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

A Compositional Framework for Open-ended Intelligence

arXiv:2606.15386v1 Announce Type: new Abstract: Open-ended intelligence is the capacity to adapt to novel problems and environments that are substantially different from those in training. We formalize open-ended intelligence as the closure induced by a finite primitive set \(P\) and a set of composition operators \(C\). We characterize properties of the induced closure \(\mathcal{L}(P,C)\) that support unbounded compositional generation across families of tasks and worlds. A mathematics of open-ended intelligence requires two pillars: a minimal set of representational primitives (e.g., states, actions) and algorithmic primitives (e.g., nearest neighbor), together with composition motifs (e.g., recursion, sequencing) that reflect an acquired compositional grammar. The closure of these two pillars enables the generation of infinite adaptive responses across a wide range of settings. The mathematics supports complementary research agendas, including evaluation metrics for explanation and interpretability, as well as building architectures where compositional generalization is native. We propose next primitive prediction as a novel architectural objective, where the training objective encourages the acquisition of reusable algorithmic primitives and their compositional grammar, such that new solutions are generated through recombination. Curriculum learning and self-play enable lifelong learning and expansion of the closure by discovering reusable primitives and transition motifs across families of tasks and worlds. We ground the framework through case studies in physics, evolution, and neuroscience.

03.
arXiv (math.PR) 2026-06-19

Model-independent upper bounds for the prices of Bermudan options with convex payoffs

arXiv:2503.13328v3 Announce Type: replace-cross Abstract: Suppose $\mu$ and $\nu$ are probability measures on $\mathbb{R}$ satisfying $\mu \leq_{cx} \nu$. Let $a$ and $b$ be convex functions on $\mathbb{R}$ with $a \geq b \geq 0$. We are interested in finding $$\sup_{\mathbf{M}} \sup_{\tau} \mathbb{E}^{\mathbf{M}} \left[ a(X) I_{ \{ \tau = 1 \} } + b(Y) I_{ \{ \tau = 2 \} } \right] $$ where the first supremum is taken over consistent models $\mathbf{M}$ (i.e., filtered probability spaces $(\Omega, \mathbf{F}, \mathbb{F}, \mathbb{P})$ such that $Z=(z,Z_1,Z_2)=(\int_{\mathbb{R}} x \mu(dx) = \int_{\mathbb{R}} y \nu(dy), X, Y)$ is a $(\mathbb{F},\mathbb{P})$ martingale, where $X$ has law $\mu$ and $Y$ has law $\nu$ under $\mathbb{P}$) and $\tau$ in the second supremum is a $(\mathbb{F},\mathbb{P})$-stopping time taking values in $\{1,2\}$. Our contributions are first to characterise and simplify the dual problem, and second to completely solve the problem under some structural assumptions on the measures $\mu$ and $\nu$ (namely that $\mu$ and $\nu$ are absolutely continuous probability measures that satisfy the Dispersion Assumption). A key finding is that the canonical set-up in which the filtration is that generated by $Z$ is not rich enough to define an optimal model and additional randomisation is required. This holds even though the marginal laws $\mu$ and $\nu$ are atom-free. The problem has an interpretation of finding the robust, or model-free, no-arbitrage bound on the price of a Bermudan option with two possible exercise dates, given the prices of co-maturing European options.

