Large language models demonstrate the intriguing ability to perform unseen tasks via in-context learning. However, it remains unclear what mechanisms inside the model drive such task-level generalization. In this work, we approach this question through the lens of off-by-one addition (i.e., 1+1=3, 2+2=5, 3+3=?), a two-step, counterfactual task with an unexpected +1 function as a second step. Leveraging circuit-style interpretability techniques such as path patching, we analyze the models' internal computations behind their performance and present three key findings. First, we identify a mechanism that explains the model's generalization from standard addition to off-by-one addition. It resembles the induction head mechanism described in prior work, yet operates at a higher level of abstraction; we therefore term it "function induction" in this work. Second, we show that the induction of the +1 function is governed by multiple attention heads in parallel, each of which emits a distinct piece of the +1 function. Finally, we find that this function induction mechanism is reused in a broader range of tasks, including synthetic tasks such as shifted multiple-choice QA and algorithmic tasks such as base-8 addition. Overall, our findings offer deeper insights into how reusable and composable structures within language models enable task-level generalization.

In recent years, deep learning-based single-channel speech separation has improved considerably, in large part driven by increasingly compute- and parameter-efficient neural network architectures. Most such architectures are, however, designed with a fixed compute and parameter budget and consequently cannot scale to varying compute demands or resources, which limits their use in embedded and heterogeneous devices such as mobile phones and hearables. To enable such use-cases we design a neural network architecture for speech separation and enhancement capable of early-exit, and we propose an uncertainty-aware probabilistic framework to jointly model the clean speech signal and error variance which we use to derive probabilistic early-exit conditions in terms of desired signal-to-noise ratios. We evaluate our methods on both speech separation and enhancement tasks where we demonstrate that early-exit capabilities can be introduced without compromising reconstruction, and that when trained on variable-length audio our early-exit conditions are well-calibrated and lead to considerable compute savings when used to dynamically scale compute at test time while remaining directly interpretable.

Document image dewarping remains a challenging task in the deep learning era. While existing methods have improved by leveraging text line awareness, they typically focus only on a single horizontal dimension. In this paper, we propose a fine-grained deformation perception model that focuses on Dual Dimensions of document horizontal-vertical-lines to improve document Dewarping called D2Dewarp. It can perceive distortion trends in different directions across document details. To combine the horizontal and vertical granularity features, an effective fusion module based on X and Y coordinate is designed to facilitate interaction and constraint between the two dimensions for feature complementarity. Due to the lack of annotated line features in current public dewarping datasets, we also propose an automatic fine-grained annotation method using public document texture images and automatic rendering engine to build a new large-scale distortion training dataset named DocDewarpHV. On three public Chinese and English benchmarks, both quantitative and qualitative results show that our method achieves better rectification results compared with the state-of-the-art methods. The code and dataset are available at https://github.com/xiaomore/D2Dewarp.

Hallucinations, defined as instances where Large Language Models (LLMs) generate false or misleading content, pose a significant challenge that impacts the safety and trust of downstream applications. We introduce UQLM, a Python package for LLM hallucination detection using state-of-the-art uncertainty quantification (UQ) techniques. This toolkit offers a suite of UQ-based scorers that compute response-level confidence scores ranging from 0 to 1. This library provides an off-the-shelf solution for UQ-based hallucination detection that can be easily integrated to enhance the reliability of LLM outputs.

Large language models (LLMs) excel at logical and algorithmic reasoning, yet their emotional intelligence (EQ) still lags far behind their cognitive prowess. While reinforcement learning from verifiable rewards (RLVR) has advanced in other domains, its application to dialogue-especially for emotional intelligence-remains underexplored. In this work, we introduce RLVER, the first end-to-end reinforcement learning framework that leverages verifiable emotion rewards from simulated users to cultivate higher-order empathetic abilities in LLMs. Within this framework, self-consistent affective simulated users engage in dialogue rollouts and produce deterministic emotion scores during conversations, serving as reward signals to guide the LLM's learning. Fine-tuning publicly available Qwen2.5-7B-Instruct model with PPO boosts its Sentient-Benchmark score from 13.3 to 79.2 while largely preserving mathematical and coding competence. Extensive experiments reveal that: (i) RLVER consistently improves multiple dialogue capabilities; (ii) Thinking and non-thinking models show distinct trends--thinking models excel in empathy and insight, while non-thinking models favor action; (iii) GRPO often yields stable gains, while PPO can push certain capabilities to a higher ceiling; (iv) More challenging environments are not always better-moderate ones can yield stronger outcomes. Our results show that RLVER is a practical route toward emotionally intelligent and broadly capable language agents.

