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01.
arXiv (CS.CL) 2026-06-15

OLaPh: Optimal Language Phonemizer

Phonemization is a critical component in text-to-speech synthesis. Traditional approaches rely on deterministic transformations and lexica, while neural methods offer potential for higher generalization on out-of-vocabulary (OOV) terms. We introduce OLaPh (Optimal Language Phonemizer), a hybrid framework that integrates extensive multilingual lexica with advanced NLP techniques and a statistical subword segmentation function. Evaluations on the WikiPron benchmark show OLaPh significantly outperforms established baselines in overall accuracy and maintains robustness on OOV data through advanced fallback mechanisms. To further explore neural generalization, we utilize the framework to synthesize a high-consistency training corpus for an instruction-tuned Large Language Model (LLM). While the deterministic framework remains more accurate overall, the LLM demonstrates strong generalization, matching or partly exceeding the framework's performance. This suggests that the LLM successfully internalized phonetic intuitions from the synthetic data that transcend the framework's capabilities. Together, these tools provide a comprehensive, open-source resource for multilingual grapheme-to-phoneme conversion (G2P) research.

02.
arXiv (CS.AI) 2026-06-16

DOG-DPO:Dynamic Optimization in Geometry for Safety Alignment

arXiv:2606.07678v2 Announce Type: replace-cross Abstract: Safety alignment for large language models relies on preference data, but current pipelines often train on large, redundant datasets. Existing data selection methods typically score each preference pair independently, collapsing directional preference information into scalar quality or diversity scores. This sample-centric view is especially limiting in multi-dataset settings, where shared safety directions coexist with dataset-specific residual risks. We propose DOG-DPO, a training-free data selection framework that treats preference pairs as structured geometric signals. DOG-DPO first represents each preference pair as a direction in model representation space. It then decomposes multi-dataset preference geometry into a global anchor subspace and dataset-specific residual subspaces. Finally, it selects subsets by maximizing diversity-based coverage, encouraging broad, non-redundant coverage of alignment directions before DPO training. Across six safety benchmarks and two model backbones, DOG-DPO achieves a strong utility-robustness trade-off using only 11% of the preference pairs. It recovers most of the safety gains of full-data training while remaining entirely teacher-free, training-free, and substantially faster than representative selection baselines.

03.
arXiv (CS.LG) 2026-06-18

Stealthy World Model Manipulation via Data Poisoning

arXiv:2606.18697v1 Announce Type: new Abstract: Model-based learning agents use learned world models to predict future states, plan actions, and adapt to new environments. However, the process of updating world models from collected experience creates a training-time attack surface: adversarially poisoned fine-tuning trajectories can manipulate the learned dynamics and thereby corrupt downstream planning. In this paper, we propose SWAAP, the first two-stage data poisoning framework for learned world models. In the first stage, SWAAP identifies a harmful target world model that induces low-return behavior under planning while remaining close to clean dynamics, using first-order bilevel optimization enabled by a transition-gradient theorem. In the second stage, SWAAP realizes this target through stealth-constrained gradient matching, modifying only a limited fraction of fine-tuning transition targets so that the induced training gradients steer the victim model toward the adversarial target, while a prediction-error regularizer encourages the poisoned targets to remain close to the world model's natural approximation error. To assess attack stealthiness, we evaluate defenses and detectability across three stages of the poisoning pipeline: pre-training detection of poisoned transitions, robust training during fine-tuning, and test-time monitoring of the resulting world model. Across diverse continuous-control tasks, SWAAP causes substantial performance degradation while keeping poisoned transitions close to clean data and evading the evaluated non-adaptive residual/CUSUM/TRIM-style defenses. These results reveal a practical vulnerability in world-model adaptation pipelines and highlight the need for robustness methods that protect both world-model training data and learned dynamics.

