arXiv:2606.02418v1 Announce Type: cross
Abstract: Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found. We introduce an LLM-guided evolutionary workflow in which language models mutate Python programs that generate bivariate-bicycle and perturbed bivariate-bicycle code ans\"atze. Across five campaigns, the system performed approximately 1{,}650 evolutionary iterations, screened about $2 \times 10^5$ candidate codes, and required ${\sim}140$ hours of computation and ${\sim}$US\$400 in LLM inference cost. Candidate codes are evaluated through a staged validation pipeline combining $\mathrm{GF}(2)$ rank computation, distance estimation and certification, mixed-integer linear programming, BLISS Tanner-graph deduplication, decomposability analysis, and local-Clifford equivalence checks. At block length $n \leq 360$, the workflow identifies 465 distinct candidate codes: 97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants. The CSS search recovers known high-performing codes and finds new finite-length representatives, including an indecomposable [[288,16,12]] code and higher-weight codes with up to $k = 50$ at distance $d = 8$. The non-CSS search produces perturbed codes matching the gross-code figure of merit at [[144,12,12]], along with additional high-distance candidates reported as certified values or upper bounds according to MILP status. Overall, these results show that LLM-guided program evolution can serve as a practical tool for structured quantum-code discovery when paired with independent evaluation.
Science Journals
arXiv:2606.02529v1 Announce Type: cross
Abstract: Incentive design studies how a central authority can influence strategic agents through payments, subsidies, or taxes, so that individual objectives align with collective welfare. This paper introduces a No-Regret Adaptive Incentive Design (RAID) framework for nonlinear games with continuous action spaces and private agent costs. In this framework, the authority (planner) designs incentives that regulate the Nash equilibrium toward a socially optimal action profile, while simultaneously learning agents' unknown preferences from repeated strategic responses. We formulate the RAID problem and construct a least-squares estimator whose strong consistency requires only diminishing excitation. Leveraging this weak excitation requirement, we propose a switching incentive policy that alternates between probing (exploration) and estimate-based (exploitation) incentives. The resulting policy achieves an $O(t^{-0.5})$ parameter estimation rate and accumulates $O(t^{0.5}\log t)$ squared social-cost regret, almost surely. We further extend the framework to an endogenous-noise response model, where standard least-squares estimation is biased due to an error-in-variables correlation between the noise and agent responses. We utilize a repeated-sampling estimator and corresponding switching policy that retain the same almost-sure convergence and regret rates. Numerical experiments validate the effectiveness and predicted convergence rates of the method.
arXiv:2606.01671v1 Announce Type: new
Abstract: In the contemporary epoch of multilingual education, learning idioms provides a fascinating gateway towards creativity, cultural values, historical context, and diverse perspectives inherent to various linguistic traditions. This paper showcases the navigation of retaining figurative and cultural semantics in low-resource Southeast Asian languages such as Hindi, Bengali, and Thai, where culturally rich idioms pose significant obstacles for computational modeling and cross-linguistic transfer due to their deep metaphorical complexity. To tackle such complexity, we present Varnika, a reconstructed multimodal idiom corpus comprising 3,533 multilingual idioms, enriched with seven idiomatic tones aligned with both textual and visual representations. Additionally, to infer informative idiomatic understanding, we introduce a Hybrid Mixture-of-Experts (HybridMoE) framework that embeds multiple idiomatic expert opinions while mitigating expert sparsity by integrating outputs from both selected and unselected experts through controlled hybridization, further augmented with Idiomatic Property Signals via masked multimodal embeddings. To analyze the performance across multiple dimensions, we propose the IDIO-TONE and Idiomatic Validation Score, a three-stage evaluation pipeline measuring (i) literal translation fidelity, (ii) visual-semantic alignment, and (iii) idiomatic meaning retention. Empirical evaluations highlight that HybridMoE achieves 5--6\% performance gains across advanced vision language models, demonstrating improved representation of figurative language and culturally embedded meaning in multilingual multimodal settings