The growing demand for oriented object detection (OOD) across various domains has driven significant research in this area. However, the high cost of dataset annotation remains a major concern. Current mainstream OOD algorithms can be mainly categorized into three types: (1) fully supervised methods using complete oriented bounding box (OBB) annotations, (2) semi-supervised methods using partial OBB annotations, and (3) weakly supervised methods using weak annotations such as horizontal boxes or points. However, these algorithms inevitably increase the cost of models in terms of annotation speed or annotation cost. To address this issue, we propose: (1) the first Partial Weakly-Supervised Oriented Object Detection (PWOOD) framework based on partially weak annotations (horizontal boxes or single points), which can efficiently leverage large amounts of unlabeled data, significantly outperforming weakly supervised algorithms trained with partially weak annotations, also offers a lower cost solution; (2) Orientation-and-Scale-aware Student (OS-Student) model capable of learning orientation and scale information with only a small amount of orientation-agnostic or scale-agnostic weak annotations; and (3) Class-Agnostic Pseudo-Label Filtering strategy (CPF) to reduce the model's sensitivity to static filtering thresholds. Comprehensive experiments on DOTA-v1.0/v1.5/v2.0 and DIOR datasets demonstrate that our PWOOD framework performs comparably to, or even surpasses traditional semi-supervised algorithms. Our code will be made publicly available.

The ability to quickly and accurately compute properties from atomic simulations is critical for advancing a large number of applications in chemistry and materials science including drug discovery, energy storage, and semiconductor manufacturing. To address this need, Meta FAIR presents a family of Universal Models for Atoms (UMA), designed to push the frontier of speed, accuracy, and generalization. UMA models are trained on half a billion unique 3D atomic structures (the largest training runs to date) by compiling data across multiple chemical domains, e.g. molecules, materials, and catalysts. We develop empirical scaling laws to help understand how to increase model capacity alongside dataset size to achieve the best accuracy. The UMA small and medium models utilize a novel architectural design we refer to as mixture of linear experts that enables increasing model capacity without sacrificing speed. For example, UMA-medium has 1.4B parameters but only ~50M active parameters per atomic structure. We evaluate UMA models on a diverse set of applications across multiple domains and find that, remarkably, a single model without any fine-tuning can perform similarly or better than specialized models. We are releasing the UMA code, weights, and associated data to accelerate computational workflows and enable the community to continue to build increasingly capable AI models.

Neural sequence-to-sequence systems deliver state-of-the-art performance for automatic speech recognition. When using appropriate modeling units, e.g., byte-pair encoding, these systems are in principle open vocabulary systems. In practice, however, they often fail to recognize words not seen during training, e.g., named entities, acronyms, or domain-specific special words. To address this problem, many context biasing methods have been proposed; however, these methods may still struggle when they are unable to relate audio and corresponding text, e.g., in case of a pronunciation-orthography mismatch. We propose a method where corrections of substitution errors can be used to improve the recognition accuracy of such challenging words. Users can add corrections on the fly during inference. We show that with this method we get a relative improvement in biased word error rate between 22% and 34% compared to a text-based replacement method, while maintaining the overall performance.

Egocentric vision is essential for both human and machine visual understanding, particularly in capturing the detailed hand-object interactions needed for manipulation tasks. Translating third-person views into first-person views significantly benefits augmented reality (AR), virtual reality (VR) and robotics applications. However, current exocentric-to-egocentric translation methods are limited by their dependence on 2D cues, synchronized multi-view settings, and unrealistic assumptions such as the necessity of an initial egocentric frame and relative camera poses during inference. To overcome these challenges, we introduce EgoWorld, a novel framework that reconstructs an egocentric view from rich exocentric observations, including point clouds, 3D hand poses, and textual descriptions. Our approach reconstructs a point cloud from estimated exocentric depth maps, reprojects it into the egocentric perspective, and then applies diffusion model to produce dense, semantically coherent egocentric images. Evaluated on four datasets (i.e., H2O, TACO, Assembly101, and Ego-Exo4D), EgoWorld achieves state-of-the-art performance and demonstrates robust generalization to new objects, actions, scenes, and subjects. Moreover, EgoWorld exhibits robustness on in-the-wild examples, underscoring its practical applicability. Project page is available at https://redorangeyellowy.github.io/EgoWorld/.