04.
arXiv (quant-ph) 2026-06-19

Random Local Stabilizer Codes in Three Dimensions without String or Self-Similar Fractal Logical Operators

作者:

arXiv:2606.19873v1 Announce Type: new Abstract: Quantum error-correcting codes (QECs) are essential components quantum computation and have deep connections to quantum phases of matter. A key obstruction to passive self-correcting QECs is the presence of string logical operators, which can generate logical errors through constant-energy-barrier processes. Haah's Codes (fracton codes) showed that three-dimensional stabilizer codes can forbid such string logical operators, but their translation-invariant structure supports self-similar fractal logical operators with a logarithmic energy barrier. We introduce the qutrit random cubic codes, a family of local qutrit Calderbank-Shor-Steane stabilizer Hamiltonians with similar cube-check structure as Haah's Code 1 but built from spatially varying stabilizers. We prove that these models retain the no-string property and numerically observe that they have properties distinct from translation-invariant fracton codes: the smallest ground-state degeneracy exponent is $k=2$ for odd $L$ and $k=4$ for even $L$; noncontractible plane-logical operators span the entire logical space; and charge-push diagnostics show that the self-similar fractal operators are absent. These results demonstrate that constrained randomness can fundamentally change the nature of stabilizer codes and improve their self-correction properties. They further point to broader families of quantum error-correcting codes and quantum phases beyond canonical topological and fracton orders.

05.
arXiv (CS.LG) 2026-06-12

BrainPro: Towards Large-scale Brain State-aware EEG Representation Learning

arXiv:2509.22050v2 Announce Type: replace Abstract: Electroencephalography (EEG) reflects underlying brain states, whose activities are distributed across brain regions and manifest as spatial patterns on the scalp. Learning these spatially structured, state-related patterns requires consistent spatial representations across datasets. However, existing EEG foundation models are typically based on self-attention, which does not preserve location-specific information and struggles to align signals recorded with different channel configurations. Moreover, brain states contain both shared and state-specific regional activity, suggesting that learning neurophysiologically plausible, state-aware representations can complement the shared representations targeted by current models and improve downstream decoding. To address these limitations, we propose BrainPro, a large EEG model that combines a retrieval-based spatial learning mechanism for cross-layout spatial alignment with a brain state-decoupling module that learns both shared and state-specific representations through parallel encoders and region-aware reconstruction. Pre-trained on a large EEG corpus, BrainPro achieves state-of-the-art performance across nine public BCI datasets spanning emotion, motor, speech, stress, mental disease, and attention tasks. Analyses of spatial filters, channel-drop robustness, and encoder contributions further validate the effectiveness of its spatial alignment and state-aware pathways. These results show that BrainPro achieves improved interpretability of learned spatial patterns and produces representations that benefit diverse EEG decoding tasks.

06.
medRxiv (Medicine) 2026-06-12

Does the method matter? Evaluating the effectiveness, efficiency and ease of hearing-aid gain self-adjustment

In conventional hearing-aid personalisation, clinicians cannot hear what their patients hear, and patients cannot often reliably detect or describe what they hear. Self-adjustment avoids this issue but requires user controls that adjust hearing-aid signal processing parameters to be effective, efficient and easy. In this study, we explored (a) the roles of interface complexity and stimulus type in the self-adjustment of hearing-aid gain, and (b) how well individuals can adjust one sound to match another to assess the same interfaces and stimuli. Adult hearing-aid users with mild to moderate symmetrical sensorineural hearing loss repeatedly adjusted the gain (a) to their preference from individual prescription (n = 41) and (b) to match their previous preferences from a random starting point (n = 32) using three interfaces representing different bass/mid/treble configurations and three stimuli (music, speech and speech-in-noise). The large interindividual variability in self-adjusted gains clustered into three patterns of deviation from initial prescription: increased relative bass, overall gain reduction, and close to initial prescription. There were no substantial effects of interface nor stimulus on self-adjustment reliability (median {sigma} = 2.8 dB), whereas absolute sound-matching error increased with increasing interface complexity and centre frequency. Neither individual matching accuracy nor questionnaire responses predicted either self-adjusted gains or reliability. Overall, these results show that many - but not all - hearing-aid users can adjust gains with reasonable reliability, and while it can be difficult to predict the behaviour from the individual, the individual applies a similar self-adjustment behaviour across different interfaces and stimuli.

