arXiv:2606.31236v1 Announce Type: new Abstract: Tactile sensors provide critical information for contact-rich manipulation, yet tactile representations and policies remain tightly coupled to each specific sensor, limiting transferability across robots and hardware platforms. We propose TactX, a framework for learning a transferable tactile representation across sensors spanning three fundamentally different transduction modalities: resistive, magnetic, and vision-based. TactX maps heterogeneous tactile observations into a shared latent space through modality-specific encoders trained on paired contact data. Such paired interactions provide a natural alignment signal across modalities, and the encoders are jointly trained across all sensor pairs, inducing a consistent latent space for all sensor types. Our experiments show that TactX aligns tactile representations across sensors while preserving object-level contact information, as evidenced by sensor-identity prediction and object classification in the learned latent space. We evaluate TactX on four contact-rich manipulation tasks: pick-and-place, plug insertion, board wiping, and object reorientation, and show that policies trained with one sensor transfer zero-shot to physically distinct sensors through the shared latent. This improves the average success rate from 27.5% for vision-only policy to 45.9%, providing a step toward sensor-agnostic tactile manipulation.
Science Journals
arXiv:2606.31310v1 Announce Type: new Abstract: Fueled by increasing model scale and multimodal inputs, Multimodal Large Language Models (MLLMs) have emerged as a promising paradigm for Spoken Language Assessment (SLA). While effective, this paradigm often overlooks the intrinsic ordinal structure of language acquisition. This paper works around the necessity of large-scale MLLMs by introducing Latent Ordinal Prototype Alignment (LOPA) for SLA, a prototype-based regularizer that enforces an ordinal geometric prior directly on the latent space. Coupled with Semantic-Anchored Layer Routing (SALR), which adaptively harvests multi-depth representations from a frozen Whisper encoder, our framework achieves an RMSE of 0.361. This performance rivals billion-parameter systems without the need for LLM-based fine-tuning. Further analysis reveals that SALR's synergy with LOPA offers interpretable, criterion-aligned preferences, thereby supporting an efficient and ordinal-aware modeling alternative to current scaling-centric models for SLA.
arXiv:2606.31187v1 Announce Type: new Abstract: Multimodal large language models (MLLMs) have rapidly advanced video understanding, achieving strong zero-shot and few-shot recognition across standard benchmarks. Yet their ability to deny an action by recognizing when an activity is not happening despite strong contextual cues remains largely unexplored. We introduce UCF101-AD, a large-scale benchmark consisting of paired Action-Presence and Action-Denial clips, designed to evaluate this capacity for denial. Each negative video in UCF101-AD preserves the same contextual and motion cues, including persons, objects, and locations, as its positive counterpart, but the defining action itself is explicitly absent. Evaluating 20 state-of-the-art MLLMs reveals a consistent failure: models that exceed 85% accuracy on the positive action classes collapse below 50% on their action-denial counterparts, indicating a strong inclination to affirm plausible actions rather than verify that they truly occur. This exposes a critical blind spot in modern video understanding: the inability to reason causally about whether a motion actually happens. To probe this issue, we explore a causal graph formulation, CausalAct, which expresses scene structure through natural-language prompts linking context, interaction, and motion. Incorporating such causal cues substantially reduces false positives, demonstrating that denial is a learnable reasoning skill. UCF101-AD provides a new lens for diagnosing and improving causal reasoning in multimodal models. Dataset and relevant code: https://github.com/raiyaan-abdullah/Learn-to-Deny.
arXiv:2606.31203v1 Announce Type: new Abstract: The scaling law for the n=2 error field (EF) penetration threshold is predicted numerically based on nonlinear single-fluid and two-fluid modeling using the TM1 code. The simulated penetration threshold of radial magnetic field br at the plasma edge is scaled to the electron density ne, temperature Te, viscous time, toroidal field Bt and the natural frequency by scanning these parameters separately. Single fluid modeling shows that the EF threshold scaling is similar with the analytical scaling law in both the Rutherford and visco-resistive regimes. However, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient on density decreases from 0.67 to 0.56 and on temperature decreases from 0.67 to 0.32, while on viscous time is around -0.45 and on toroidal field decreases slightly from -1.15 to -1, when the ratio ExB over electron diamagnetic drift frequency varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular rotation frequency (or natural frequency), and there is a minimum in the required field amplitude when electron fluid frequency near 0. In addition, the enduring mystery of non-zero penetration threshold at zero plasma natural frequency in EF experiments is resolved by two-fluid simulations. We find that the very small island and smooth bifurcation in EF penetration near zero frequency is hard to detect in the experiment, leading to a finite penetration threshold within the capability of the experimental measurements.