Sparse autoencoders (SAEs) have recently emerged as a powerful tool for interpreting the features learned by large language models (LLMs). By reconstructing features with sparsely activated networks, SAEs aim to recover complex superposed polysemantic features into interpretable monosemantic ones. Despite their wide applications, it remains unclear under what conditions SAEs can fully recover the ground truth monosemantic features from the superposed polysemantic ones. In this paper, we provide the first theoretical analysis with a closed-form solution for SAEs, revealing that they generally fail to fully recover the ground truth monosemantic features unless the ground truth features are extremely sparse. To improve the feature recovery of SAEs in general cases, we propose a reweighting strategy targeting at enhancing the reconstruction of the ground truth monosemantic features instead of the observed polysemantic ones. We further establish a theoretical weight selection principle for our proposed weighted SAE (WSAE). Experiments across multiple settings validate our theoretical findings and demonstrate that our WSAE significantly improves feature monosemanticity and interpretability.

We propose a new Bayesian approach to generalize the federated Alternating Direction Method of Multipliers (ADMM). We show that the solutions of variational-Bayesian (VB) objectives are associated with a duality structure that not only resembles the structure of ADMM's fixed-points but also generalizes it. For example, ADMM-like updates are recovered when the VB objective is optimized over the isotropic-Gaussian family, and new non-trivial extensions are obtained for other exponential-family distributions. These extensions include a Newton-like variant that converges in one step on quadratic objectives and an Adam-like variant that yields up to 7% accuracy boosts for deep heterogeneous cases. Our work opens a new Bayesian way to generalize ADMM and other primal-dual methods.

It is important for Large Language Models (LLMs) to be aware of the boundary of their knowledge, distinguishing queries they can confidently answer from those that lie beyond their capabilities. Such awareness enables models to perform adaptive inference, such as invoking retrieval-augmented generation (RAG), engaging in slow and deep thinking, or abstaining from answering when appropriate. These mechanisms are key to developing efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which estimates if a model is capable of answering a given query before generating any tokens, thus avoiding the generation cost. To this end, we propose a novel, training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens to provide a reliable signal of uncertainty. Empirical studies on both factual question answering and mathematical reasoning tasks demonstrate that our Internal Confidence outperforms several baselines in quality of confidence while being computationally cheaper. Furthermore, we demonstrate its benefits in adaptive inference settings, showing that for RAG and model cascading it reduces inference costs while preserving overall performance.

Reliability of deep learning models is critical for deployment in high-stakes applications, where out-of-distribution or adversarial inputs may lead to detrimental outcomes. Evidential Deep Learning, an efficient paradigm for uncertainty quantification, models predictions as Dirichlet distributions of a single forward pass. However, EDL is particularly vulnerable to adversarially perturbed inputs, making overconfident errors. Conflict-aware Evidential Deep Learning (C-EDL) is a lightweight post-hoc uncertainty quantification approach that mitigates these issues, enhancing adversarial and OOD robustness without retraining. C-EDL generates diverse, task-preserving transformations per input and quantifies representational disagreement to calibrate uncertainty estimates when needed. C-EDL's conflict-aware prediction adjustment improves detection of OOD and adversarial inputs, maintaining high in-distribution accuracy and low computational overhead. Our experimental evaluation shows that C-EDL significantly outperforms state-of-the-art EDL variants and competitive baselines, achieving substantial reductions in coverage for OOD data (up to $\approx$55%) and adversarial data (up to $\approx$90%), across a range of datasets, attack types, and uncertainty metrics.

Quality-Diversity (QD) algorithms have shown remarkable success in discovering diverse, high-performing solutions, but rely heavily on hand-crafted behavioral descriptors that constrain exploration to predefined notions of diversity. Leveraging the equivalence between policies and occupancy measures, we present a theoretically grounded approach to automatically generate behavioral descriptors by embedding the occupancy measures of policies in Markov Decision Processes. Our method, AutoQD, leverages random Fourier features to approximate the Maximum Mean Discrepancy (MMD) between policy occupancy measures, creating embeddings whose distances reflect meaningful behavioral differences. A low-dimensional projection of these embeddings that captures the most behaviorally significant dimensions can then be used as behavioral descriptors for CMA-MAE, a state of the art blackbox QD method, to discover diverse policies. We prove that our embeddings converge to true MMD distances between occupancy measures as the number of sampled trajectories and embedding dimensions increase. Through experiments in multiple continuous control tasks we demonstrate AutoQD's ability in discovering diverse policies without predefined behavioral descriptors, presenting a well-motivated alternative to prior methods in unsupervised Reinforcement Learning and QD optimization. Our approach opens new possibilities for open-ended learning and automated behavior discovery in sequential decision making settings without requiring domain-specific knowledge. Source code is available at https://github.com/conflictednerd/autoqd-code.