07.
arXiv (quant-ph) 2026-06-12

Quasi-local Edge Mode in XXX Spin Chain/Circuit with Interaction Boundary Defect

arXiv:2603.17835v2 Announce Type: replace-cross Abstract: We study the Heisenberg spin-1/2 model on a semi-infinite chain - or, equivalently, a trotterized unitary SU(2) symmetric six-vertex quantum circuit - with a boundary defect where the interaction between the two spins nearest the edge differs from that in the bulk. For sufficiently strong boundary interaction we explicitly construct a conserved operator quasi-localized near the boundary using a matrix-product ansatz. This quasi-local edge mode leads to non-decaying boundary correlation functions, corresponding to a nonzero boundary Drude weight. The correlation length of the edge mode diverges at a finite critical value of the boundary interaction, signaling a transition to ergodic boundary dynamics for subcritical interactions.

08.
Science (Express) 2026-05-28

A Hormone Cell Atlas maps the human endocrine system at cellular resolution | Science

作者: 未知作者

Hormones act across tissues and organs to coordinate physiological functions. Drawing inspiration from the Human Cell Atlas, we analyzed expression of 379 hormone and receptor genes in a transcriptomic dataset comprising 14 million single cells and nuclei across 47 human tissues. Using hormone2cell, we mapped putative hormone-producing and hormone-receiving cell types, defining tissue-specific and cross-tissue endocrine signatures. We predicted non-classical sites of hormone expression, including secretin in plasmacytoid dendritic cells, inferred convergent hormone action and endocrine feedback loops, and implicated cell populations in monogenic endocrine disorders. In a cross-tissue integration of adipocyte datasets, we uncovered dynamic endocrine programs across depots, within adipocyte subtypes and through adipogenic differentiation. Cumulatively, the Hormone Cell Atlas ( hormonecellatlas.org.uk ) provides a comprehensive framework for dissecting hormonal impact on health and disease.

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

Feature Attribution in Directed Acyclic Graphs Using Edge Intervention

arXiv:2606.15273v1 Announce Type: new Abstract: Shapley value-based feature attribution methods face challenges in scenarios involving complex feature interactions and causal relationships, even when a causal structure is provided. Existing methods typically adopt a node-centric view, attributing importance solely to individual features. Consequently, they often fail to simultaneously capture the externality and exogenous influence of features, leading to unreasonable interpretations. To overcome these limitations, we propose a novel feature attribution method called DAG-SHAP, which is based on edge intervention. DAG-SHAP treats each feature edge as an individual attribution object, ensuring that both externality and exogenous contributions of features are appropriately captured. Additionally, we introduce an approximation method for efficiently computing DAG-SHAP. Extensive experiments on both real and synthetic datasets validate the effectiveness of DAG-SHAP. Our code is available at https://github.com/ZJU-DIVER/DAG-SHAP.

10.
arXiv (CS.CL) 2026-06-16

SHARD: Safe and Helpful Alignment via Self-Reframing Distillation

Large language models often struggle with sensitive prompts. They may refuse outright, provide generic safety boilerplate, or fail to address the user's legitimate informational needs that can be answered safely. We introduce SHARD, a self-reframing distillation method to improve safe-helpfulness. It first rewrites sensitive prompts to surface benign intent using philosophical guidelines, then reframes its original responses into safe, more helpful ones, and finally fine-tunes the model on its self-reframed responses. Across DNA and the English subset of LINGUASAFE, SHARD improves helpfulness for most model families while preserving safety. It also remains competitive with distillation from a larger teacher model, suggesting that models can internalize safe and helpful behavior elicited from their own. Warning: This paper contains content that may be offensive or harmful.

11.
arXiv (math.PR) 2026-06-17

Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions

arXiv:2508.15032v2 Announce Type: replace Abstract: It is shown that two conjectures put forward in the recent article Iksanov and Kostohryz (2025) are true. Namely, we prove a functional central limit theorem (FCLT) and a law of the iterated logarithm (LIL) for a random Dirichlet series $\sum_p \frac{\eta_p}{p^{1/2+s}}$ as $s\to 0+$, where $\eta_1$, $\eta_2,\ldots$ are independent identically distributed random variables with zero mean and finite variance, and $\sum_p$ denotes the summation over the prime numbers. As a consequence, an FCLT and an LIL are obtained for $\log \sum_{n\geq 1} \frac{f(n)}{n^{1/2+s}}$ as $s\to 0+$, where $f$ is a Rademacher random multiplicative function.