arXiv:2606.31284v1 Announce Type: new Abstract: Quantile regression aims to estimate the conditional quantiles of a response variable from observed data. In a Bayesian setting, Gaussian process quantile regression provides uncertainty quantification but faces significant computational challenges due to the nonconjugacy of the asymmetric Laplace likelihood and the cost of posterior inference. We develop a sparse Gaussian process framework in which the quantile function is represented through a reduced set of inducing variables and posterior inference is performed using a Laplace approximation. A decomposition of the predictive uncertainty into conditional-prior and posterior-induced variance components is then exploited to drive two complementary adaptive mechanisms: inducing-input infilling and data acquisition. These mechanisms are combined within a sequential algorithm that allocates computational effort toward the dominant source of predictive uncertainty and adaptively controls model complexity. Numerical experiments on benchmark problems demonstrate the accuracy of the Laplace approximation, the benefits of variance-based inducing-input placement, and the effectiveness of the proposed sequential enrichment strategy compared with predefined data-acquisition strategies.
arXiv:2606.31204v1 Announce Type: new Abstract: Synthetic data generation has emerged as a powerful tool for improving data scalability in computer vision. Recent diffusion-based pipelines have demonstrated strong photorealism. However, how to enforce precise 3D structure and pose consistency in generated images remains challenging. Existing methods leverage visual prompts such as edge maps to guide diffusion models, but often suffer from over-conditioning artifacts that degrade image realism and limit dataset quality. In this paper, we present a diffusion-based image generation framework that enforces 3D structural alignment while preserving photorealism through adaptive conditioning. Our framework, Adaptive Conditioning for 3D-Aware Synthetic Data Generation (AC3S), introduces a self-supervised visual prompt modulator that dynamically adjusts the strength of ControlNet conditioning, preventing over-conditioning and enabling the diffusion model to retain its generative expressiveness. To further enhance diversity and semantic consistency, we develop a multi-agent vision language model framework that composes detailed and 3D-aware prompts aligned with the underlying geometric structure. Together, these components enable the scalable generation of high-quality synthetic datasets with accurate 2D and 3D annotations. Extensive experiments demonstrate that our method significantly improves image quality and downstream utility.
arXiv:2606.31320v1 Announce Type: new Abstract: Safe online reinforcement learning requires policies to respect safety constraints while maintaining smooth optimization dynamics. Existing approaches typically rely on either strict safety enforcement via action interventions, which introduce discontinuities in system interaction and learning, or soft safety constraint formulations, which preserve smooth learning but provide limited safety assurance. We propose AutoSafe, a safety-aware policy architecture that integrates structured safety monitoring and intervention directly into the action generation process. This design enables smooth, risk-dependent transitions between performance-driven and safety-preserving behaviors, resulting in continuous online interaction and learning dynamics. Empirical results across a suite of continuous-control benchmarks demonstrate strong safety enforcement without sacrificing learning smoothness. We further validate AutoSafe on a physical cart-pole system, highlighting its practical effectiveness for safe online learning in the real world.