04.
medRxiv (Medicine) 2026-06-22

GCH1 p.Ser80Asn Confers Risk for Parkinson's Disease in East Asian Populations

Introduction: GCH1 has been implicated in Parkinson's disease (PD), but its risks variants and associations are not well defined. Objectives: To investigate the clinical relevance and PD risk associated with the GCH1 p.Ser80Asn variant. Methods: We first identified a segregating GCH1 p.Ser80Asn variant in a Malaysian Chinese PD family via whole genome sequencing (WGS). We assessed its risk association using multi-ancestry WGS data from the Global Parkinson's Genetics Program (GP2) (n=22,372PD vs n=8,826Controls) and meta-analysis of East Asian (EAS) cohorts (n=4,712PD vs 38,733Controls). Clinico-demographic details of affected variant carriers were collated. Results: The GCH1 p.Ser80Asn variant was enriched in GP2 EAS PD populations (n=9/2,757; 0.33%) but not detected in other ancestries. Meta-analysis revealed increased PD risk in EAS populations (odds ratio:5.1; 95%CI:2.3-10.7; p=2.89x10-5). Affected carriers (mean age at onset:56.3+-12.5 years) had additional occurrence of dystonia, while dementia was rare. Conclusions: The GCH1 p.Ser80Asn variant is a rare, EAS-enriched risk variant for PD.

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

LatentLens: Revealing Highly Interpretable Visual Tokens in LLMs

Transforming a large language model (LLM) into a vision-language model (VLM) can be achieved by mapping the visual tokens from a vision encoder into the embedding space of an LLM. Intriguingly, this mapping can be as simple as a shallow MLP transformation. To understand why LLMs can so readily process visual tokens, we need interpretability methods that reveal what is encoded in the visual token representations at every layer of LLM processing. In this work, we introduce LatentLens, a novel approach for mapping latent representations to descriptions in natural language. LatentLens encodes a large text corpus and stores contextualized token representations for each token in that corpus. Visual token representations are then compared to these contextualized representations and the top-nearest neighbor representations serve as descriptions of the visual token. We evaluate this method on 15 different VLMs, showing that commonly used methods, such as LogitLens, substantially underestimate the interpretability of visual tokens. With LatentLens instead, the majority of visual tokens are interpretable across all studied models and all layers. Qualitatively, we show that the descriptions produced by LatentLens are semantically meaningful and provide more fine-grained interpretations for humans compared to individual tokens. More broadly, our findings contribute new evidence on the alignment between vision and language representations and open up new directions for analyzing the latent representations of LLMs.

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

Learning When to Sample: Confidence-Aware Selective Sampling for Efficient Chain-of-Thought Reasoning

Large language models (LLMs) can achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet they often generate unnecessarily long reasoning paths that incur high inference cost. Self-consistency-based approaches push accuracy higher still, but they require sampling and aggregating multiple reasoning trajectories, leading to substantial computational overhead. In this paper, we introduce a confidence-aware selective sampling framework that, at inference time, analyzes a single reasoning trajectory to adaptively determine whether to rely on that trajectory alone or trigger multi-path sampling. The framework uses trajectory-level numeric features and sentence-level linguistic features extracted from reasoning states to guide selective multi-path reasoning. We train it on MedQA and evaluate it in-domain on MedQA and under calibration-only transfer on MathQA, MedMCQA, and MMLU, without further fine-tuning. Experimental results show that the proposed framework maintains comparable performance to full and efficient multi-path reasoning baselines, with accuracy changes of $-0.41 \pm 0.58$ and $-0.31 \pm 0.58$ percentage points, respectively, while reducing token usage by $71.7 \pm 5.0%$ and $36.6 \pm 9.1%$. These findings demonstrate that reasoning trajectories contain rich signals for uncertainty estimation, enabling a simple, transferable mechanism to balance accuracy and efficiency in LLM reasoning.

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

Convex Approximation of Two-Layer ReLU Networks for Hidden State Differential Privacy

arXiv:2407.04884v4 Announce Type: replace Abstract: The hidden state threat model of differential privacy (DP) assumes that the adversary has access only to the final trained machine learning (ML) model, without seeing intermediate states during training. However, the current privacy analyses under this model are restricted to convex optimization problems, reducing their applicability to multi-layer neural networks, which are essential in modern deep learning applications. Notably, the most successful applications of the hidden state privacy analyses in classification tasks have only been for logistic regression models. We demonstrate that it is possible to privately train convex problems with privacy-utility trade-offs comparable to those of 2-layer ReLU networks trained with DP stochastic gradient descent (DP-SGD). This is achieved through a stochastic approximation of a dual formulation of the ReLU minimization problem, resulting in a strongly convex problem. This enables the use of existing hidden state privacy analyses and provides accurate privacy bounds also for the noisy cyclic mini-batch gradient descent (NoisyCGD) method with fixed disjoint mini-batches. Empirical results on benchmark classification tasks demonstrate that NoisyCGD can achieve privacy-utility trade-offs on par with DP-SGD applied to 2-layer ReLU networks.