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

Beyond a Single Explanation of the Adam–SGD Gap

arXiv:2606.14259v1 Announce Type: new Abstract: Prior work has identified several factors that can contribute to the performance gap between Adam and SGD, spanning data aspects, architecture design, and optimization properties. Yet these explanations are often studied in isolation, leaving their relative importance unclear. In this work, we revisit these hypotheses through a controlled empirical study across vision, language, genomics, and graph tasks, spanning modern and classical architectures, and carefully designed training setups. Our results suggest that no single factor consistently explains the Adam–SGD gap. For instance, the Adam advantage can (1) persist under a uniform vocabulary distribution yet nearly disappear under a heavy-tailed one; (2) reverse in favor of SGD in softmax-attention models; and (3) become larger under soft architectural modifications, e.g., when ReLU is replaced by a GeLU nonlinearity. This suggests that the gap arises from nontrivial data and architecture interactions, rather than from a single common factor. Yet, we observe a pattern across our settings: a crossover batch size at which the relative advantage shifts from SGD to Adam as the batch size scales. These empirical results are captured by our theoretical gap model, which predicts this batch-size-dependent crossover. Our perspective helps reconcile several existing hypotheses while offering practical insights across domains.

13.
arXiv (CS.AI) 2026-06-12

Brick: Spatial Capability Routing for the Mixture-of-Models (MoM) Paradigm

arXiv:2606.13241v1 Announce Type: new Abstract: Defining query difficulty is one of the hardest problems in deployment engineering. Existing LLM routers rely on surface features such as domain labels, keywords, and token count, ignoring the within-domain variance that actually determines model success. Frontier models cost ten to one hundred times more than local open-weight models, so at production scale even small per-request savings become a direct cloud-bill lever. We present Brick, a multimodal router that scores each model on six capability dimensions, combines this with a per-query difficulty estimate, and dispatches via a cost-penalized geometric rule. A continuous preference knob lets operators slide between max-quality and max-saving profiles at deploy time. On a benchmark of 5,504 queries, Brick at max-quality reaches 76.98% accuracy, beating the best single model (75.02%) and all tested routers. At a neutral cost-quality profile, Brick achieves 74.11% accuracy at 4.71x lower cost than always using the strongest model. At min-cost, it cuts cost 22.15x with 11.85 points accuracy loss. Median latency drops from 51.2s to 22.8s.

14.
arXiv (CS.CL) 2026-06-11

Context-Driven Incremental Compression for Multi-Turn Dialogue Generation

Modern conversational agents condition on an ever-growing dialogue history at each turn, incurring redundant attention and encoding costs that grow with conversation length. Naive truncation or summarization degrades fidelity, while existing context compressors lack cross-turn memory sharing or revision, causing information loss and compounding errors in long dialogues. We revisit the context compression under conversational dynamics and empirically present its fragility. To improve both efficiency and robustness, we introduce Context-Driven Incremental Compression (C-DIC), which treats a conversation as interleaved contextual threads and stores revisable per-thread compression states in a single, compact dialogue memory. At each turn, a lightweight retrieve, revise, and write-back loop shares information across turns and updates stale memories, stabilizing long-horizon behavior. In addition, we adapt truncated backpropagation-through-time (TBPTT) to our multi-turn setting, learning cross-turn dependencies without full-history backpropagation. Extensive experiments on long-form dialogue benchmarks demonstrate superior performance and efficiency of C-DIC; notably, C-DIC shows stable inference latency and perplexity over hundreds of dialogue turns, supporting a scalable path to high-quality dialogue modeling.

