arXiv:2602.08141v2 Announce Type: replace Abstract: Two parameters scale factor leading to bouncing cosmology is considered. We show that at some model parameters we obtain the deceleration parameter $q_0\approx -0.535$ at the current epoch which is in agreement with the Planck data. The equation for the transition point when the universe expands from acceleration to deceleration phases is obtained. We find the equation for the function $F(T)$ within the teleparallel gravity with torsion field $T$ which provides bouncing cosmology. For some parameters of the model the function $F(T)$ was computed. At the same time, in the framework of entropic cosmology, the associated entropy was obtained for particular model parameters. The equation of state for dark energy was obtained.
Science Journals
arXiv:2605.15308v1 Announce Type: new Abstract: LLM-driven program evolution has emerged as a powerful tool for automated scientific discovery, yet existing frameworks offer no principled guide for designing their individual components and provide no guarantee that the search converges. We introduce SMCEvolve, which recasts program search as sampling from a reward-tilted target distribution and approximates it with a Sequential Monte Carlo (SMC) sampler. From this view, three core mechanisms emerge as principled components: adaptive parent resampling, mixture of mutation with acceptance, and automatic convergence control. We further provide a finite-sample complexity analysis that bounds the LLM-call budget required to reach a target approximation error. Across math, algorithm efficiency, symbolic regression, and end-to-end ML research benchmarks, SMCEvolve surpasses state-of-the-art evolving systems while using fewer LLM calls under self-determined termination. The code is available at https://github.com/kongwanbianjinyu/SMCEvolve.
arXiv:2602.01568v2 Announce Type: replace Abstract: Multi-robot coordination often exhibits hierarchical structure, with some robots' decisions depending on the planned behaviors of others. While game theory provides a principled framework for such interactions, existing solvers struggle to handle mixed information structures that combine simultaneous (Nash) and hierarchical (Stackelberg) decision-making. We study N-robot forest-structured mixed-hierarchy games, in which each robot acts as a Stackelberg leader over its subtree while robots in different branches interact via Nash equilibria. We derive the Karush-Kuhn-Tucker (KKT) first-order optimality conditions for this class of games and show that they involve increasingly high-order derivatives of robots' best-response policies as the hierarchy depth grows, rendering a direct solution intractable. To overcome this challenge, we introduce a quasi-policy approximation that removes higher-order policy derivatives and develop an inexact Newton method for efficiently solving the resulting approximated KKT systems. We prove local exponential convergence of the proposed algorithm for games with non-quadratic objectives and nonlinear constraints. The approach is implemented in a highly optimized Julia library (MixedHierarchyGames.jl) and evaluated in hardware and simulated multi-agent experiments, demonstrating real-time convergence for complex mixed-hierarchy information structures.
arXiv:2605.15455v1 Announce Type: new Abstract: Chatbot behavior is often opaque to users, as responses can shift unpredictably across a conversation, drifting toward sycophancy, toxicity, or other unsafe responses. This can leave users vulnerable, either being misled by overly agreeable AI or manipulated by a harmful chatbot that no longer behaves as intended. To address this, we introduce multi-turn neural transparency, an interface that surfaces an LLM's internal neural activations in real time to help users anticipate and recognize how behaviors change across turns. We construct behavioral vectors for six personality traits using methods from mechanistic interpretability, identifying directions in activation space that correlate with trait expression ($R^2 \geq 0.9$) via contrastive system prompts, and visualize trait expression using a sunburst and drift panel that updates at each turn. In a randomized controlled study (N = 246), participants predicted trait expression from a system prompt alone, then rated observed behavior after interacting with the chatbot for both assistant and role-play personas. We find that participants without visualization struggled to accurately evaluate traits (RMSE $\approx$ 0.6-0.7), while the inclusion of neural transparency significantly improved both anticipation and evaluation compared to no visualization (d = -0.34 to -0.49). The multi-turn dynamic visualization additionally outperformed the static single-turn visualization on holistic evaluation of model behavior (d = -0.32). Transparency also reduced overconfidence: participants without visualization grew more confident despite no gain in accuracy. These findings suggest that surfacing internal model representations to everyday users is a meaningful step toward more transparent and informed human-AI interaction.