A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that $f(x) \approx y$ for any $(x, y)$ drawn from the same distribution. Neural networks and kernel-based methods are commonly employed for this task due to their capacity for fast and parallel computation. The approximation capabilities, or expressive power, of these methods have been extensively studied over the past 35 years. In this paper, we will present examples of key ideas in this area found in the literature. We will discuss emerging trends in machine learning including the role of shallow/deep networks, approximation on manifolds, physics-informed neural surrogates, neural operators, and transformer architectures. Despite function approximation being a fundamental problem in machine learning, approximation theory does not play a central role in the theoretical foundations of the field. One unfortunate consequence of this disconnect is that it is often unclear how well trained models will generalize to unseen or unlabeled data. In this review, we examine some of the shortcomings of the current machine learning framework and explore the reasons for the gap between approximation theory and machine learning practice. We will then introduce our novel research to achieve function approximation on unknown manifolds without the need to learn specific manifold features, such as the eigen-decomposition of the Laplace-Beltrami operator or atlas construction. In many machine learning problems, particularly classification tasks, the labels $y_j$ are drawn from a finite set of values.

We present pyCub, an open-source physics-based simulation of the humanoid robot iCub, along with exercises to teach students the basics of humanoid robotics. Compared to existing iCub simulators (iCub SIM, iCub Gazebo), which require C++ code and YARP as middleware, pyCub works without YARP and with Python code. The complete robot with all articulations has been simulated, with two cameras in the eyes and the unique sensitive skin of the iCub comprising 4000 receptors on its body surface. The exercises range from basic control of the robot in velocity, joint, and Cartesian space to more complex tasks like gazing, grasping, or reactive control. The whole framework is written and controlled with Python, thus allowing to be used even by people with small or almost no programming practice. The exercises can be scaled to different difficulty levels. We tested the framework in two runs of a course on humanoid robotics. The simulation, exercises, documentation, Docker images, and example videos are publicly available at https://rustlluk.github.io/pyCub.

Synthetically augmenting training datasets with diffusion models has become an effective strategy for improving the generalization of image classifiers. However, existing approaches typically increase dataset size by 10-30x and struggle to ensure generation diversity, leading to substantial computational overhead. In this work, we introduce TADA (TArgeted Diffusion Augmentation), a principled framework that selectively augments examples that are not learned early in training using faithful synthetic images that preserve semantic features while varying noise. We show that augmenting only this targeted subset consistently outperforms augmenting the entire dataset. Through theoretical analysis on a two-layer CNN, we prove that TADA improves generalization by promoting homogeneity in feature learning speed without amplifying noise. Extensive experiments demonstrate that by augmenting only 30-40% of the training data, TADA improves generalization by up to 2.8% across diverse architectures including ResNet, ViT, ConvNeXt, and Swin Transformer on CIFAR-10/100, TinyImageNet, and ImageNet, using optimizers such as SGD and SAM. Notably, TADA combined with SGD outperforms the state-of-the-art optimizer SAM on CIFAR-100 and TinyImageNet. Furthermore, TADA shows promising improvements on object detection benchmarks, demonstrating its applicability beyond image classification. Our code is available at https://github.com/BigML-CS-UCLA/TADA.

Legal Judgment Prediction (LJP) is a pivotal task in legal AI. Existing semantic-enhanced LJP models integrate judicial precedents and legal knowledge for high performance. But they neglect legal reasoning logic, a critical component of legal judgments requiring rigorous logical analysis. Although some approaches utilize legal reasoning logic for high-quality predictions, their logic rigidity hinders adaptation to case-specific logical frameworks, particularly in complex cases that are lengthy and detailed. This paper proposes a rule-enhanced legal judgment prediction framework based on first-order logic (FOL) formalism and comparative learning (CL) to develop an adaptive adjustment mechanism for legal judgment logic and further enhance performance in LJP. Inspired by the process of human exam preparation, our method follows a three-stage approach: first, we initialize judgment rules using the FOL formalism to capture complex reasoning logic accurately; next, we propose a Confusion-aware Contrastive Learning (CACL) to dynamically optimize the judgment rules through a quiz consisting of confusable cases; finally, we utilize the optimized judgment rules to predict legal judgments. Experimental results on two public datasets show superior performance across all metrics. The code is publicly available{https://anonymous.4open.science/r/RLJP-FDF1}.