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

Imperfect Visual Verification for Code Edition : A Case Study on TikZ

arXiv:2606.15693v1 Announce Type: cross Abstract: LLMs have significantly advanced code generation, enabling the synthesis of functional programs. While recent systems achieve strong performance on many coding benchmarks, tasks involving programs such as TikZ that generate visual artifacts remain challenging, in particular on visual code customization. Unlike generation from scratch, customization requires localized, semantics-preserving edits: the model must locate relevant code, modify it according to the instruction, and preserve the remaining structure and rendering. Approaches based on post-hoc iterative refinement/correction where a verifier provides feedback to guide corrections, have shown promise. However, in the case of programs with a visual outcome such as in TikZ, where correctness is harder or likely impossible to formalize and evaluate automatically, deterministic verifiers do not exist. Hence, developers can only rely on imperfect verifiers. In this paper, we conduct an empirical study to answer:to what extent can iterative refinement remain effective when the verifier itself is unreliable?} We use TikZ as a focused case study that isolates the core difficulties of the problem (weak code structure, fine-grained visual semantics, and difficult feature localization) in a controlled and challenging setting. We define visual code customization as an iterative editing problem with an imperfect oracle, and introduce a framework for analyzing such iterative refinements. We conduct a large-scale study and evaluate multiple LLM-based and tool-augmented visual verifiers within iterative refinement pipelines, and perform extensive manual annotation of refinement trajectories to assess verifier behavior and feedback quality. Our findings show that even imperfect verifiers can determine with moderate accuracy whether visual instructions are applied to code, achieving F1-scores up to 0.815. Feedback improves iterative refinement, especially for weaker models, adding 11–20 perfect customizations for Qwen3-vl-30b-a3b-Instruct, while stronger models like Gemini-3 gain fewer improvements (+5) but benefit more from accurate verification that prevents premature acceptance. Feedback is effective only when it precisely identifies image issues, provides actionable guidance, addresses all relevant problems, and remains grounded in the original instruction.

16.
arXiv (CS.CL) 2026-06-12

KCSAT-ML: Probing Reasoning Models with Nationwide-Cohort Human Difficulty

Math reasoning benchmarks have proliferated, yet most lack a per-item difficulty signal grounded in actual human performance. We introduce KCSAT-ML, a decade (2014-2025) of Korean College Scholastic Ability Test (KCSAT; Suneung) mathematics: 664 problems with a 339-item core set carrying official per-item error rates from nationwide cohorts of hundreds of thousands of examinees. We pair the benchmark with Difficulty-aligned Reasoning Gain (DRG): a score-orthogonal metric that asks whether a model's mistakes concentrate on the items humans found hard, or on items humans found easy. Together they expose, across a wide range of VLMs (and LLMs via OCR), three patterns: (i) low-budget accuracy collapses on the high-human-error tail at every model size; (ii) test-time scaling (TTS) raises token use roughly linearly with cohort error rate, while accuracy gains follow a non-monotonic curve; (iii) within a single family, TTS flips between anti-scaling on the hardest items and overthinking on easier ones – two faces of the same alignment failure. On DRG, models with near-identical accuracy can sit at near-opposite values: one model gets wrong what humans also find hard, while another solves the hardest items yet fails on items humans find easy – a contrast that aggregate accuracy hides. Our code and dataset builder will be open-sourced at https://github.com/naver-ai/KCSAT-ML.

17.
arXiv (CS.AI) 2026-06-17

SP-GCRL: Influence Maximization on Incomplete Social Graphs

arXiv:2605.12513v2 Announce Type: replace-cross Abstract: Influence maximization (IM) in real platforms is challenged by incomplete, noisy social graphs and non-stationary diffusion dynamics. We propose SP-GCRL, a social-propagation-aware graph contrastive reinforcement learning framework that learns end-to-end seed selection under partial observability.We first introduce a social-propagation-aware nonlinear diffusion function to model reinforcement/diminishing effects and probability drift under repeated exposure; we then construct dual structural views and perform contrastive learning to obtain node representations robust to missing edges and weak ties, while replacing expensive strategy metrics with a GAT-based regression surrogate to improve efficiency and scalability; finally, we use DDQN to learn an end-to-end seed selection policy on top of these representations. Experiments on multiple real-world networks show that SP-GCRL achieves significant gains over heuristic and learning-based baselines across budgets and topologies, while maintaining strong large-scale scalability.