arXiv:2605.15307v1 Announce Type: new Abstract: Motion-centric video editing remains difficult for large generative video models, which often respond well to appearance changes but struggle to produce specific, localized actions or state transitions in an existing clip. We introduce Sound Sparks Motion, a training-free framework that enables motion editing in an audio-visual video generation model by tuning its internal multimodal conditioning signals at test time. Rather than modifying model weights, our method tunes only two lightweight variables: an audio latent derived from the source video and a residual perturbation in the text-conditioning. We find that this combination can encourage motion edits that the underlying model often struggles to realize under prompt-only control. Since there is no direct way to evaluate temporal alignment between text and motion, we guide the tuning process using a vision-language model that provides feedback indicating whether the intended motion appears in the generated video. This simple supervision yields an effective semantic objective for motion editing, while regularization and perceptual-temporal constraints help preserve content and visual quality. Beyond per-video tuning, we show that the learned latent controls are transferable across videos, suggesting that they capture reusable motion-edit directions rather than overfitting to a single example. Our results highlight multimodal conditioning tuning, particularly through the audio pathway, as a promising direction for motion-aware video editing, and suggest that test-time tuning can serve as a lightweight probing mechanism that helps reveal latent motion controls embedded in the model's multimodal conditioning. Code and data are available via our project page: https://amirhossein-razlighi.github.io/Sound_Sparks_Motion/
arXiv:2605.15304v1 Announce Type: new Abstract: The relations connecting propositions in discourse such as cause (A because B) or concession (A although B) are a subject of intense interest in Computational Linguistics and Pragmatics, but challenging to study and compare across languages. Recent progress in standardizing discourse relation inventories across datasets offers the potential to facilitate such studies, but is hindered by the complexity of relevant data and the lack of easily accessible interfaces to analyze it. In this paper we present DiscoExplorer, a new open source web interface, capable of running on local computers, which we use to make datasets from the DISRPT Shared Task on discourse relation classification publicly available, covering 16 different languages. We present the query language, search and visualization facilities for relations and signaling devices such as connectives, as well as some example studies.
arXiv:2605.15301v1 Announce Type: new Abstract: Large language models (LLMs) still struggle with the rigorous reasoning demands of hard competitive programming. While recent multi-agent frameworks attempt to bridge this reliability gap, they remain fundamentally stateless: they rely on static retrieval and discard the valuable problem-solving and debugging experience gained from previous tasks. To address this, we present Solvita, an agentic evolution framework that enables continuous learning without requiring weight updates to the underlying LLM. Solvita reorganizes problem-solving into a closed-loop system of strategy selection, program synthesis, certified supervision, and targeted hacking, executed by four specialized agents: Planner, Solver, Oracle, and Hacker. Crucially, each agent is paired with a trainable, graph-structured knowledge network. As the system operates, outcome signals, such as pass/fail verdicts, test certification quality, and adversarial vulnerabilities discovered by the Hacker, are recast as reinforcement learning updates to these network weights. This allows the agents to dynamically route future queries based on past successes and failures, effectively accumulating transferable reasoning experience over time. Evaluated across CodeContests, APPS, AetherCode, and live Codeforces rounds, Solvita establishes a new state-of-the-art among code-generation agents, outperforming existing multi-agent pipelines and nearly doubling the accuracy of single-pass baselines.