arXiv:2606.31100v1 Announce Type: new Abstract: Whole slide image (WSI) analysis is central to computational pathology, with multiple instance learning (MIL) emerging as the standard pipeline for slide-level diagnosis. However, conventional approaches formulate WSI diagnosis as a flat classification task over discrete labels, contradicting the inherently hierarchical, coarse-to-fine nature of clinical reasoning. Although recent hierarchical classifiers and vision-language models (VLMs) have sought to address this structural gap, they either fail to capture semantic continuity between related diagnoses or suffer from unconstrained text generation that produces taxonomic hallucinations and parent-child label violations. To address these limitations, we propose TaxoMIL, a taxonomy-constrained framework that reformulates WSI diagnosis as a multi-granularity text generation task. TaxoMIL utilizes a dual-head Transformer decoder to generate coarse- and fine-level diagnostic text, and introduces taxonomy-guided objectives that explicitly structure the label embedding space and strictly ground slide-level visual representations within the clinical taxonomy. Extensive experiments across three diverse WSI datasets demonstrate that TaxoMIL consistently outperforms state-of-the-art MIL classifiers and VLM-based generative methods, yielding accurate and hierarchy-aware diagnostic predictions. The code is released at https://github.com/QuIIL/TaxoMIL
arXiv:2606.31278v1 Announce Type: new Abstract: Editing multiple elements of an image in a single forward pass is a practical alternative to multi-turn image manipulation, offering improved efficiency and potentially better harmonization. However, when several instructions target different regions, semantic interference often leads to attribute leakage and poor edit disentanglement, especially as the number of edits increases. In this work, we propose MICE (Multi-Instance Concurrent Editing), a training-free strategy for scalable multi-instance image editing with Multimodal Diffusion Transformers. MICE modifies the additive bias of joint attention to regulate interactions between instance-specific edit instructions, latent, and context tokens identified via user-provided segmentation masks. Specifically, MICE allows intra-instance attention, penalizes interactions between neighboring region tokens, and suppresses unrelated cross-instance attention. As a result, our method enforces attribute binding while preserving global visual consistency. We evaluate MICE on LoMOE-Bench and introduce MICE-Bench, a more challenging benchmark with an average of 8.5 concurrent edits per image. The experiments demonstrate that our approach outperforms strong baselines and recent competitors in terms of visual quality preservation and faithfulness to the editing instructions.
arXiv:2606.31323v1 Announce Type: new Abstract: Generating diverse, coherent, and plausible content from partially given inputs remains a fundamental challenge for diffusion models. Existing approaches face clear limitations: training-based approaches offer strong task-specific results but require costly computation, and they generalize poorly across tasks. Training-free approaches offer better efficiency, but they do not explicitly optimize over unobserved variables, leading to globally inconsistent results. To address these limitations, we introduce Accelerated Likelihood Maximization (ALM), a novel training-free sampling strategy integrated into the reverse diffusion process that significantly extends the applicability of diffusion models beyond simple generation tasks. Unlike previous methods that implicitly influence missing regions through pre-generated region constraints, we directly optimize the unobserved region during the sampling process, enabling globally coherent and plausible generation. Furthermore, we incorporate an acceleration strategy that significantly improves computational efficiency without sacrificing performance. Experimental results demonstrate that ALM consistently outperforms state-of-the-art methods in various data domains and tasks, establishing a powerful paradigm for versatile content generation.
arXiv:2606.31308v1 Announce Type: new Abstract: This paper investigates the capability of Large Language Models (LLMs) to detect and classify floating-point errors statically in software code. We introduce InterFLOPBench, a benchmark of 90 C kernels with 1 130 test samples designed to evaluate LLMs across six categories of floating-point error: cancellation, comparison, division by zero, overflow, underflow and NaN, compared across 14 LLMs. The evaluation framework treats floating-point error detection as a multi-label classification problem and employs the F1-score metric to measure performance. Results demonstrate that latest models (Qwen 3 32b, Gemini 2.5 Flash, Phi 4 Reasoning, DeepSeek R1T2, and gpt-oss 20b and 120b) achieve a performance greater than 0.88 overall F1-score. Performance varies between error categories, between explicit operations such as division by zero (Average F1-score: 0.8479) and more subtle numerical phenomena such as underflow (Average F1-score: 0.6059) and cancellation (Average F1-score: 0.6164).
arXiv:2606.31332v1 Announce Type: new Abstract: Protein automodeling from cryo-EM density maps faces unique challenges in enforcing physicochemical validity and managing conformational heterogeneity. Current solvers are often limited to static predictions or require computationally intensive heuristic searches. We present CryoACE, an end-to-end framework that reconstructs precise atomic graphs for both homogeneous and heterogeneous structures. Our method features two key innovations: an atom-centric reconstruction paradigm, where density features are sampled directly at atomic coordinates and iteratively recycled to refine structures, replacing expensive voxel convolutions for efficient multimodal fusion; and a training-free guidance mechanism that leverages predicted local resolution priors to resolve dynamic ambiguity. Validated on a newly constructed high-quality dataset, CryoACE significantly outperforms existing baselines on static benchmarks and, for the first time, unveils atomic-level dynamic conformations on complex real-world datasets like EMPIAR-10345 without relying on pre-built static structures.