18.
arXiv (CS.CV) 2026-06-15

A Robust Point Cloud Analysis Framework Inspired By Primary Visual Cortex

Despite significant advancements in point cloud analysis, reducing energy consumption and improving robustness remain understudied, largely due to the inherent limitations of Convolutional Neural Networks (CNNs). To address this issue, we draw inspiration from the primary visual cortex and propose a Dendritic-Connected Continuous-Coupled Neural Network (DC-CCNN), a novel Brain-Inspired Neural Network (BINN) architecture for point cloud analysis. By combining discrete and continuous encoding, our design replaces traditional Multilayer Perceptrons (MLPs) with more efficient and robust BINNs. Building upon this framework, we further propose an extended model, DC-CCNN++, to improve robustness under complex corruption conditions. Specifically, we introduce a Neuro-Inspired Robust Modulation-and-Readout Module (NRMR) to enhance feature stability and decision robustness through global-context gain modulation and dual-code evidence integration. We also design a Cortically Inspired Progressive Variability Training (CPVT) strategy, which progressively exposes the model to structured environmental variability while preserving stable clean-sample anchors during training. Experimental results show that DC-CCNN++ improves the performance of brain-inspired networks on point cloud analysis while maintaining performance comparable to state-of-the-art methods. Compared with the original DC-CCNN, it achieves stronger results on both classification and part segmentation, and exhibits enhanced robustness against sparsity, occlusion, Gaussian noise, salt-and-pepper noise, and spatial transformations. With its efficiency, robustness, and biologically grounded design, DC-CCNN++ provides a promising alternative to traditional deep learning methods for point cloud analysis. Code is available at https://anonymous.4open.science/r/DC-CCNNpp-44E3.

19.
arXiv (CS.AI) 2026-06-11

Sustainability assessment using multimodal AI agents

arXiv:2507.17012v2 Announce Type: replace Abstract: Reducing the rapidly growing environmental impact of the computing industry requires assessing the emissions of electronics at scale. However, a traditional life cycle assessment (LCA) of an electronic device, which maps materials and processes to environmental impacts, often requires proprietary or unavailable data. Here, we reimagine conventional sustainability assessment by introducing a multimodal multi-agent AI system that emulates the collaborative process between LCA professionals and stakeholders (such as product managers and engineers) to automatically estimate the carbon footprint of electronic devices. The agents iteratively construct a complete life-cycle inventory by leveraging a structured data abstraction and software tools that mine information from the public internet, including repair communities and government regulatory databases. This reduces data gaps and data collection from weeks or months of expert time to under one minute. The system can calculate carbon footprint within 19% of expert LCAs with zero proprietary data (typical of the variation between human LCAs). We also show that by encoding domain-specific knowledge, environmental impact estimation can be reframed as a data-driven prediction task, in which both unknown products and emission factors are represented as weighted combinations of similar ones with known emissions.

20.
arXiv (CS.CV) 2026-06-15

Connections Between Pairs of Filters Improve the Accuracy of Convolutional Neural Networks

While researchers continue to find new and improved network structures for CNNs, most of the newly invented architectures still rely on the traditional pattern of stacking convolutional blocks and separating them with pointwise activation functions. However, there are drawbacks to a network purely building on pointwise nonlinearities. One alternative is to introduce a pairwise connection between two filters of a network. Typical connection functions use multiplications or the minimum operation to realize logical AND connections. In this paper, we go one step further by demonstrating that CNNs can benefit from more general connections, which include parameters that are learned. With such parameters, the network is able to implement different connections in different network layers and better adapt the connection function to the task at hand.

21.
Nature (Science) 2026-06-10

Building user-driven climate adaptation products

Climate adaptation products have traditionally been developed using a supply-driven model reliant on available climate information, leading to usability gaps1–4. To better meet user needs, the climate services field has recognized a need to shift towards a demand-driven model emphasizing co-production, that is, user-driven, scientifically informed products created through shared knowledge practices1–5. However, co-production can be challenging, especially for researchers unfamiliar with the approach or for digital and software-based products with complex user needs2,5–8. User-centred design, from the human–computer interaction field, offers a process that could complement co-production approaches to product development, yet its potential remains underexplored2. Here we show how user-centred design can be integrated into, and strengthen, co-production approaches for building user-driven climate adaptation products. Through a systematic review of the co-production and user-centred design literature, we identify key processes, mechanisms and best practices for both approaches. Our findings offer practical guidance for researchers and propose an integrated approach for developing climate adaptation products that are useful, usable and used. A systematic review and analysis shows how user-centred design can be integrated into, and strengthen, co-production approaches for building user-driven climate adaptation products.