arXiv:2605.15300v1 Announce Type: new Abstract: Most Vision Language Models (VLMs) directly map outputs from ViT encoders to the LLM via a lightweight projector. While effective, recent analysis suggests this architecture suffers from an alignment challenge: visual features remain distant from the text space in the initial layers of the LLM, forcing the model to waste critical depth~\cite{zhang-etal-2024-investigating,artzy-schwartz-2024-attend} on superficial modality alignment rather than deep understanding and complex reasoning. In this work, we propose Deep Pre-Alignment (DPA), a novel architecture that replaces the standard ViT encoder with a small VLM as perceiver, ensuring visual features are deeply aligned with the text space of the target large language model. Comprehensive experiments demonstrate the effectiveness of DPA. On the 4B parameter scale, DPA outperforms baselines by 1.9 points across 8 multimodal benchmarks, with gains widening to 3.0 points at the 32B scale. Moreover, by offloading alignment to the perceiver, DPA achieves a 32.9\% reduction in language capability forgetting over 3 text benchmarks. We further demonstrate that these gains are consistent across different LLM families including Qwen3 and LLaMA 3.2, highlighting the generality of our approach. Beyond performance, DPA also offers a seamless upgrade path for current VLM development, requiring only a modular replacement for the visual encoder with marginal computation overhead.
arXiv:2510.05676v2 Announce Type: replace Abstract: Graph-based methods are becoming increasingly popular in machine learning due to their ability to model complex data and relations. Insurance fraud is a prime use case, since fraudulent claims are often the result of organised criminals that stage accidents or the same persons filing erroneous claims on multiple policies. One challenge is that graph-based approaches struggle to find meaningful representations of the data because of the high class imbalance present in fraud data. In addition, insurance graphs are heterogeneous and dynamic, given the changing relations among people, companies and policies. As a result, gradient-boosted tree approaches on tabular data still dominate the field. Therefore, we present a novel inductive graph gradient boosting machine (G-GBM) for supervised learning on heterogeneous and dynamic graphs. G-GBM combines the class-imbalance robustness of gradient boosting with heterogeneous graph information encoded through interpretable path-level feature concatenations, while preserving access to the original tabular feature space. In addition, the explicit representation of neighbourhood information enables transparent SHAP-based explanations at the metapath and feature level. We demonstrate G-GBM for insurance fraud detection on an open-source and a real-world, proprietary dataset, and find that G-GBM performs on par or better than the state-of-the-art. The associated insurance fraud dataset is publicly released to facilitate reproducibility.
arXiv:2605.15299v1 Announce Type: new Abstract: In search and recommendation systems, predictive models often suffer from temporal instability when certain input features introduce volatility in output scores. This instability can degrade model reliability and user experience especially in multi-stage systems where consistent predictions are critical for downstream decision making. We introduce Fortress, a general framework for enhancing model stability and accuracy by identifying and pruning features that contribute to inconsistent prediction scores over time. Fortress leverages historical snapshots temporally partitioned datasets capturing score fluctuations for the same entity across periods and follows a four-step process: (1) collect historical snapshots, (2) identify samples with unstable predictions, (3) isolate and remove instability-inducing features, and (4) retrain models using only stable features. While semantic features from LLMs and BERT-based models improve generalization, they often lack full query or entity coverage. Engagement-based features offer strong predictive power but tend to introduce temporal instability. Fortress mitigates this trade-off by suppressing the volatility of engagement signals while retaining their predictive value leading to more stable and accurate models. We validate Fortress on a query-to-app relevance model in a large-scale app marketplace. Offline experiments demonstrate notable improvements in prediction stability (measured by Coefficient of Variation) and classification performance (measured by PR-AUC).
arXiv:2602.00841v4 Announce Type: replace Abstract: Visual Place Recognition (VPR) demands representations robust to drastic environmental and viewpoint shifts. Existing aggregation paradigms either depend on extensive supervised training or rely on first-order pooling, often struggling to preserve structural correlations under extreme shifts or incurring high adaptation costs. In this work, we propose Riemannian Invariant Aggregation (RIA), a unified geometric framework that explicitly models second-order scene structure on the Symmetric Positive Definite (SPD) manifold. By treating perturbations as tractable congruence transformations, RIA leverages geometry-aware Riemannian mappings to project covariance descriptors into a linearized Euclidean space, effectively preserving invariant structural components while suppressing noise. Extensive evaluations demonstrate that RIA achieves zero-shot performance comparable to supervised methods, and establishes state-of-the-art accuracy with simple fine-tuning, particularly in unstructured environments. The source code will be released.
