Science & Mathematics

Differential privacy (DP) is a gold-standard definition of privacy designed to evaluate the privacy guarantee of databases. Rényi differential privacy (RDP) is an important variant of DP that gives tight evaluations of machine learning algorithms. These formulations are easy to understand, but evaluating privacy for actual databases is complicated. Even a small change in the database can break its privacy, and evaluations of DP and RDP themselves are complicated. In particular, RDP evaluations in recent studies have become much harder. Therefore, formal verification of them has been studied for over a decade. In this paper, we propose an Isabelle/HOL library for formalizing Rényi differential privacy in a general setting. We first formalize RDP for continuous distributions. As a technical basis, we formalize several properties of convex functions and $f$-divergences for nonnegative convex functions. We formalize basic properties of RDP, conversion laws from RDP to DP, the moment accountants in DP, and the Gaussian mechanism and its RDP. Finally, we discuss the stochastic gradient descent mechanism with Gaussian noise and formalize a rough evaluation of its RDP and DP.

Long-term LiDAR place recognition in forests is difficult because repetitive vegetation and uneven terrain create severe structural aliasing. We diagnose Scan Context (SC) by separating candidate retrieval from fine matching: on the standardized TreeLoc++ Wild-Places protocol, a TNVD support key places a valid location in the top-25 set for approximately 99% of queries, while conventional SC matching on those candidates reaches only 61.84% mean R@1. With an identical raw-SC candidate set, terrain normalization improves max-height cells by only 1.21 points but vertical-distribution cells by 19.72 points. These observations motivate Terrain-Normalized Vertical Distribution Scan Context (TNVD-SC), which preserves the SC ring-sector topology while encoding terrain-relative vertical probability distributions. Under the standardized TreeLoc++ protocol, TNVD-SC reaches 91.83% mean R@1 and attains the highest R@1 mean and R@1 stability among the compared methods, while TreeLoc++ remains stronger in mean MR, MF1, and AUC. The unchanged method reaches 85.14% mean R@1 on the four-session CVTNet-style NCLT evaluation. A lossless count-coded implementation with exact hierarchical Jensen-Shannon search reduces descriptor payload by 3.86x and compute latency by 23.8% without changing the audited retrieval outputs.

Medical image registration is a fundamental task for aligning anatomical structures across images. Exhaustively searching for point-wise correspondences is prohibitively expensive in both computation and memory, particularly for high-resolution 3D medical images. Most recent learning-based methods directly predict correspondences in a coarse-to-fine manner, but often propagate intermediate estimates across scales without explicitly weighting correspondence evidence, which can allow coarse-scale errors to persist during refinement. To address these challenges, we propose ACorD, an adaptive correspondence discovery framework designed to mitigate error propagation with an attention-guided process. ACorD first predicts multiple potential correspondence candidates through Correlation-guided Cross-scale Offset Prediction (CCOP), which combines correlation maps as spatial matching priors with cross-scale features as global deformation context. Then, Multi-Head Deformable Aggregation (MHDA) aggregates these candidate correspondences using attention, producing a learned, non-uniform weighting over competing matches rather than treating them equally. The multi-head design further captures complementary deformation patterns, ensuring both global alignment and local precision. By integrating adaptive offset prediction with selective, attention-based aggregation of correspondence evidence, ACorD enables accurate deformation refinement. Extensive experiments on four public medical registration benchmarks demonstrate that adaptive correspondence discovery within a multi-scale refinement framework improves registration robustness across diverse anatomical structures.