08.
arXiv (CS.LG) 2026-06-15

A Water Efficiency Dataset for African Data Centers

arXiv:2412.03716v3 Announce Type: replace Abstract: Artificial intelligence (AI) computing and data centers consume large amounts of freshwater, both directly for cooling and indirectly for electricity generation. While most attention has been paid to developed countries such as the U.S., this paper presents the first-of-its-kind dataset that combines nation-level weather and electricity generation data to estimate water usage effectiveness for data centers in 41 African countries across five different climate regions. We also use our dataset to evaluate and estimate the water consumption of inference on two large language models (i.e., Llama-3-70B and GPT-4) in 11 selected African countries. Our estimates suggest that writing a 10-page report using Llama-3-70B could consume as much as {0.66 liters} of water, while the water consumption by GPT-4 for the same task may go up to about {59 liters}. For writing a medium-length email of 120-200 words, Llama-3-70B and GPT-4 could consume about {0.13 liters} and {2.9 liters} of water, respectively. All the numbers for generative model inference tasks are based on public information available in 2024, when we initially prepared the analysis. Since then, AI inference systems have improved substantially. For example, recent disclosures suggest that energy efficiency improved by more than 30x between May 2024 and May 2025. Accordingly, our 2024 estimates should be interpreted as historical reference values rather than as representative of current performance. Interestingly, given the same AI model, 9 of the 11 selected African countries consume less water than the global average, mainly because of lower water intensities for electricity generation.

09.
arXiv (CS.CV) 2026-06-18

Recognizing and Reconstructing a Multi-Unit Floor Plan

Digital twins have a major potential to form a significant part of urban management in emergency planning, as they allow more efficient designing of the escape routes, better orientation in exceptional situations, and faster rescue intervention. Nevertheless, creating the twins still remains a largely manual effort, due to a lack of 3D-representations, which are available only in limited amounts for some new buildings. Thus, in this paper we aim to synthesize 3D information from commonly available 2D architectural floor plans. We propose two novel pixel-wise segmentation methods based on the MDA-Unet and MACU-Net architectures with improved skip connections, an attention mechanism, and a training objective together with a reconstruction part of the pipeline, which vectorizes the segmented plans to create a 3D model. The proposed methods are compared with two other state-of-the-art techniques and several benchmark datasets. On the commonly used CubiCasa benchmark dataset, our methods have achieved the mean F1 score of 0.86 over five examined classes, outperforming the other pixel-wise approaches tested. We have also made our code publicly available to support research in the field.

10.
bioRxiv (Bioinfo) 2026-06-18

Deciphering shared and divergent tissue architectures from cross-species spatial transcriptomics

Authors:

The integration of spatial transcriptomics (ST) data across species is essential for cross-species and translational studies, but remains challenging due to molecular divergence and anatomical differences between organisms. We present STACAME, a graph attention autoencoder-based framework to decipher shared and divergent tissue architectures from cross-species ST data by explicitly modeling both orthologous and species-specific genes. STACAME aligns ST slices in a spatially aware manner, identifies homologous and species-specific domains, and enables a suite of downstream comparative analyses. We demonstrate its utility by integrating ST datasets from diverse tissues, including hippocampus, isocortex, embryo, breast, liver, and cerebellum, across multiple species such as human, macaque, marmoset, mouse, and zebrafish. STACAME supports cross-species spatial domain alignment, the detection of shared and divergent spatially variable genes, development alignment and comparison, and the 3D integration of tissue architecture. This flexible approach facilitates the translation of findings from model organisms to humans, providing a unified computational platform for cross-species spatial transcriptomics.