arXiv:2605.15298v1 Announce Type: new Abstract: Vision-language-action models have advanced rapidly, but robot trajectories alone provide limited coverage for learning broad physical understanding. PhysBrain 1.0 studies a complementary route: converting large-scale human egocentric video into structured physical commonsense supervision before robot adaptation. Our data engine extracts scene elements, spatial dynamics, action execution, and depth-aware relations, then turns them into question-answer supervision for training PhysBrain VLMs. The resulting physical priors are further transferred to VLA policies through a capability-preserving and language-sensitive adaptation design. Across multimodal QA benchmarks and embodied control benchmarks, including ERQA, PhysBench, SimplerEnv-WidowX, LIBERO, and RoboCasa, PhysBrain 1.0 achieves SOTA results and shows especially strong out-of-domain performance on SimplerEnv. These results suggest that scaling physical commonsense from human interaction video can provide an effective bridge from multimodal understanding to robot action.
arXiv:2605.15295v1 Announce Type: new Abstract: Machine learning (ML) algorithms are increasingly deployed in high-stakes decision-making domains such as loan approvals, hiring, and recidivism predictions. While existing fairness metrics (e.g., statistical parity, equal opportunity) effectively quantify outcome-oriented disparities, they offer limited insight into the procedure or explanation behind biased decisions. To address this gap, we propose Group-level Explanation Stability Disparity (GESD), a \textit{procedural-oriented} fairness metric that measures disparities in the stability, robustness, and sensitivity of model explanations across different subgroups in a protected category. %GESD is explainer-agnostic, model-agnostic, and extends the scope of fairness analyses to the level of explainability. We further integrate GESD into a multi-objective optimization framework that jointly optimizes for utility, outcome-based fairness, and explanation-based fairness called FEU (Fairness--Explainability--Utility). Empirical results on multiple benchmark datasets show that GESD effectively captures group-wise discrepancies in explanation quality, and that FEU improves both utility and fairness over state-of-the-art methods. By bridging outcome-based and explanation-based fairness, GESD offers a comprehensive tool for diagnosing and mitigating bias in predictive modeling. Our code and datasets are available on GitHub {\hyperlink{https://github.com/horlahsunbo/GESD}{https://github.com/horlahsunbo/GESD}}
arXiv:2605.15294v1 Announce Type: new Abstract: A DFA separates two disjoint languages $L_1$ and $L_2$ if it accepts every word in $L_1$ and rejects every word in $L_2$. Algorithms for active learning of small separating DFAs have many applications, e.g., for learning network invariants, learning contextual assumptions in compositional verification, learning state machines from large amounts of log data, and learning bug pattern descriptions. We propose a simple active learning algorithm, inspired by $L^{\#}$, that learns a minimal separating DFA for disjoint languages $L_1$ and $L_2$ if one exists. Experiments show that our algorithm significantly outperforms existing active learning algorithms on both randomly generated and industrial benchmarks.
arXiv:2605.15290v1 Announce Type: new Abstract: Hyperparameter transfer across model architectures dramatically reduces the amount of compute necessary for tuning large language models (LLMs). The maximal update parameterization ({\mu}P) ensures transfer through principled mathematical analysis but can be challenging to derive for new model architectures. Building on the spectral feature-learning view of Yang et al. (2023a), we make two advances. First, we promote spectral norm conditions on the weights from a heuristic to the definition of feature learning, and as a consequence arrive at the Complete-P depth and weight-decay scalings without recourse to lazy-learning. Second, we consider a modified spectral norm that preserves the valid scaling law of network weights when weight matrices are not full rank. This enables (to our knowledge, the first) derivation of {\mu}P scalings for grouped-query attention (GQA). We demonstrate the efficacy of our theoretical derivations by showing learning rate transfer across the GQA repetition hyperparameter as well as experiments regarding transfer over weight decay.
