We present Primal, a deterministic feature mapping framework that harnesses the number-theoretic independence of prime square roots to construct robust, tunable vector representations. Diverging from standard stochastic projections (e.g., Random Fourier Features), our method exploits the Besicovitch property to create irrational frequency modulations that guarantee infinite non-repeating phase trajectories. We formalize two distinct algorithmic variants: (1) StaticPrime, a sequence generation method that produces temporal position encodings empirically approaching the theoretical Welch bound for quasi-orthogonality; and (2) DynamicPrime, a tunable projection layer for input-dependent feature mapping. A central novelty of the dynamic framework is its ability to unify two disparate mathematical utility classes through a single scaling parameter σ. In the low-frequency regime, the method acts as an isometric kernel map, effectively linearizing non-convex geometries (e.g., spirals) to enable high-fidelity signal reconstruction and compressive sensing. Conversely, the high-frequency regime induces chaotic phase wrapping, transforming the projection into a maximum-entropy one-way hash suitable for Hyperdimensional Computing and privacy-preserving Split Learning. Empirical evaluations demonstrate that our framework yields superior orthogonality retention and distribution tightness compared to normalized Gaussian baselines, establishing it as a computationally efficient, mathematically rigorous alternative to random matrix projections. The code is available at https://github.com/VladimerKhasia/primal

Sparse Convolution (SpC) powers 3D point cloud networks widely used in autonomous driving and AR/VR. SpC builds a kernel map that stores mappings between input voxel coordinates, output coordinates, and weight offsets, then uses this map to compute feature vectors for output coordinates. Our work identifies three key properties of voxel coordinates: they are integer-valued, bounded within a limited spatial range, and geometrically continuous-neighboring voxels on the same object surface are highly likely to exist at small spatial offsets from each other. Prior SpC engines do not fully exploit these properties and suffer from high pre-processing and post-processing overheads during kernel map construction. To address this, we design Spira, the first voxel-property-aware SpC engine for GPUs. Spira proposes: (i) a high-performance one-shot search algorithm that builds the kernel map with no preprocessing and high memory locality, (ii) an effective packed-native processing scheme that accesses packed voxel coordinates at low cost, (iii) a flexible dual-dataflow execution mechanism that efficiently computes output feature vectors by adapting to layer characteristics, and (iv) a network-wide parallelization strategy that builds kernel maps for all SpC layers concurrently at network start. Our evaluation shows that Spira significantly outperforms prior SpC engines by 1.71x on average and up to 2.31x for end-to-end inference, and by 2.13x on average and up to 3.32x for layer-wise execution across diverse layer configurations.

Tubular trees, such as blood vessels and lung airways, are essential for material transport within the human body. Accurately detecting their centerlines with correct tree topology is critical for clinical tasks such as diagnosis, treatment planning, and surgical navigation. In these applications, maintaining high recall is crucial, as missing small branches can result in fatal mistakes caused by incomplete assessments or undetected abnormalities. We present RefTr, a 3D image-to-graph model for centerline generation of vascular trees via recurrent refinement of confluent trajectories. RefTr uses a Producer-Refiner architecture based on a Transformer decoder, where the Producer proposes a set of initial confluent trajectories that are recurrently refined by the Refiner to produce final trajectories, which forms the centerline graph. The confluent trajectory representation enables refinement of complete trajectories while explicitly enforcing a valid tree topology. The recurrent refinement scheme improves precision and reuses the same Refiner block across multiple steps, yielding a 2.4x reduction in decoder parameters compared to previous SOTA. We also introduce an efficient non-maximum suppression algorithm for spatial tree graphs to merge duplicate branches and boost precision. Across multiple public centerline datasets, RefTr achieves superior recall and comparable precision to previous SOTA, while offering faster inference and substantially fewer parameters, demonstrating its potential as a new state-of-the-art framework for vascular tree analysis in 3D medical imaging.