11.
arXiv (CS.CL) 2026-06-17

LLM Features Can Hurt GNNs: Concatenation Interference on Homophilous Graph Benchmarks

Adding LLM-generated node features to graph neural networks (GNNs) is widely reported to improve accuracy on standard benchmarks. We document a contrasting observation: when LLM features are introduced through pure input concatenation (rather than joint training, distillation, or prompt-conditioning), they can systematically degrade accuracy on the same homophilous benchmarks where end-to-end LLM pipelines succeed. With an MLP backbone on the Planetoid public split and bag-of-words original features, concatenating SBERT-encoded GPT-4o-mini TAPE features reduces PubMed test accuracy by -17.0 +/- 0.3 pp and Cora by -4.3 +/- 0.6 pp (CiteSeer -0.6 +/- 0.8 pp, within seed noise). The drop attenuates as we relax each condition (GCN / GCNII / GAT backbones, random splits, smaller encoders) and reverses on medium-homophily WikiCS (+4.4 pp) and ogbn-arxiv (+11.7 pp). To predict when concatenation helps versus hurts, we report a simple measure of LLM-alone discriminability, Delta_sig. Across 9 datasets Delta_sig correlates with the concatenation cost more strongly than homophily at point estimate (r^2 = 0.38 vs. 0.06; N=9, bootstrap CIs overlap). The bootstrap-best change-point is tau = 13.8 pp, and the rule "Delta_sig

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

Is Code Better Than Language for Algorithmic Reasoning

arXiv:2606.15589v1 Announce Type: cross Abstract: For tool-augmented language models, comparing natural-language reasoning with code-execution pipelines is difficult because the comparison changes both the intermediate representation and the execution mechanism. We separate these factors with an intermediate intervention: the model expresses its reasoning as executable code, and the language model simulates that code in context to produce an answer. On a 40-task verifiable algorithmic benchmark, deterministic code execution outperforms natural-language reasoning by +31.6pp. We observe that the intermediate intervention is not meaningfully different from natural-language reasoning (+0.15pp). These results suggest that, in our evaluated setting, changing the intermediate representation alone does not explain the tool-use advantage, providing evidence for the performance gains requiring reliable external execution. We formalize this intuition with a simple statistical decision-theoretic model that characterizes when execution dominates end-to-end risk in our disentangled trace-generation/execution regime. We validate our theory using a reconstruction intervention that leverages a proxy language model to infer natural-language reasoning traces from code representations, recovering performance comparable to the original natural-language reasoning pipeline. All experiments are at https://github.com/TerryTong-Git/ToolProj.

13.
arXiv (CS.AI) 2026-06-19

Superhuman Safe and Agile Racing through Multi-Agent Reinforcement Learning

arXiv:2605.22748v2 Announce Type: replace-cross Abstract: Autonomous systems have achieved superhuman performance in isolation or simulation, yet they remain brittle in shared, dynamic real-world spaces. This failure stems from the dominant single-agent paradigm for physical applications, where other actors are ignored or treated as environmental noise, preventing effective coordination. Here we show that multi-agent reinforcement learning provides the essential safety scaffolding required for real-world interaction. Using high-speed quadrotor racing as a high-stakes testbed, we train agents to navigate complex aerodynamic interactions and strategic maneuvering with a variable number of racers. Through league-based self-play, agents evolve sophisticated anticipatory behaviors, including proactive collision avoidance, overtaking, and handling multi-agent physical interactions, including aerodynamic downwash. Our agents outperform a champion-level human pilot in multi-player races at speeds exceeding 22 m/s, while simultaneously reducing collision rates by 50 % compared to state-of-the-art single-agent baselines. Crucially, training with diverse artificial agents enables zero-shot generalization to safer human interaction. These results suggest that the path to robust robotic co-existence lies not in isolated safety constraints, but in the rigorous demands of multi-agent interaction. Multimedia materials are available at: https://rpg.ifi.uzh.ch/marl