arXiv:2606.31110v1 Announce Type: new Abstract: Artificial neural networks (NNs) and machine learning (ML) algorithms are poorly understood from a theoretical perspective, which makes it difficult to fully realize their potential and overcome their weaknesses. For instance, ML algorithms train NN weights by moving them along a low-dimensional subspace of their allowed values, but this implicitly low-dimensional learning structure is not properly exploited to improve training because its nature is not well understood. Moreover, trained NNs are easily confused by pervasive adversarial attacks whose theoretical underpinnings are still unclear. This thesis aims to improve our theoretical understanding of NNs and ML, with a particular focus on adversarial attacks and implicitly low-dimensional learning. For this purpose, we use mathematical tools from statistical mechanics to study different types of NNs and ways in which they can fit the data. In particular, we study two classes of models that fit the data with various degrees of learning and memorization: dense associative memory (DAM) and restricted Boltzmann machines (RBM). In the process, we investigate connections between different versions of these models that are useful to make analytical investigations more efficient.
arXiv:2606.31339v1 Announce Type: new Abstract: Agentic artificial intelligence is increasingly used to decompose industrial tasks, propose robot actions, and adapt execution plans in dynamic cyber-physical environments. However, autonomous proposal generation alone does not guarantee that multi-robot industrial systems preserve task dependencies, resource ownership, safety holds, or repair boundaries during long-horizon execution. This paper introduces a verification-gated agentic mission-state governance framework for intelligent industrial multi-robot systems. The framework maintains two synchronized state objects: an evolving task forest for persistent hierarchy, delayed grounding, and repairable substructures; and a governed blackboard for online execution state, robot traces, resource locks, world beliefs, proposals, verification records, and scene-temporary constraints. From each forest--blackboard snapshot, a derived execution coupling topology exposes cross-branch dependencies for proposal verification, parallel-commit eligibility, and bounded repair. Candidate assignments, repairs, deferrals, and constraint updates may be generated by heuristic, optimization, or agentic reasoning modules, but they can update the committed mission state only after deterministic verification and atomic commit. We evaluate the framework in an indoor factory multi-robot scenario, 30-seed remote-construction stress benchmarks, structural ablations, and scalability probes. The results show improved verified and safety-audited mission-state progress with fewer invalid commitments, lock conflicts, duplicate assignments, abandoned nodes, and disruptive repairs under modeled mission predicates. The study positions agentic AI as a proposal-generating layer governed by inspectable mission-state verification rather than as an unchecked execution authority.
arXiv:2606.31344v1 Announce Type: new Abstract: Spatial models are of increasing interest in traditional computer science domains and beyond. Spatial minimisation procedures are crucial for efficient model checking of such models that are often large in size. For the recent notion of spatial bisimilarity for quasi-discrete closure models, called `Compatible Paths' (CoPa) bisimilarity, an effective minimisation method is proposed, and shown to be correct. Reasoning about space represented by quasi-discrete closure models involves two different conditional reachability modalities: a forward reachability, similar to that used in temporal logic, and a backward modality, representing the fact that a point can be reached from another point, under certain conditions. The core of our minimisation method is the encoding of closure models as labelled transition systems, enabling minimisation algorithms for branching bisimilarity to compute CoPa equivalence classes. A prototype toolchain, VoxMinX, is proposed to validate the minimisation method. VoxMinX preserves the relationship between equivalence classes and sets of pixels in the original image. Experimental validation of the toolchain via benchmark examples demonstrates a promising speed-up in model checking of spatial properties for models of realistic size.
arXiv:2606.31283v1 Announce Type: new Abstract: We conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions to investigate the Lagrangian velocity statistics. We show how polymers modulate the power spectral density of the Lagrangian velocity and the Lagrangian integral timescale by varying the Reynolds number, forcing method, and polymer relaxation time. As the polymer relaxation time increases, the attenuation of the power spectral density extends successively from high to low frequencies, and the Lagrangian integral timescale increases. To clarify the mechanism underlying the modulation of the Lagrangian velocity statistics, we decompose the Lagrangian velocity into the contributions from vortices at different length scales. Using this scale-decomposition analysis, we demonstrate that the observed modulation of the Lagrangian velocity statistics results from polymer-induced suppression of vortices that proceeds from smaller to larger scales.