arXiv:2604.21251v5 Announce Type: replace Abstract: Large language models (LLMs) trained on unfiltered corpora inherently risk retaining sensitive information, necessitating selective knowledge unlearning for regulatory compliance and ethical safety. However, existing parameter-modifying methods face fundamental limitations: high computational costs, uncontrollable forgetting boundaries, and strict dependency on model weight access. These constraints render them impractical for closed-source models, yet current non-invasive alternatives remain unsystematic and reliant on empirical experience. To address these challenges, we propose the Controllable Alignment Prompting for Unlearning (CAP) framework, an end-to-end prompt-driven unlearning paradigm. CAP decouples unlearning into a learnable prompt optimization process via reinforcement learning, where a prompt generator collaborates with the LLM to suppress target knowledge while preserving general capabilities selectively. This approach enables reversible knowledge restoration through prompt revocation. Extensive experiments demonstrate that CAP achieves precise, controllable unlearning without updating model parameters, establishing a dynamic alignment mechanism that overcomes the transferability limitations of prior methods.
arXiv:2604.26086v2 Announce Type: replace Abstract: Accurate quantification of protein-nanoparticle interactions is essential for applications in nanobiotechnology, nanomedicine, and drug delivery. Motivated by recent computational and experimental work, we combine coarse-grained united-atom (UA) models with molecular docking to characterize protein adsorption on SiO_2 nanoparticles. We construct orientation-resolved heatmaps in which polar and azimuthal angles uniquely specify the relative protein-nanoparticle pose, and the map amplitude reports binding propensity via the minimum UA adsorption energy or the docking score. Each angular bin corresponds to a distinct docked complex, enabling systematic comparison of binding geometries across models. To relate docking score landscapes to Boltzmann-averaged UA adsorption energetics, we analyze eight birch pollen allergen proteins previously studied experimentally. Similarity between the two orientational distributions is quantified using the Jensen-Shannon divergence (JSD). We find encouraging agreement between the two approaches in several cases, while also identifying limitations and routes for improvement, including optimized angular resolution and iterative refinement of interaction parameters. Overall, this framework provides a quantitative bridge between coarse-grained energetics and docking outputs at protein-nanoparticle interfaces, supporting improved predictive modeling and mechanistic insight into protein-nanoparticle binding landscapes.
arXiv:2605.15458v1 Announce Type: new Abstract: Video diffusion models have made rapid progress in perceptual realism and temporal coherence, but they remain primarily optimized for plausible generation rather than verifiable reasoning. This limitation is especially pronounced in tasks where generated videos must satisfy explicit spatial, temporal, or logical constraints. Inspired by the role of reinforcement learning with verifiable rewards (RLVR) in reasoning-oriented language models, we introduce VideoRLVR, a practical recipe for optimizing video diffusion models with rule-based feedback. VideoRLVR formulates video reasoning as the generation of verifiable visual trajectories and consists of an SDE-GRPO optimization backbone, dense decomposed rewards, and an Early-Step Focus strategy for efficient training. The Early-Step Focus strategy restricts policy optimization to the early denoising phase, reducing training latency by about 40% while preserving performance. We evaluate VideoRLVR on Maze, FlowFree, and Sokoban, three procedurally generated domains with objective success criteria. Across these tasks, VideoRLVR consistently improves over supervised fine-tuning baselines, with dense decomposed rewards proving especially important in low-success-rate settings. Our RL-optimized model also outperforms the evaluated proprietary and open-source video generation models on these verifiable reasoning benchmarks and out-of-domain benchmarks. These results suggest that verifiable RL can move video models beyond perceptual imitation toward more reliable rule-consistent visual reasoning.