22.
arXiv (math.PR) 2026-06-12

Sphere Packings in Higher Dimension (after Boaz Klartag)

arXiv:2606.13313v1 Announce Type: cross Abstract: Let $\delta_n^L$ be the maximal density of a lattice sphere packing in the $n$-dimensional Euclidean space. We explain how Boaz Klartag proved the inequality $\delta_n^L \geq c n^2 2^{-n}$ where $c>0$ is a universal constant. In higher dimension, even for non-lattice sphere packings, this new lower bound is a substantial improvement. Klartag's proof uses the probabilistic method in two different ways. The first, very standard, relies on the statistical properties of a uniformly chosen random lattice. The second, completely new, studies the stochastic evolution of an ellipsoid constrained to contain non nonzero lattice points in the interior.

23.
arXiv (CS.AI) 2026-06-16

Adaptive inference and function vectors in deep transformers

arXiv:2606.16694v1 Announce Type: cross Abstract: Transformers are widely used as a general-purpose substrate for learning complex correlations between a large collection of coupled variables, but their internal mechanisms have remained mysterious. We introduce a theory of a deep transformer as a mean-field interacting system that implements distributed inference, subject to constraints on communication, locality and depth. We show that such a system can exploit internal state representations ('function vectors') to infer a latent context variable at increasingly finer scales over its layers. In an in-context regression task, the theory predicts a non-trivial relationship between non-Gaussian, hierarchical structure in the latent context variable, and transformer depth. Predictions are tested using constrained linear attention transformers and demonstrate adaptive inference in deep architectures. Feedforward blocks and depth enable transformers to implement a much richer class of in-context learning algorithms than previously described.

24.
arXiv (math.PR) 2026-06-17

Cutoff for asymmetric shelf shuffle

arXiv:2606.18039v1 Announce Type: new Abstract: A mechanical shuffler consists of $m$ shelves. A deck of $n$ cards, arranged in increasing order, is dealt from the bottom sequentially. Each card is assigned a shelf uniformly at random and placed on the top (bottom) of the existing pile with probability $p$ ($1-p$) independently. We refer to this as asymmetric shelf-shuffle. We find the law $\nu_{n, m}^{(p)}$ of the permutation induced by the asymmetric shelf-shuffle and show that the pair consisting of the number of descents and the number of valleys is a sufficient statistic. This generalizes a result of Diaconis, Fulman, and Holmes (Ann. Appl. Prob., 2013) corresponding to the case $p=1/2$. For $p=1/2$, Chen and Ottolini (ECP, 2025) established the cutoff in the total variation distance near $\lfloor n^{5/4}\rfloor$. We establish the cutoff for the asymmetric shelf shuffle. Let $\nu_n$ be the uniform measure on the set of all permutations $S_n$ of $\{1, \ldots, n\}$. For a fixed $p\neq 1/2$ and $c>0$, we show that \[\operatorname{TV}\left(\nu_{n, \lfloor cn^{3/2}\rfloor }^{(p)}, \nu_n\right)=1-2\Phi\left(-\frac{|2p-1|}{4\sqrt{3}c}\right)+O_{c, p}(n^{-1/2})\;.\] We also establish the cutoff in the separation distance near $m\approx n^{2}$ and in the relative entropy near $m=n^{3/2}$. In both cases, we also obtain the cutoff profile explicitly.

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

GroupToM-Bench: Benchmarking Group Theory of Mind and Nonlinear Social Emergence in MLLMs

True general intelligence requires not only a model of the physical world but also a social world model: the capacity to infer how individual mental states interact and crystallize into group-level outcomes. Despite notable progress in individual-level Theory of Mind (ToM) reasoning, existing multimodal large language models fail at this broader task. Collective behavior emerges non-linearly from social tensions, conformity dynamics, and structural constraints, meaning it cannot be recovered by merely summing individual intentions. We present GroupToM-Bench, the first multimodal benchmark for group-level ToM, built around a causal chain spanning micro-level BDI states (belief, desire, intention), meso-level group tension and structural constraints, and macro-level outcome prediction and mechanistic attribution. To probe this full arc, we develop a seven-level cognitive audit framework. Experiments reveal a gap between current models and human baselines, highlighting a failure to process social structures and non-linear collective dynamics.