to in-sequence decision logic and the optimal size of the interface region between two surface code patches on a superconducting chip. Based on our simulations, we show possible near-term improvements in lattice surgery protocols that facilitate fault-tolerant quantum computing in superconducting circuit architectures.

21.
arXiv (CS.LG) 2026-06-18

ThousandWorlds: A benchmark for climate emulation of potentially habitable exoplanets

arXiv:2606.18338v1 Announce Type: new Abstract: The search for life beyond Earth will depend on detecting faint signatures in the atmospheres of potentially habitable exoplanets. Interpreting those signatures requires understanding the host planet's climate: the same molecule may signal life on one planet and abiotic chemistry on another. Global climate models (GCMs) provide this understanding, but individual runs can require up to millions of core-hours and substantial domain expert time. Machine-learning emulators could remove this bottleneck, but progress has been limited by the absence of a curated, multi-model exoclimate dataset. We introduce ThousandWorlds, an ML-ready benchmark for exoclimate emulation and for the broader regime of low-data, multi-simulator, parameter-to-field regression. The dataset contains approximately 1800 simulations from five GCMs, mapping eight planet parameters to 3D atmospheric fields including temperature, humidity, winds, clouds, and radiation. Three nested subsets define progressively harder challenges: single-simulator regression, multi-simulator regression with complete observations, and multi-simulator regression with structured missingness. We propose two evaluation protocols: one for ranking methods, and one that measures performance relative to the disagreement between GCMs themselves. We evaluate seven baselines spanning simple methods, deep learning, and Gaussian processes. GP-based methods perform best, suggesting that ThousandWorlds exposes a regime where off-the-shelf deep learning does not yet succeed. Data: https://doi.org/10.57967/hf/8695. Code: https://github.com/edstevenson/ThousandWorlds.

22.
arXiv (math.PR) 2026-06-15

A random approach to the multibonacci sequence

arXiv:2606.14294v1 Announce Type: cross Abstract: This paper presents a random approach to the multibonacci sequence. We generalise the model introduced by Benjamin, Levin, Mahlburg, and Quinn, which is based on a random tiling method using dominoes and squares that leads to the Fibonacci sequence, and which was extended to the tribonacci case in a previous work by the authors. Our approach employs tiling with linear $k$-ominoes, $k=1,\ldots,s$, combined with specific colouring, to generate a weighted multibonacci sequence. For a natural random variable~$X$ defined by this model, we establish the distribution of $X$ in terms of multibonacci numbers and compute $\mathbb{E}[X] = 2^{s+1}-3$.

23.
arXiv (math.PR) 2026-06-17

Diffuse Interface Energies with Microscopic Heterogeneities II: Rare Events

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

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

Assessing Reliability of Symbol Detection in Concept Bottleneck Models

Concept Bottleneck Models (CBMs) are a relevant tool for explainable Artificial Intelligence because they make their predictions through human-interpretable symbols. However, high task accuracy does not guarantee that these symbols are detected faithfully: jointly trained CBMs may encode task-specific shortcuts in the bottleneck, making their explanations unreliable. In this paper, we study concept-detection reliability by swapping independently trained concept detectors and classification heads that share the same symbolic vocabulary. We use the resulting performance degradation, concept-level metrics, and symbol-wise uncertainty estimates to identify concepts that are especially prone to spurious firing. Finally, we propose a reliability-aware training strategy in which a shared concept detector is optimized with multiple classification heads and penalized for relying on globally or instance-wise unreliable symbols. On CUB-200-2011 with full concept supervision, detectors and heads are almost freely interchangeable (swap drop below one accuracy point, relative retention above $99\%$, and no concept detected below chance), whereas on a controlled synthetic task we show that, as the concept-supervision weight is reduced, models keep near-perfect task accuracy while swapped accuracy and agreement with the ground-truth concepts collapse to chance. Our reliability-aware training substantially mitigates this leakage, roughly doubling swap accuracy in the leaky regime.

25.
arXiv (CS.CL) 2026-06-16

Understanding the Behaviors of Environment-aware Information Retrieval

Recent retrieval-augmented generation (RAG) approaches have demonstrated strong capability in handling complex queries, yet current research overlooks a critical challenge: different retrievers require fundamentally different query formulation strategies for optimal performance. In this work, we present the first systematic analysis of how LLMs can learn to adapt their query formulation strategies for different retrievers via reinforcement learning (RL). Our empirical study reveals that RL effectively teaches an LLM to tailor its queries to specific retriever characteristics. We discover that different retrievers exhibit surprisingly distinct optimal query styles (e.g., descriptive vs. question-like), suggesting strategies learned for one retriever ineffective for another. We further show that performance can be enhanced by incorporating retriever-specific human guidance and by scaling model size. To facilitate learning over multi-retrieval-step trajectories, we introduce a branching-based rollout technique that improves training stability. Our work provides the first empirical evidence and actionable insights for building truly retriever-aware RAG systems. Code and resources are available at https://github.com/LCO-Embedding/Envs-aware-Information-Retrieval.