arXiv:2604.26733v4 Announce Type: replace Abstract: Live future prediction refers to the task of making predictions about real-world events before they unfold. This task is increasingly studied using large language model-based agent systems, and it is important for building agents that can continually learn from the real world. It can provide a large number of prediction questions grounded in diverse real-world events, while preventing answer leakage. To leverage the advantages of future prediction, we present FutureWorld, a live agentic reinforcement learning environment that closes the training loop between prediction, outcome realization, and parameter updates. Specifically, we modify and extend verl-tool, resulting in a new framework that we call verl-tool-future. Unlike standard reinforcement learning training frameworks that rely on immediate rewards, verl-tool-future stores prediction-time rollouts, backfills rewards after real-world outcomes become available, and then replays the completed trajectories for policy update. Across three open-source agents, successive FutureWorld training rounds lead to consistent improvements in prediction accuracy, probabilistic scoring, and calibration, demonstrating that delayed real-world outcome feedback can serve as an effective reinforcement learning signal.
arXiv:2601.23068v2 Announce Type: replace Abstract: Computing the importance of features in supervised classification tasks is critical for model interpretability. Shapley values are a widely used approach for explaining model predictions, but require direct access to the underlying model, an assumption frequently violated in real-world deployments. We investigate whether meaningful feature attributions can be obtained in a zero-shot setting, using only the input data distribution and no evaluations of the target model. Because multiple models can produce identical predictions yet yield different Shapley decompositions, the mapping from data to attributions is not uniquely identifiable. We therefore target attributions that are "true to the data" rather than "true to the model", learning a posterior mean attribution under a meta-training prior. To this end, we introduce ExplainerPFN, a tabular foundation model built on TabPFN, pretrained on synthetic structural causal datasets supervised with exact or near-exact Shapley values, that predicts feature attributions for unseen tabular datasets without model access, gradients, or example explanations. Our contributions are fourfold: (1) we show that few-shot surrogate explainers achieve high SHAP fidelity with as few as two reference observations; (2) we propose ExplainerPFN, the first zero-shot method for estimating Shapley-value-style feature attributions without access to the underlying model or reference explanations, providing a principled attribution where no existing explainer can be applied; (3) we release an open-source implementation including the full training pipeline and synthetic data generator; and (4) through extensive experiments on real and synthetic datasets, we show that ExplainerPFN achieves performance competitive with few-shot surrogate explainers that rely on 2-10 SHAP examples.
arXiv:2601.21798v2 Announce Type: replace Abstract: Large Language Models(LLMs) have revolutionized text generation and multimodal perception,but their capabilities in 3D content generation remain underexplored. Existing methods compromise by producing either low-resolution meshes or coarse structural proxies, failing to capture finegrained geometry natively. In this paper, we propose CG-MLLM, a novel Multi-modal Large Language Model (MLLM) capable of 3D captioning and high-resolution 3D generation in a single framework. Leveraging the Mixture-ofTransformer architecture, CG-MLLM decouples disparate modeling needs, where the Token-level Autoregressive (TokenAR) Transformer handles token-level content, and the Block-level Autoregressive (BlockAR) Transformer handles blocklevel content. By integrating a pre-trained visionlanguage backbone with a specialized 3D VAE latent space, CG-MLLM facilitates long-context interactions between standard tokens and spatial blocks within a single integrated architecture. Experimental results show that CG-MLLM significantly outperforms existing MLLMs in generating high-fidelity 3D objects, effectively bringing high-resolution 3D content creation into the mainstream LLM paradigm. Beyond generation, we further observe that learning to produce 3D content transfers back to perception, strengthening the model's image-based 3D understanding.
arXiv:2605.00424v2 Announce Type: replace Abstract: Agent skills - structured packages of instructions, scripts, and references that augment a large language model (LLM) without modifying the model itself - have moved from convenience to first-class deployment artifact. The runtime that loads them inherits the same problem package managers and operating systems have always faced: a piece of content claims a behavior; the runtime must decide whether to believe it. We argue this paper's central thesis up front: a skill is untrusted code until it is verified, and the runtime that loads it must enforce that default rather than infer trust from a signature, a clearance, or a registry of origin. Without skill verification, a human-in-the-loop (HITL) gate must fire on every irreversible call - which is operationally untenable and degrades into rubber-stamping at any non-trivial scale. With skill verification treated as a separate, gated process, HITL fires only for what is unverified, and the system becomes sustainable. We give a trust schema that includes an explicit verification level on every skill manifest; a capability gate whose HITL policy is a function of that verification level; a biconditional correctness criterion that any candidate verification procedure must satisfy on an adversarial-ensemble exercise; and a portable runtime profile with ten normative guidelines abstracted from a working open-source reference implementation. The contribution is harness- and model-agnostic; nothing here requires retraining, fine-tuning, or proprietary infrastructure.