As Large Language Models (LLMs) are increasingly deployed in real-world applications, balancing helpfulness and safety has become a central challenge. A natural approach is to incorporate safety constraints into Reinforcement Learning from Human Feedback (RLHF), where recent studies have shown promising progress. However, these methods often rely on auxiliary networks or multi-stage pipelines, thereby increasing complexity. In this work, we revisit the original safety alignment objective and show that, under mild assumptions, it admits a closed-form optimal policy. We further derive a provably equivalent and tractable objective, enabling direct optimization. Building on this insight, we propose SafeDPO, a lightweight method that preserves the optimal solution of the underlying safety-constrained objective while requiring only one additional hyperparameter and minimal modifications to existing preference-based training methods. SafeDPO eliminates the need for reward models, cost models, and online sampling, relying only on preference data and safety indicators. Despite its simplicity, SafeDPO achieves competitive safety-helpfulness trade-offs compared to existing safety alignment methods. Experiments on the PKU-SafeRLHF-30K benchmark demonstrate that SafeDPO substantially improves safety while maintaining competitive helpfulness. Ablation studies further show that the additional hyperparameter provides a flexible mechanism to enhance safety while preserving the theoretical optimum, and confirm that SafeDPO scales reliably to LLMs with up to 13B parameters. Overall, our results highlight that a simple, theory-driven objective can provide a lightweight yet effective solution for safety alignment in practice.

We study the convergence properties and escape dynamics of Stochastic Gradient Descent (SGD) in one-dimensional landscapes, separately considering infinite- and finite-variance noise. Our main focus is to identify the time scales on which SGD reliably moves from an initial point to the local minimum in the same ''basin''. Under suitable conditions on the noise distribution, we prove that SGD converges to the basin's minimum unless the initial point lies too close to a local maximum. In that near-maximum scenario, we show that SGD can linger for a long time in its neighborhood. For initial points near a ''sharp'' maximum, we show that SGD does not remain stuck there, and we provide results to estimate the probability that it will reach each of the two neighboring minima. Overall, our findings present a nuanced view of SGD's transitions between local maxima and minima, influenced by both noise characteristics and the underlying function geometry.

Out-of-distribution (OOD) detection and segmentation are crucial for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. While prior research has primarily focused on unimodal image data, real-world applications are inherently multimodal, requiring the integration of multiple modalities for improved OOD detection. A key challenge is the lack of supervision signals from unknown data, leading to overconfident predictions on OOD samples. To address this challenge, we propose Feature Mixing, an extremely simple and fast method for multimodal outlier synthesis with theoretical support, which can be further optimized to help the model better distinguish between in-distribution (ID) and OOD data. Feature Mixing is modality-agnostic and applicable to various modality combinations. Additionally, we introduce CARLA-OOD, a novel multimodal dataset for OOD segmentation, featuring synthetic OOD objects across diverse scenes and weather conditions. Extensive experiments on SemanticKITTI, nuScenes, CARLA-OOD datasets, and the MultiOOD benchmark demonstrate that Feature Mixing achieves state-of-the-art performance with a $10 \times$ to $370 \times$ speedup. Our source code and dataset will be available at https://github.com/mona4399/FeatureMixing.

We study best-arm identification in stochastic multi-armed bandits under the fixed-confidence setting, focusing on instances with multiple optimal arms. Unlike prior work that addresses the unknown-number-of-optimal-arms case, we consider the setting where the number of optimal arms is known in advance. We derive a new information-theoretic lower bound on the expected sample complexity that leverages this structural knowledge and is strictly tighter than previous bounds. Building on the Track-and-Stop algorithm, we propose a modified, tie-aware stopping rule and prove that it achieves asymptotic instance-optimality, matching the new lower bound. Our results provide the first formal guarantee of optimality for Track-and-Stop in multi-optimal settings with known cardinality, offering both theoretical insights and practical guidance for efficiently identifying any optimal arm.