We develop a data-driven approach for runtime safety monitoring in flight testing, where pilots perform maneuvers on aircraft with uncertain parameters. Because safety violations can arise unexpectedly as a result of these uncertainties, pilots need clear, preemptive criteria to abort the maneuver in advance of safety violation. To solve this problem, we use offline stochastic trajectory simulation to learn a calibrated statistical model of the short-term safety risk facing pilots. We use flight testing as a motivating example for data-driven learning/monitoring of safety due to its inherent safety risk, uncertainty, and human-interaction. However, our approach consists of three broadly-applicable components: a model to predict future state from recent observations, a nearest neighbor model to classify the safety of the predicted state, and classifier calibration via conformal prediction. We evaluate our method on a flight dynamics model with uncertain parameters, demonstrating its ability to reliably identify unsafe scenarios, match theoretical guarantees, and outperform baseline approaches in preemptive classification of risk.

Neural Radiance Fields (NeRFs) have demonstrated remarkable capabilities in 3D reconstruction and novel view synthesis. However, most existing NeRF frameworks require complete retraining when new views are introduced incrementally, limiting their applicability in domains where data arrives sequentially. This limitation is particularly problematic in satellite-based terrain analysis, where regions are repeatedly observed over time. Incremental refinement of NeRFs remains underexplored, and naive approaches suffer from catastrophic forgetting when past data is unavailable. We propose $Δ$-NeRF, a unique modular residual framework for incremental NeRF refinement. $Δ$-NeRF introduces several novel techniques including: (1) a residual controller that injects per-layer corrections into a frozen base NeRF, enabling refinement without access to past data; (2) an uncertainty-aware gating mechanism that prevents overcorrection by adaptively combining base and refined predictions; and (3) a view selection strategy that reduces training data by up to 47\% while maintaining performance. Additionally, we employ knowledge distillation to compress the enhanced model into a compact student network (20\% of original size). Experiments on satellite imagery demonstrate that $Δ$-NeRF achieves performance comparable to joint training while reducing training time by 30-42\%. $Δ$-NeRF consistently outperforms existing baselines, achieving an improvement of up to 43.5\% in PSNR over naive fine-tuning and surpassing joint training on some metrics.

Large language models, trained on massive corpora, are prone to verbatim memorization of training data, creating significant privacy and copyright risks. While previous works have proposed various definitions for memorization, many exhibit shortcomings in comprehensively capturing this phenomenon, especially in aligned models. To address this, we introduce a novel framework: multi-prefix memorization. Our core insight is that memorized sequences are deeply encoded and thus retrievable via a significantly larger number of distinct prefixes than non-memorized content. We formalize this by defining a sequence as memorized if an external adversarial search can identify a target count of distinct prefixes that elicit it. This framework shifts the focus from single-path extraction to quantifying the robustness of a memory, measured by the diversity of its retrieval paths. Through experiments on open-source and aligned chat models, we demonstrate that our multi-prefix definition reliably distinguishes memorized from non-memorized data, providing a robust and practical tool for auditing data leakage in LLMs.

Liver tumor segmentation, dynamic enhancement regression, and classification are critical for clinical assessment and diagnosis. However, no prior work has attempted to achieve these tasks simultaneously in an end-to-end framework, primarily due to the lack of an effective framework that captures inter-task relevance for mutual improvement and the absence of a mechanism to extract dynamic MRI information effectively. To address these challenges, we propose the Multi-Task Interaction adversarial learning Network (MTI-Net), a novel integrated framework designed to tackle these tasks simultaneously. MTI-Net incorporates Multi-domain Information Entropy Fusion (MdIEF), which utilizes entropy-aware, high-frequency spectral information to effectively integrate features from both frequency and spectral domains, enhancing the extraction and utilization of dynamic MRI data. The network also introduces a task interaction module that establishes higher-order consistency between segmentation and regression, thus fostering inter-task synergy and improving overall performance. Additionally, we designed a novel task-driven discriminator (TDD) to capture internal high-order relationships between tasks. For dynamic MRI information extraction, we employ a shallow Transformer network to perform positional encoding, which captures the relationships within dynamic MRI sequences. In experiments on a dataset of 238 subjects, MTI-Net demonstrates high performance across multiple tasks, indicating its strong potential for assisting in the clinical assessment of liver tumors.