arXiv:2606.31367v1 Announce Type: new Abstract: The proliferation of multimedia content on social platforms has fueled multimodal misinformation, where images are used to reinforce false claims. Consequently, Multimodal Fact-Checking (MFC) has emerged as an increasingly important research area. However, current progress is hindered by a reliance on synthetic training data and curated benchmarks that fail to capture the complexity of in-the-wild data. Furthermore, existing detection models rely on restricted intra-modality consistency or unconstrained all-to-all fusion, failing to capture nuanced relations between posts and external evidence. To address these limitations, we introduce X-POSE, a benchmark of real-world, community-annotated multimodal posts from X (formerly Twitter), augmented with full-length news articles retrieved via VLM-optimized search. Additionally, we propose TRENT, a novel MFC model that performs evidence triangulation using three parallel cross-attention streams alongside a relational fusion mechanism that explicitly models entailment and contradiction. Extensive evaluations demonstrate that TRENT consistently outperforms state-of-the-art specialized models and commercial VLMs. The code, prompt templates, and dataset are available at https://github.com/stevejpapad/evidence-triangulation
arXiv:2606.31288v1 Announce Type: new Abstract: We demonstrate the application of Flow Matching, a technique originating from generative Artificial Intelligence, to probabilistic inversion in geophysical settings, such as seismic Full-Waveform inversion. We adapt the well-established mathematical theory of Flow Matching from generative Artificial Intelligence to the context of probabilistic inversion. We evaluate the approach with two case studies: a simple 2D velocity model to illustrate the general features of the method, and the OpenFWI dataset to show its capabilities for probabilistic inversion of more complex seismic velocity models.
arXiv:2606.31325v1 Announce Type: new Abstract: We present HistoriQA-ThirdRepublic: a French-language dataset of multi-hop historical questions derived from parliamentary debates and newspapers of the French Third Republic. Designed in collaboration with a historian, the corpus captures complex reasoning patterns typical of historical inquiry, including cross-source synthesis, temporal reasoning, and the integration of sparse evidence. The dataset is made of 1782 questions and emphasizes multi-hop connections across heterogeneous historical documents, providing a resource for evaluating retrieval-augmented and large language model systems in domain-specific contexts. We describe the methodology for constructing the corpus, including the selection and alignment of sources, question validation, and metadata integration. While the dataset focuses on French historical documents, our methodology can be readily adapted to other languages and national corpora. Finally, we demonstrate how the corpus can support realistic evaluation scenarios for multi-hop question answering, bridging the gap between NLP benchmarks and the needs of historical scholarship.
arXiv:2606.31370v1 Announce Type: new Abstract: In cryptographic practice, where protocols impose strict time bounds, implementations demand predictable resource usage, and real-world systems require immediate verification for security and usability, a short key or certificate is useful only if it can be expanded or verified within a bounded time; otherwise a compact representation that requires superpolynomial work to expand offers no operational guarantee within a bounded-time protocol. This paper formalises that gap by introducing \emph{witness complexity} \(\gam(x)\), the minimum running time over near-shortest descriptions of a string on a universal Turing machine. \(\gam\) differs from Shannon entropy and Kolmogorov complexity \(\KC\): low \(\KC\) can coexist with high \(\gam\). We prove invariance up to polynomial factors; a conditional separation (assuming \(\PneqNP\)). An unconditional lower bound from incomputability of \(\KC\); a biconditional characterisation of \(\PeqNP\) via the class-relative variant \(\gP\); and polynomial-time tractability for structured \(\classNP\) families. Part II develops companion measures and shows an unconditional gap between grammar size and derivation cost, positioning \(\gam\) as a metric for the usability of keys and certificates.
arXiv:2606.31397v1 Announce Type: new Abstract: State-based fine-tuning has emerged as a compelling alternative to weight-based adaptation for transformers, updating lightweight controls into states rather than model weights, offering substantial memory savings while retaining parameter efficiency. However, most existing state-based methods typically apply only per-block control updates, which limits inter-block information exchange and restricts representational adaptation. Meanwhile, prior mechanisms that enable cross-block communication often introduce considerable computational overhead, reducing their practicality for efficient fine-tuning. We introduce Mixture-of-Control (MoC), a lightweight fine-tuning framework that adaptively integrates local and global control signals to enhance representation learning. MoC treats block-wise control states as experts in a sparse mixture-of-experts process, enabling efficient communication across transformer blocks. Empirical results across diverse transformer-based benchmarks demonstrate that MoC outperforms state-based methods while maintaining a comparable memory and computational efficiency.