This paper presents a comparative analysis of Large Language Models (LLMs) and traditional Optical Character Recognition (OCR) systems on Urdu newspapers, addressing challenges posed by complex multi-column layouts, low-resolution scans, and the stylistic variability of the Nastaliq script. To handle these challenges, we fine-tune YOLOv11x models for article- and column-level text block extraction and train a SwinIR-based super-resolution module that enhances image quality for downstream text recognition, improving accuracy by an average of 50%. We further introduce the Urdu Newspaper Benchmark (UNB), a manually annotated dataset for Urdu OCR comprising 829 paragraph images with a total of 9,982 sentences. Using UNB and the OpenITI corpus, we conduct a systematic comparison between traditional CNN+RNN-based OCR systems and modern LLMs, presenting detailed insertion, deletion, and substitution error analyses alongside character-level confusion patterns. We find that Gemini-2.5-Pro achieves the best performance on UNB (WER 0.133), while fine-tuning GPT-4o on just 500 in-domain samples yields a 6.13% absolute WER improvement, demonstrating the adaptability of LLMs to low-resource, morphologically complex scripts like Urdu. The UNB dataset and fine-tuned models are publicly available at https://github.com/sameearif/urdu-newspaper-benchmark.

Time-series tasks often benefit from signals expressed across multiple representation spaces (e.g., time vs. frequency) and at varying abstraction levels (e.g., local patterns vs. global semantics). However, existing pre-trained time-series models entangle these heterogeneous signals into a single large embedding, limiting transferability and direct zero-shot usability. To address this, we propose TSPulse, family of ultra-light pre-trained models (1M parameters) with disentanglement properties, specialized for various time-series diagnostic tasks. TSPulse introduces a novel pre-training framework that augments masked reconstruction with explicit disentanglement across spaces and abstractions, learning three complementary embedding views (temporal, spectral, and semantic) to effectively enable zero-shot transfer. In-addition, we introduce various lightweight post-hoc fusers that selectively attend and fuse these disentangled views based on task type, enabling simple but effective task specializations. To further improve robustness and mitigate mask-induced bias prevalent in existing approaches, we propose a simple yet effective hybrid masking strategy that enhances missing diversity during pre-training. Despite its compact size, TSPulse achieves strong and consistent gains across four TS diagnostic tasks: +20% on the TSB-AD anomaly detection leaderboard, +25% on similarity search, +50% on imputation, and +5-16% on multivariate classification, outperforming models that are 10-100X larger on over 75 datasets. TSPulse delivers state-of-the-art zero-shot performance, efficient fine-tuning, and supports GPU-free deployment. Models and source code are publicly available at https://huggingface.co/ibm-granite/granite-timeseries-tspulse-r1.

We propose a novel unsupervised framework for \emph{Invariant Risk Minimization} (IRM), extending the concept of invariance to settings where labels are unavailable. Traditional IRM methods rely on labeled data to learn representations that are robust to distributional shifts across environments. In contrast, our approach redefines invariance through feature distribution alignment, enabling robust representation learning from unlabeled data. We introduce two methods within this framework: Principal Invariant Component Analysis (PICA), a linear method that extracts invariant directions under Gaussian assumptions, and Variational Invariant Autoencoder (VIAE), a deep generative model that separates environment-invariant and environment-dependent latent factors. Our approach is based on a novel ``unsupervised'' structural causal model and supports environment-conditioned sample-generation and intervention. Empirical evaluations on synthetic dataset, modified versions of MNIST, and CelebA demonstrate the effectiveness of our methods in capturing invariant structure, preserving relevant information, and generalizing across environments without access to labels.

Existing visual token pruning methods target prompt alignment and visual preservation with static strategies, overlooking the varying relative importance of these objectives across tasks, which leads to inconsistent performance. To address this, we derive the first closed-form error bound for visual token pruning based on the Hausdorff distance, uniformly characterizing the contributions of both objectives. Moreover, leveraging $ε$-covering theory, we reveal an intrinsic trade-off between these objectives and quantify their optimal attainment levels under a fixed budget. To practically handle this trade-off, we propose Multi-Objective Balanced Covering (MoB), which reformulates visual token pruning as a bi-objective covering problem. In this framework, the attainment trade-off reduces to budget allocation via greedy radius trading. MoB offers a provable performance bound and linear scalability with respect to the number of input visual tokens, enabling adaptation to challenging pruning scenarios. Extensive experiments show that MoB preserves 96.4% of performance for LLaVA-1.5-7B using only 11.1% of the original visual tokens and accelerates LLaVA-Next-7B by 1.3-1.5$\times$ with negligible performance loss. Additionally, evaluations on Qwen2-VL and Video-LLaVA confirm that MoB integrates seamlessly into advanced MLLMs and diverse vision-language tasks.