14.
arXiv (CS.CV) 2026-06-17

CIAN: Multi-Stage Framework for Event-Enriched Image Captioning via Retrieval-Augmented Generation

Event-enriched image captioning describes not only visible content but also the broader context of events, including timing, location, and participants, capabilities missing in most pixel-bound models. We propose the Contextual Image-Article Narrator (CIAN), a multi-stage framework that enriches captions with external narratives. CIAN retrieves relevant articles using SigLIP, summarizes them to guide a Narrative Generation stage with a LoRA-fine-tuned Qwen model, and applies N-Gram-based Refinement for fluency and coherence. On the OpenEvents-V1 benchmark, CIAN achieves high retrieval performance (mAP 0.979) and improves caption quality, increasing CIDEr from 0.030 to 0.094. These results highlight the effectiveness of retrieval-augmented reasoning combined with linguistic refinement for generating context-aware, human-like captions.

15.
arXiv (CS.AI) 2026-06-11

Continual Quadruped Robots Coordination via Semantic Skill Discovery

arXiv:2606.08102v2 Announce Type: replace-cross Abstract: Multi-quadruped coordination has attracted increasing attention due to its enhanced payload capacity, broader contact coverage, and improved adaptability to challenging tasks. Existing methods for multi-quadruped manipulation typically focus on predefined or closed task families, often relying on multi-agent reinforcement learning (MARL) to train task-specific coordination policies. However, such methods struggle in open-ended continual learning settings, where tasks arrive sequentially and robots are expected to acquire new coordination skills while reusing previously learned ones without catastrophic forgetting. To address this challenge, we propose Conquer, a semantic skill-library framework that formulates continual multi-quadruped coordination as a retrieve-adapt-update process. First, to accommodate varying team sizes across tasks, we design a team-structured Self-Allies-Goal (SAG) backbone that supports variable-cardinality robot teams by explicitly modeling each robot's own state, teammate context, and task goal. For each incoming task, Conquer constructs a task-level semantic descriptor from pre-execution information and retrieves a relevant skill from the library for adaptation. After successful execution, Conquer updates the skill library by extracting trajectory-level semantic descriptors and organizing them according to semantic distance, thereby enabling continual skill accumulation and cross-task knowledge transfer. Simulation experiments show that Conquer achieves a final average success rate of 95.6%, demonstrating strong forward transfer and negligible catastrophic forgetting. Real-world rollouts on Unitree Go2 teams further validate the deployment feasibility of Conquer for practical multi-quadruped coordination. Simulation and real-robot demonstration videos are available at: https://conquer-project.pages.dev/.

16.
arXiv (math.PR) 2026-06-17

Persistence diagrams of random triangular matrices over finite fields

arXiv:2606.17895v1 Announce Type: cross Abstract: Let us consider a random infinite lower triangular matrix, where the entries on and below the diagonal are i.i.d. uniform random elements of a fixed finite field. We investigate the evolution of the span of the first $n$ rows of this matrix as $n$ grows. Many properties of this evolving subspace can be captured with the help of the verbose persistence diagram, which is a standard tool in stochastic topology and topological data analysis. We give an explicit formula for the distribution of the persistence diagram. We prove a law of large numbers for the distribution of lifetimes. We also describe the fluctuations of the persistent Betti numbers.