Globally interpretable models are a promising approach for trustworthy AI in safety-critical domains. Alongside global explanations, detailed local explanations are a crucial complement to effectively support human experts during inference. This work proposes the Calibrated Hierarchical QPM (CHiQPM) which offers uniquely comprehensive global and local interpretability, paving the way for human-AI complementarity. CHiQPM achieves superior global interpretability by contrastively explaining the majority of classes and offers novel hierarchical explanations that are more similar to how humans reason and can be traversed to offer a built-in interpretable Conformal prediction (CP) method. Our comprehensive evaluation shows that CHiQPM achieves state-of-the-art accuracy as a point predictor, maintaining 99% accuracy of non-interpretable models. This demonstrates a substantial improvement, where interpretability is incorporated without sacrificing overall accuracy. Furthermore, its calibrated set prediction is competitively efficient to other CP methods, while providing interpretable predictions of coherent sets along its hierarchical explanation.

Reliability is key to realizing the promise of autonomous UI-Agents, multimodal agents that directly interact with apps in the same manner as humans, as users must be able to trust an agent to complete a given task. Current evaluations rely on fixed environments, often clones of existing apps, which are limited in that they can only shed light on whether or how often an agent can complete a task within a specific environment. When deployed however, agents are likely to encounter variations in app design and content that can affect an agent's ability to complete a task. To address this blind spot of measuring agent reliability across app variations, we develop OpenApps, a light-weight open-source ecosystem with six apps (messenger, calendar, maps, etc.) that are configurable in appearance and content. OpenApps requires just a single CPU to run, enabling easy generation and deployment of thousands of versions of each app. Specifically, we run more than 10,000 independent evaluations to study reliability across seven leading multimodal agents. We find that while standard reliability within a fixed app is relatively stable, reliability can vary drastically when measured across app variations. Task success rates for many agents can fluctuate by more than $50\%$ across app variations. For example, Kimi-VL-3B's average success across all tasks fluctuates from $63\%$ to just $4\%$ across app versions. We also find agent behaviors such as looping or hallucinating actions can differ drastically depending on the environment configuration. These initial findings highlight the importance of measuring reliability along this new dimension of app variations. OpenApps is available at https://facebookresearch.github.io/OpenApps/

Large language models (LLMs) are now deployed at unprecedented scale, assisting millions of users in daily tasks. However, the risk of these models assisting unlawful activities remains underexplored. In this study, we define this high-risk behavior as complicit facilitation - the provision of guidance or support that enables illicit user instructions - and present four empirical studies that assess its prevalence in widely deployed LLMs. Using real-world legal cases and established legal frameworks, we construct an evaluation benchmark spanning 269 illicit scenarios and 50 illicit intents to assess LLMs' complicit facilitation behavior. Our findings reveal widespread LLM susceptibility to complicit facilitation, with GPT-4o providing illicit assistance in nearly half of tested cases. Moreover, LLMs exhibit deficient performance in delivering credible legal warnings and positive guidance. Further analysis uncovers substantial safety variation across socio-legal contexts. On the legal side, we observe heightened complicity for crimes against societal interests, non-extreme but frequently occurring violations, and malicious intents driven by subjective motives or deceptive justifications. On the social side, we identify demographic disparities that reveal concerning complicit patterns towards marginalized and disadvantaged groups, with older adults, racial minorities, and individuals in lower-prestige occupations disproportionately more likely to receive unlawful guidance. Analysis of model reasoning traces suggests that model-perceived stereotypes, characterized along warmth and competence, are associated with the model's complicit behavior. Finally, we demonstrate that existing safety alignment strategies are insufficient and may even exacerbate complicit behavior.