arXiv:2606.31315v1 Announce Type: new Abstract: Speculative decoding accelerates inference by using a lightweight draft model to generate candidate tokens in parallel, and are then verified by the target model, enabling lossless acceleration. Recently, diffusion-based speculative decoding further improves parallelism by generating multiple tokens per forward pass via block-level diffusion, achieving state-of-the-art (SOTA) performance. However, existing methods adopt a fixed inference block size and assume a uniform optimal decoding strategy across all inputs. In this paper, we show that this assumption is suboptimal, as the optimal block size varies across samples and plays a critical role in speculative decoding performance. Moreover, these values exhibit a clear local structure, concentrating around the training block size, which reduces the problem to a low-dimensional and structured decision space. Based on these insights, we propose BlockPilot, a sample-adaptive policy that predicts the optimal block size from the prefilling representation. Specifically, we formulate block size selection as a lightweight policy learning problem and propose an instance-adaptive decision mechanism that predicts the optimal block size based on the representation of the prefilling stage. The prediction is performed only once after prefilling, allowing for seamless integration. Extensive experiments demonstrate that our method is plug-and-play, introduces minimal overhead, and consistently improves efficiency, achieving an acceptance length of 5.92 and a 4.20$\times$ speedup on Qwen3-4B under temperature $T=1$.
A Self-Negotiation Framework for Ethical Decision-Making during Task Interruptions in Service Robots
arXiv:2606.31357v1 Announce Type: new Abstract: Service robots operating in public environments frequently encounter interruptions when multiple users request service simultaneously. Resolving such conflicts requires ethical decision-making, as prioritizing one user request can disadvantage another. Current approaches rely on static rules or centralized arbitration and do not support autonomous, ethics-based conflict resolution. This paper addresses the question of how a single robot can arbitrate between multiple users during task interruptions and make ethically aligned decisions without relying on external coordination. We introduce a self-negotiation framework that represents each user by an ethical profile that captures their contextual ethical preferences and conditions, and resolves conflicts through an internal negotiation process. The framework is implemented in a modular ROS-based implementation and evaluated in simulation with a realistic interruption scenario. The results show that the system consistently produces user ethical preference-aligned outcomes, supports multilateral negotiation among users, and responds within 1.5 seconds, with near-linear runtime growth under increasing user input.
arXiv:2606.31380v1 Announce Type: new Abstract: Acoustic scattering arises in a wide range of applications, including medical imaging, geophysical exploration, acoustic metamaterials, etc. In this paper, we develop a fast and highly accurate algorithm for acoustic scattering by multiple quasi-axisymmetric objects, whose axis of rotation is an arbitrary curve. The method is based on a Nystr\"om discretization that combines Gauss-Legendre quadrature with the trapezoidal rule. To treat the singular integrals that occur when target points are close to or coincide with source points, we reformulate them as evaluations of the modal Green's function and its derivatives, which are computed efficiently using the fast Fourier transform and convolution. The multiple scattering solver is then constructed by coupling the single scatterer discretizations through inter-body boundary integral interactions. We also present a convergence analysis for scattering problems with smooth geometries. Numerical examples demonstrate the efficiency and accuracy of the proposed method for solving multiple scattering problems involving up to 1000 quasi-axisymmetric structures.
arXiv:2606.31853v1 Announce Type: cross Abstract: We investigate logics that generalize both intuitionistic logic and quantum logic. In earlier work, we introduced Ex-logic, an extension of Holliday's fundamental logic that coincides with the intersection of orthologic and the implication-free fragment of intuitionistic logic. In this paper, we add an implication connective to Ex-logic and axiomatize iEx-logic, the intersection of full intuitionistic logic and orthomodular logic with the implication connective interpreted as the Sasaki hook. As a consequence, we obtain a characterization of the lattice of logics extending iEx-logic as the product of the lattice of intermediate logics and the lattice of orthomodular logics. We also explore the robustness of our algebraic approach by briefly discussing extensions of iEx-logic with modal operators.