17.
arXiv (quant-ph) 2026-06-11

Additivity and chain rules for quantum entropies via multi-index Schatten norms

arXiv:2502.01611v3 Announce Type: replace Abstract: The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched Rényi entropy of quantum channels. For that, we generalize the results of [Devetak, Junge, King, Ruskai, CMP 2006] to multi-index Schatten norms. As an application, we strengthen the additivity statement of [Van Himbeeck and Brown, 2025] thus allowing the analysis of time-adaptive quantum cryptographic protocols. In addition, we establish chain rules for Rényi conditional entropies that are similar to the ones used for the generalized entropy accumulation theorem of [Metger, Fawzi, Sutter, Renner, CMP 2024].

18.
medRxiv (Medicine) 2026-06-22

Three multimodal large language models fail at clinically actionable breast pathology in three different directions

Background. Breast cancer treatment depends on histopathological features, such as grade and receptor-defined subtype; however, specialist pathologist access is constrained when the workforce is limited. Commercial multimodal large language models (MLLMs) accept hematoxylin and eosin (H&E) image tiles through paid interfaces without local hardware or fine-tuning. However, prior pathology evaluations addressed only coarse tasks. Whether they reach treatment-determining accuracy and whether vendors agree remain unclear. Methods. We aimed to evaluate three vendor-designated flagship MLLMs (Claude Sonnet 4.6, Gemini 2.5 Pro, GPT-5.5) in 427 invasive breast cancer cases. Each case went to all three with identical H&E tiles and prompts, and the subtype was inferred in the second call. The reference was an institutional sign-out report of an immunohistochemistry-derived subtype. We calculated the concordance, sensitivity, specificity, Cohen's kappa, and pairwise McNemar and Bowker tests. Findings. Claude ranked highest by raw histologic-type concordance but lowest by kappa, classifying all 23 lobular and seven micropapillary carcinomas as invasive breast carcinoma of no special type. The models anchored the Nottingham grade to three modal grades. None of the models reliably identified human epidermal growth factor receptor 2-positive disease. The failure direction was vendor-specific: Claude and GPT-5.5 were under-detected, whereas Gemini was over-called. Twelve prompt variants (4,056 calls) did not recover sensitivity. Interpretation. No current commercial MLLM reaches deployment-ready accuracy for any treatment-determining feature of breast pathology. As each vendor fails in its own fixed direction, changing vendors alters the type of error rather than removing it; therefore, the value of these models is assistive rather than autonomous. At USD 0.20-0.50 per case, they may serve as supervised draft generators that leave the diagnosis with the pathologist.

19.
bioRxiv (Bioinfo) 2026-06-20

A network approach to DNA methylation clocks

Biological age predicts health and lifespan better than chronological age, but remains difficult to measure. One leading molecular proxy for biological age is DNA methylation, which underlies age predictors known as "clocks". These clocks use penalized linear regression to predict chronological age from methylation levels using selected cytosine–guanine pairs (CpGs) along DNA. Although they predict chronological age within a few years and track mortality risk, there are several issues. Different clocks share a vanishingly small number of CpG sites, many of which show weak associations with age. Also, the clocks often do not transfer across methylation array platforms. This paper takes a network approach to better understand these issues. By using 12 public datasets from human blood, we build a co-methylation network of the sites that show the strongest age correlation. After pruning weak links, we find that it has a small number of large modules of covarying CpGs surrounded by many small modules and singleton sites. These modules are biologically interpretable, as they are associated with CpG island contexts and enriched for distinct Gene Ontology functions. We also map five established clocks onto this network (Horvath, Hannum, AltumAge, Skin & Blood, and Han) and find that they select some CpGs from the same module. This suggests that they are more similar than they appear. The network structure also suggests new ways to build clocks. A simple clock that retains one CpG per module matches the performance of established clocks. A second one, built from module-level principal components, outperforms all five established clocks in three validation cohorts and is transferable across array platforms (Illumina Infinium Methylation 450K or EPIC arrays). Overall, the network perspective shifts attention from individual CpG sites to modules of covarying sites. This perspective helps explain why DNA methylation clocks perform so well despite their differences and provides a more systematic approach for developing the next generation of aging biomarkers.