arXiv:2605.15288v1 Announce Type: new Abstract: The Electron-Ion Collider (EIC) is a next-generation particle accelerator facility designed to probe the fundamental structure of matter such as the origins of nucleon mass, spin, and the dynamic behavior of quarks and gluons within nucleon and nucleus. As the electromagnetic calorimeter in the barrel region, the Barrel Imaging Calorimeter (BIC) is tasked with precise energy measurements of electrons and photons as well as efficient separation of these particles from background pions. The BIC integrates Pb/SciFi sampling layers and AstroPix silicon pixel sensors for three-dimensional shower imaging. The Korean group has actively contributed through silicon chip testing, module assembly, prototype development, beam test, readout system design, and detailed simulations. This presentation highlights the recent progress and plans for the R\&D of the Barrel Imaging Calorimeter in Korea.
arXiv:2605.15285v1 Announce Type: new Abstract: Derivative-Informed Operator Learning (DIOL), i.e. learning a (nonlinear) operator and its derivatives, is an open research frontier at the foundations of the influential field of Operator Learning (OL). In particular, Universal Approximation Theorems (UATs) of nonlinear operators and their derivatives are foundational open questions and delicate problems in nonlinear functional analysis. In this manuscript, we prove the first UATs of non-linear $k$-times differentiable operators between Banach spaces and their derivatives, uniformly on compact sets and in weighted Sobolev norms for general finite input measures, via OL architectures. Our results are the first complete generalizations of the corresponding influential classical results in [Hornik, 1991] to infinite-dimensional settings and OL. We discuss several open areas where DIOL and our UATs find applications: high-order accuracy in OL, fast constrained optimization in Banach spaces (e.g. optimal control of PDEs, inverse problems) and numerical methods for infinite-dimensional PDEs (e.g. HJB PDEs on Banach spaces from optimal control of PDEs, SPDEs, path-dependent systems, partially observed systems, mean-field control). We parameterize nonlinear operators via Encoder-Decoder Architectures, renowned classes in OL due to their generality, including classical architectures, such as DeepONets, Deep-H-ONets, PCA-Nets. Our results are based on four key features that allow us to prove UATs in full generality: (i) Approximation Properties of Banach spaces. (ii) $k$-times continuous differentiability in the sense of Bastiani (weaker than $k$-times continuous Fr\'echet differentiability). (iii) Natural compact-open topologies for UA; indeed, we show that UA in standard compact-open topologies induced by operator norms is violated even for Fr\'echet derivatives. (iv) Construction of novel weighted Sobolev spaces for the UA.
arXiv:2601.21702v3 Announce Type: replace Abstract: We consider Representation Misdirection (RM), a class of large language model (LLM) unlearning methods that achieve forgetting by redirecting the forget-representations, that is, latent representations of forget-samples, toward a target vector. Despite being important, the roles of the target vector used in RM, however, remain underexplored. Here, we approach and revisit RM through the lens of the Linear Representation Hypothesis. Specifically, if one can identify a one-dimensional representation corresponding to a high-level concept, the Linear Representation Hypothesis enables linear operations on this concept vector within the forget-representation space. Under this view, we hypothesize that, beyond forgetting, machine unlearning via RM elicits controllable emergent side behaviors and stronger side capabilities corresponding to the high-level concept. Our hypothesis is empirically validated across a wide range of tasks, including behavioral control (e.g., controlling unlearned models' truthfulness, sentiment, refusal, and language) and capability enhancement (e.g., improving unlearned models' in-context learning (ICL) capability). Our findings reveal that this phenomenon could be either a hidden risk if misused or a mechanism that can be harnessed for developing unlearned models that require stronger capabilities and controllable behaviors.