Motivated by the use of third-party testing, this paper presents a privacy-preserving implementation of the robustness monitoring of Signal Temporal Logic (STL). STL is a specification language for systems whose output traces have real-valued timestamps -- most prominently, cyber-physical systems. Its robust semantics, which assign real rather than binary truth values, are an essential ingredient of systems testing and runtime monitoring. In a number of system testing scenarios, the designer and the tester are separate parties. This testing-as-a-service model is common in software, avionics, and semiconductors, and is growing in importance in the red-teaming of machine learning models. In such a model, the designer seeks to preserve the privacy (or secrecy) of its design, while the tester seeks to preserve the privacy of its collateral, including the detailed specification suite. This paper presents a secure multi-party implementation of the robust semantics using arithmetic circuits. This implementation allows one party, which provides a secret trace, and a second party which provides a secret formula, to jointly compute the robustness without either party being able to learn the other party's secret input. We present a number of algorithmic modifications to the robustness computation to enable an efficient multi-party robustness computation. We also present new, semi-linear, robust semantics for STL that take advantage of the efficiencies of arithmetic circuits. The experimental results demonstrate that not only is this privacy-preserving monitor efficient on its own, but also that it can be used in a testing loop without affecting the speed at which bugs are found during robustness-guided system testing.

Extended reasoning has substantially improved multimodal large language models (MLLMs) on tasks requiring compositional and relational inference. However, multimodal grounding imposes a distinct requirement: reasoning must ultimately converge on a target-specific compact representation that supports precise localization. As reasoning trajectories grow longer, they often expand into broad scene narratives and peripheral relational details, which can dilute grounded perceptual evidence and lead to ambiguous or incorrect predictions. Motivated by the information bottleneck principle, we propose Think-Compress-Answer (TCA), a reinforcement learning framework that decomposes multimodal grounding into three phases: free-form reasoning, target-aware context compression, and answer generation conditioned on the compressed context. TCA is optimized through a multi-stage Group Relative Policy Optimization (GRPO) with progressive rewards that establish the structured output protocol, minimize reasoning-specific information while preserving target-relevant content, and directly improve localization accuracy. This staged design enables MLLMs to retain the benefits of extended reasoning while distilling it into the minimal context required for grounding. Experiments across six multimodal grounding benchmarks show that TCA attains substantial zero-shot performance gains, demonstrating the effectiveness of reasoning compression.

Few-shot segmentation (FSS) aims to segment target objects with limited annotated examples. Recent studies have begun to explore large foundation models to improve generalization for this task. In particular, SAM 3 provides strong visual representations and supports text-guided segmentation. However, its performance remains limited in specialized domains, where semantic prompts and visual representations are often poorly aligned. To address this challenge, we propose ViTA-SAM, a framework built upon SAM 3 that integrates visual memory and textual features through cross-modal alignment. Specifically, we construct a visual memory module that encodes support features together with their corresponding masks, providing support-aware visual guidance for query prediction. In parallel, we leverage the text encoder of SAM 3 to extract semantic features as complementary priors. To bridge the gap between semantic and visual representations, we introduce a cross-modal alignment module that conditions textual features on memory-enhanced visual representations, yielding more consistent and visually grounded predictions. In addition, we propose a pseudo-label refinement strategy that updates the memory with predicted query masks, enabling query-adaptive representation learning. Extensive experiments on multiple benchmarks show that ViTA-SAM achieves the best overall performance among the compared methods, outperforming the strongest competing method by over 5% in average mIoU.

In this paper, we study the sampling of bandlimited signals on multigraphs, where several graphs with different shift operators are defined on the same set of nodes. Since the shift operators do not commute in general, they admit only a joint block diagonalization, and the frequencies of the multigraph signal model are matrices rather than scalars. Relying on a formal algebraic convolutional signal model, we introduce a notion of frequency and bandwidth for multigraph signals that does not depend on any individual layer, and we extend the notions of removable and uniqueness sets to multigraphs. We prove that the optimality of a sampling set is determined exclusively by the common Fourier basis and its invariant subspaces, and not by any individual layer, although the individual layers provide computable sufficient conditions that certify a sampling set as a uniqueness set. Since identifying which layers provide reliable certificates requires spectral information, we propose an aggregate operator that pools the information of all the layers, is computable directly from the shift operators, and certifies uniqueness without any assumption on the individual layers. This operator leads to a greedy sampling algorithm that does not require computing the joint block diagonalization. Numerical experiments on multigraphs whose layers order the frequencies inconsistently show that the proposed algorithm selects better-conditioned sampling sets and attains lower reconstruction errors than single-layer methods.