20.
arXiv (CS.AI) 2026-06-19

Hybrid Diffusion Transformer for Instruction-Guided Audio Editing via Rectified Flow

arXiv:2606.20101v1 Announce Type: cross Abstract: Audio editing aims to modify specific content in an existing audio clip according to a natural language instruction while preserving the remaining acoustic content. Despite the remarkable progress of diffusion models, existing training-based editing methods mainly rely on the local inductive biases and cross-attention interaction in convolutional U-Net backbones, which often hinder long-range semantic alignment and precise understanding and localization of instructions. In contrast, diffusion transformers provide stronger global modeling and multimodal fusion, but existing editing architectures usually adopt a simple stack of MMDiT and DiT blocks. Applying joint attention over concatenated audio and text tokens in all blocks results in quadratic complexity with respect to token length. To balance editing performance and efficiency, we propose a hybrid two-stage diffusion transformer architecture for instruction-guided audio editing based on rectified flow matching. It performs joint attention over audio and text tokens to establish coarse semantic alignment at low-resolution stage, then switches to alternating joint-attention and cross-attention blocks to refine editing details at high-resolution stage. This coarse-to-fine strategy enables efficient and accurate instruction-guided audio editing. Experiments show that the proposed framework achieves notable performance gains on challenging editing tasks involving overlapping audio events and complex instructions, while substantially improving editing efficiency with a compact model.

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

GrapNet: A Programmable Dynamic-Architecture Neural Graph Substrate

Authors:

arXiv:2606.18923v1 Announce Type: new Abstract: Programmability is a missing first-class interface in fixed-tensor neural networks: editing a relation, freezing a subgraph, auditing a local function, or changing the execution backend should be an operation on the neural program rather than ad-hoc parameter surgery. GrapNet studies this graph-as-network setting. The graph is the architecture and executable program, not an input data graph. Each compute node owns its next-layer child references and a trainable allocation vector aligned with those references; deleting a relation physically removes both the child reference and the corresponding allocation coordinate. Structural rules and execution policies live outside the node core, so the same child-owned graph can be grown, frozen, structurally edited, grouped into trainable family blocks, routed by attention over active relations, or lowered to dense snapshots after topology stabilizes. GrapNet composes with conventional modules through a vector-valued parent interface: dense layers, CNN encoders, ResNet feature extractors, attention blocks, and transformer representations can all feed one sensory GrapNode per coordinate. The evaluation is organized as a programmability stress suite rather than as a new replay benchmark. In a matched ten-seed Split Fashion-MNIST study, a plastic GrapNet+ER head reaches 63.16 percent seen-class accuracy versus 51.08 percent for a parameter-larger dense MLP+ER under the same seen-class loss and replay memory, with paired delta 12.08 points and p=1.3e-5. On Split CIFAR-10 with a frozen ImageNet ResNet-18 encoder, the same substrate improves the online head over MLP-256 by 3.81 points, with p=0.0026. These results support GrapNet as an editable neural graph substrate whose core value is structural programmability with faithful execution views.

22.
arXiv (CS.AI) 2026-06-11

Towards a Bridge Layer Between Bibliographic and Formalized Mathematical Knowledge

Authors:

arXiv:2606.11430v1 Announce Type: cross Abstract: Mathematical knowledge is split between bibliographic databases (e.g., MathSciNet, zbMATH Open) and formal proof libraries (e.g., Lean mathlib), preventing unified access between published results and their formalizations. We propose a relational bridge-database that aligns publication metadata with formal artifacts, providing an interoperability layer between mathematical literature and machine-verifiable proofs. We introduce a paper-level formalization score that measures how much of a publication is covered in formal systems. As a feasibility study, we show how such scores can be estimated via cross-document alignment between informal texts and Lean formalizations, enabling large-scale analysis of formalization coverage. This framework is a first step toward integrating bibliographic and formal mathematical ecosystems into scalable, machine-actionable knowledge graphs linking publications to formal proof objects.