We present the Emotion-Gradient Metacognitive Recursive Self-Improvement (EG-MRSI) framework, a novel architecture that integrates introspective metacognition, emotion-based intrinsic motivation, and recursive self-modification into a unified theoretical system. The framework is explicitly capable of overwriting its own learning algorithm under formally bounded risk. Building upon the Noise-to-Meaning RSI (N2M-RSI) foundation, EG-MRSI introduces a differentiable intrinsic reward function driven by confidence, error, novelty, and cumulative success. This signal regulates both a metacognitive mapping and a self-modification operator constrained by provable safety mechanisms. We formally define the initial agent configuration, emotion-gradient dynamics, and RSI trigger conditions, and derive a reinforcement-compatible optimization objective that guides the agent's development trajectory. Meaning Density and Meaning Conversion Efficiency are introduced as quantifiable metrics of semantic learning, closing the gap between internal structure and predictive informativeness. This Part I paper establishes the single-agent theoretical foundations of EG-MRSI. Future parts will extend this framework to include safety certificates and rollback protocols (Part II), collective intelligence mechanisms (Part III), and feasibility constraints including thermodynamic and computational limits (Part IV). Together, the EG-MRSI series provides a rigorous, extensible foundation for open-ended and safe AGI.

iPhone portrait-mode images contain a distinctive pattern in out-of-focus regions simulating the bokeh effect, which we term Apple's Synthetic Defocus Noise Pattern (SDNP). If overlooked, this pattern can interfere with blind forensic analyses, especially PRNU-based camera source verification, as noted in earlier works. Since Apple's SDNP remains underexplored, we provide a detailed characterization, proposing a method for its precise estimation, modeling its dependence on scene brightness, ISO settings, and other factors. Leveraging this characterization, we explore forensic applications of the SDNP, including traceability of portrait-mode images across iPhone models and iOS versions in open-set scenarios, assessing its robustness under post-processing. Furthermore, we show that masking SDNP-affected regions in PRNU-based camera source verification significantly reduces false positives, overcoming a critical limitation in camera attribution, and improving state-of-the-art techniques.

Trajectory prediction is crucial for autonomous driving, enabling vehicles to navigate safely by anticipating the movements of surrounding road users. However, current deep learning models often lack trustworthiness as their predictions can be physically infeasible and illogical to humans. To make predictions more trustworthy, recent research has incorporated prior knowledge, like the social force model for modeling interactions and kinematic models for physical realism. However, these approaches focus on priors that suit either vehicles or pedestrians and do not generalize to traffic with mixed agent classes. We propose incorporating interaction and kinematic priors of all agent classes--vehicles, pedestrians, and cyclists with class-specific interaction layers to capture agent behavioral differences. To improve the interpretability of the agent interactions, we introduce DG-SFM, a rule-based interaction importance score that guides the interaction layer. To ensure physically feasible predictions, we proposed suitable kinematic models for all agent classes with a novel pedestrian kinematic model. We benchmark our approach on the Argoverse 2 dataset, using the state-of-the-art transformer HPTR as our baseline. Experiments demonstrate that our method improves interaction interpretability, revealing a correlation between incorrect predictions and divergence from our interaction prior. Even though incorporating the kinematic models causes a slight decrease in accuracy, they eliminate infeasible trajectories found in the dataset and the baseline model. Thus, our approach fosters trust in trajectory prediction as its interaction reasoning is interpretable, and its predictions adhere to physics.

We present Noise-to-Meaning Recursive Self-Improvement (N2M-RSI), a minimal formal model showing that once an AI agent feeds its own outputs back as inputs and crosses an explicit information-integration threshold, its internal complexity will grow without bound under our assumptions. The framework unifies earlier ideas on self-prompting large language models, Gödelian self-reference, and AutoML, yet remains implementation-agnostic. The model furthermore scales naturally to interacting swarms of agents, hinting at super-linear effects once communication among instances is permitted. For safety reasons, we omit system-specific implementation details and release only a brief, model-agnostic toy prototype in Appendix C.