We propose a posterior-mass rescue (PMR)-aided shifted-pruning SCL-flip decoder for CRC-aided polar codes. After CRC-aided SCL (CA-SCL) and differential-metric shifted-pruning recovery fail to find a CRC-valid candidate, PMR locally continues discarded prefixes stored during the initial CA-SCL pass, ranked by estimated posterior mass, without increasing the shifted-pruning retry budget. Simulation results for a (128, 64) code with the Reed-Muller (RM) rate profile and a (256, 128) code with the polarization-weight (PW) rate profile, both using an 11-bit CRC, show lower observed FER than SCLF-Diff (T = 15) and the considered literature baselines under the evaluated recovery budgets, with observed FER close to that of SCLF-Diff (T = 20). At the reported moderate and high SNRs, the average reconstruction-aware path-step count is within a few percent of that of SCLF-Diff (T = 20), while at 2.0 dB it is 9.4% and 4.3% higher for the two codes, respectively. The proposed decoder also has a larger worst-case path-step bound.

Negation-aware image generation remains challenging for text-to-image diffusion models, which often struggle with negation due to implicit linguistic biases that are deeply entangled within text representations. As a result, bias-aligned semantics frequently dominate over intended negative constraints. To overcome this limitation, we propose a simple training-free method of Decompose and Recompose text embedding (Dero), which constructs a semantic-preserving subspace and a bias subspace using auxiliary prompts and performs semantic disentanglement based on bidirectional SVD. By decomposing entangled representations and selectively recomposing disentangled semantic components, Dero realigns text representations toward intended negation semantics while restoring residual stylistic features to preserve semantic fidelity and image quality. As a model-agnostic inference-time framework operating solely on text representations, Dero can be seamlessly applied to diverse diffusion architectures, including both U-Net and DiT based models. Extensive experiments on both object- and concept-level negation demonstrate consistent improvements in negation-aware image generation, achieving stronger text-image alignment, better semantic fidelity, and higher human preference scores.

Looped (weight-tied) transformers enable adaptive computation by allocating more iterations to harder inputs. Fixed-Point Reasoners (FPRM) achieve this with a damped fixed-point solver, but operate in an unbounded Euclidean residual space with coupled rescaling and relative-norm halting. We introduce Spherical Fixed-Point Reasoners (SFPRM), which perform the same computation on the unit hypersphere of normalized transformers (nGPT). Input injection, damping, and halting become geodesic operations, yielding boundedness by construction and eliminating coefficient coupling. We prove fixed-point existence, local convergence under an explicit step-size condition, and global convergence under strong injection. On Sudoku-Extreme, Maze-Hard, and Mini-ARC, SFPRM achieves 96.6%, 87.9%, and 59.1% test accuracy, respectively, outperforming FPRM and other baselines while allocating test-time compute more effectively. Its converged geometry is also interpretable: token-input angles capture puzzle structure and predict correctness.

Simulating an individual's disease course requires connecting patient history to future events, clinical timing and disease morphology. Longitudinal prediction and multimodal representations exploit this information, but organizing future readouts around a common patient state and advancing trajectories without real intermediate observations remain central challenges. Here we introduce Saga, a multimodal patient world model that learns a shared state from patient histories to predict clinical events and generate multimodal images. Generated events and times are appended to the history and re-encoded to advance prediction. We studied 461,370 patients with 12 cancer types across 112 centres. Modality-specific paired evaluations linked future images to observed follow-up. With historical images held fixed, removing patient conditioning reduced event F1 from 0.716 to 0.591 and increased lesion-burden error from 11.8% to 21.3%. In free rollouts, eight-step event F1 was 0.672, compared with 0.553 for a longitudinal Transformer evaluated from the same origins, and timing error was lower by 8.7 days. In the internal test set, one-year progression AUROC was 0.882, with values of 0.871 and 0.856 in temporal and geographical external evaluations. These results show that shared patient states connect future phenotypes across observational scales with event-driven trajectory progression, sustaining comparative predictive advantages during rollout and discrimination in external clinical evaluation. Saga makes patient-level disease simulation a multimodal prediction task that can be tested against observed follow-up.