23.
arXiv (CS.AI) 2026-06-12

Hellinger Multimodal Variational Autoencoders

arXiv:2601.06572v4 Announce Type: replace-cross Abstract: Multimodal variational autoencoders (VAEs) are widely used for weakly supervised generative learning with multiple modalities. Predominant methods aggregate unimodal inference distributions using either a product of experts (PoE), a mixture of experts (MoE), or their combinations to approximate the joint posterior. In this work, we revisit multimodal inference through the lens of probabilistic opinion pooling, an optimization-based approach. We start from Hölder pooling with $\alpha=0.5$, which corresponds to the unique symmetric member of the $\alpha-divergence$ family, and derive a moment-matching approximation, termed Hellinger. We then leverage such an approximation to propose HELVAE, a multimodal VAE that avoids sub-sampling, yielding an efficient yet effective model that: (i) learns more expressive latent representations as additional modalities are observed; and (ii) empirically achieves better trade-offs between generative coherence and quality, outperforming state-of-the-art multimodal VAE models.

24.
arXiv (CS.AI) 2026-06-18

NeSyCat Torch: A Differentiable Tensor Implementation of Categorical Semantics for Neurosymbolic Learning

arXiv:2606.19279v1 Announce Type: new Abstract: Neurosymbolic semantics is fragmented: classical, fuzzy, probabilistic and neural systems each define truth by their own inductive rules. NeSyCat, extending ULLER, subsumes them under a single inductive definition of truth, parametric in a strong monad and an aggregation structure on truth-values. NeSyCat has so far lacked an account of predicates and functions learned by neural networks. We provide NeSyCat Torch as the missing link and interpret computational symbols via neural networks, implementing the framework in probabilistic programming and tensor-based backends. We use the distribution monad for reference semantics and metric evaluation, and complement it by a monad for numerically stable, differentiable training: the lazy log-tensor monad over the log-semiring. For efficient training in batches, we furthermore employ a batch monad. The axioms are the source code: written once in monad-based do-notation, monadic bind performs marginalisation, lazily pruning unneeded branches. On MNIST addition, our HaskTorch, JAX, and PyTorch implementations outperform LTN and DeepProbLog in speed and accuracy, while achieving nearly the accuracy of DeepStochLog. However, unlike DeepStochLog, we stay in a uniform framework that applies to many first-order NeSy approaches. Namely, the construction is parametric in the monad; instantiating it with, e.g., the Giry monad extends the approach to continuous probability (working out a neural representation here is left for future work).

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

Context-Aware Feature-Fusion for Co-occurring Object Detection in Autonomous Driving

Object detection in autonomous driving requires precise localization and an inherent understanding of the relational context between co-occurring objects. In extremely complex heterogeneous environments rare classes, small-scale objects, and frequently appearing objects are difficult for standard object detection frameworks to handle. In this paper, we propose a novel framework called Context-Centric Feature Fusion (CCFF), which utilizes two attention-based modules, Local Context Fusion Module (LCFM) uses the RoI-to-RoI self-attention mechanism to resolve spatial interactions, mainly considering small and partially obscured objects, while Global Context Attention Module (GCAM) converts the co-occurrence of objects priors by pooling top-K RoI features into a global context attention token, avoiding the computational overhead of pixel-level global pooling. This fusion of local and object-centric global features yields contextualized embeddings that enhance classification results and co-occurring objects detection. Our method is evaluated on two datasets, Cityscapes and BDD100K which demonstrate significant improvement on relational consistency, achieving a Category-level Consistency Strategy (CCS) of 0.973 and 0.969, respectively. Furthermore, our approach produces substantial gains in small object detection (AP_S: 14.1%) and successfully recovers rare classes such as "Train" that are typically lost in large distributions. Our efficiency report shows that the framework processes images in real time with a 0.2 FPS overhead. The code is available at https://github.com/BinayKSingh/CCFF.