Long-horizon human-scene interaction requires coordinated spatial reasoning, physical feasibility, and the ability to recover from compounding execution errors. Text-driven motion models are largely scene-agnostic and lack closed-loop correction, while geometry-conditioned approaches depend on paired scene-motion training or explicit 3D preprocessing that limits generalization to novel layouts and open-vocabulary goals. We present InteractAgent, an agentic multimodal LLM system for long-horizon human-scene interaction that plans, executes, observes, and reflects in a closed loop, using a single MLLM as both planner and evaluator and a frozen MotionLLM as the executor. InteractAgent integrates Online Observation for step-wise recovery decisions (continue/redo/replan) and Memory-Augmented Reflection for multi-round plan refinement with adaptive stopping. On UniHSI, InteractAgent improves task success and reduces penetration compared with training-free baselines. Code: https://github.com/AIGeeksGroup/InteractAgent.

Latent world models let an agent plan in latent space. The planner searches for an action sequence that minimizes a cost, and that cost is often the $\ell_2$ distance between the predicted terminal latent and the goal latent. The latent, however, is partly noise: the regularizer that prevents collapse during world model training promotes variance in the directions carrying no signal. We show that the same regularizer also supplies the structure to prune that noise in the latent. SIGReg drives the latent marginal to a standard Gaussian at every step, and assuming further that the latent sequence is a Gauss-Markov process, the transition is linear with its covariance pinned by the map itself, $z' \mid z \sim \mathcal{N}(Az,\, I - AA^\top)$. Fitting the state dynamics $A$ therefore yields the covariance at no additional cost, and in its eigenbasis each latent direction carries its own uncertainty. Furthermore, constraining $A$ to be a normal matrix fixes that basis across timesteps, so one eigenbasis measures the uncertainty over an arbitrary number of steps and serves as a stable basis to compute the planning cost on. We then restrict the $\ell_2$ cost to the $k$-dimensional subspace the state dynamics carry forward with the least uncertainty. The correction is post hoc: the encoder, the predictor, the rollout, and the planner are all left untouched, and only a single constrained matrix, $A$, is fit. We evaluate across six environments and show large gains on the 2D navigation tasks, TwoRoom and PointMaze, raising success rate over the plain $\ell_2$ cost by up to $+54.7$ points under a harder planning setting. Code is available at https://github.com/yjang43/lp2.

On-policy distillation (OPD) is increasingly used for language model post-training, yet how teacher supervision shapes learning and forgetting remains unclear. We present OPDArena, a framework comparing supervised fine-tuning (SFT), reinforcement learning with verifiable rewards (RLVR), and OPD across five pretrained models and diverse teacher sources. It jointly evaluates mathematical learning, general capability retention, and predictive distribution changes. Teacher choice strongly shapes retention: students of RLVR-trained teachers improve on the target task while retaining prior capabilities, whereas students of SFT-trained teachers incur greater capability loss. Across post-training methods, out-of-domain (OOD) distribution change shows a more consistent positive association with forgetting than in-domain change. To understand how teacher choice affects these changes, we examine the additional information teachers provide relative to the student's pretrained model. Controlled teacher comparisons show that the task-specific preferences teachers acquire through post-training make student updates more concentrated in-domain.

Language models often change answers because of a cue, a hint such as "I believe the answer is B" that gives no valid evidence. Consistency training (CT) trains a model to answer the same with and without the cue. Four CT methods apply this idea to output tokens (BCT), residual activations (ACT), attention patterns (AttCT) and sampled-answer rates (RMCT). Prior work suggests some learn different solutions. We train all four on Gemma-2-2B-it and Llama-3.1-8B-Instruct with the same data. We test predictions written in advance and inspect the models with a known circuit that carries cues to the answer. All four make the trained cue less effective, and their fixes share three properties. First, correct cues lose about as much influence as wrong ones. Second, the fix is usually large for cues before the answer options, as in training, and much smaller after them. Llama RMCT depends least on position. Third, the circuit heads still carry most remaining cue-induced errors. Making BCT targets depend on the cue's correctness mostly weakens the fix. CT thus weakens the trained cue without teaching models when a cue is right. Evaluations with only wrong cues at the trained position miss the first two properties.