arXiv:2503.22939v4 Announce Type: replace
Abstract: The integration of heterogeneous multi-omics datasets at a systems level remains a central challenge for developing analytical and computational models in precision cancer diagnostics. This paper introduces Multi-Omics Graph Kolmogorov-Arnold Network (MOGKAN), a deep learning framework that utilizes messenger-RNA, micro-RNA sequences, and DNA methylation samples together with Protein-Protein Interaction (PPI) networks for cancer classification across 31 different cancer types. The proposed approach combines differential gene expression with DESeq2, Linear Models for Microarray (LIMMA), and Least Absolute Shrinkage and Selection Operator (LASSO) regression to reduce multi-omics data dimensionality while preserving relevant biological features. The model architecture is based on the Kolmogorov-Arnold theorem principle and uses trainable univariate functions to enhance interpretability and feature analysis. MOGKAN achieves classification accuracy of 96.28 percent and exhibits low experimental variability in comparison to related deep learning-based models. The biomarkers identified by MOGKAN were validated as cancer-related markers through Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis. By integrating multi-omics data with graph-based deep learning, our proposed approach demonstrates robust predictive performance and interpretability with potential to enhance the translation of complex multi-omics data into clinically actionable cancer diagnostics.
arXiv:2505.18877v4 Announce Type: replace
Abstract: Low-Rank Adaptation (LoRA) lowers the computational and memory overhead of fine-tuning large models by updating a low-dimensional subspace of the pre-trained weight matrix. Albeit efficient, LoRA exhibits suboptimal convergence and noticeable performance degradation, due to inconsistent and imbalanced weight updates induced by its nonunique low-rank factorizations. To overcome these limitations, this article identifies the optimal low-rank factorization per step that minimizes an upper bound on the loss. The resultant refactored low-rank adaptation (RefLoRA) method promotes a flatter loss landscape, along with consistent and balanced weight updates, thus speeding up stable convergence. Extensive experiments evaluate RefLoRA on natural language understanding, and commonsense reasoning tasks with popular large language models including DeBERTaV3, LLaMA-7B, LLaMA2-7B and LLaMA3-8B. The numerical tests corroborate that RefLoRA converges faster, outperforms various benchmarks, and enjoys negligible computational overhead compared to state-of-the-art LoRA variants.
arXiv:2606.02486v1 Announce Type: new
Abstract: Vision-Language-Action (VLA) models generalize across static manipulation but fail when objects move during task execution. They map the current observation to an action and assume the scene is stationary between observation and execution, so at any non-trivial object speed the resulting latency exceeds the time available to grasp. We close this gap with AHEAD (Anticipatory Horizon Extrapolation with Adaptive Dynamics), a predict-then-act wrapper that augments a frozen VLA with a motion-aware latent world model. A small world model trained on manipulation video forecasts future patch tokens in the VLA's feature space, conditioned on per-token velocity and acceleration from optical flow. A language-and-motion saliency mask concentrates prediction on task-relevant patches, and the model rolls forward for an adaptive horizon, halting when prediction uncertainty crosses a threshold. The frozen action decoder then receives the predicted future tokens in place of the current ones. AHEAD adds 4.9M parameters to a frozen 7B OpenVLA and reaches 79 to 97% success across 20 dynamic simulation scenarios where the strongest baseline reaches 31 to 58%. On a physical UFactory xArm 7, AHEAD succeeds on 29/30 to 30/30 on three conveyor and rolling-ball tasks, 23/30 on paddle interception, and 19/30 on projectile catching where every baseline scores 0/30.
arXiv:2606.02490v1 Announce Type: new
Abstract: This work studies neural architectures for classifying symmetric positive-definite matrices, focusing on congruence-like layers, in which the input matrix is multiplied on the left and right by a (possibly rectangular) weight matrix $W$ and its transpose. Such layers lie at the core of the celebrated SPDNet and have also been employed independently for dimensionality reduction on positive-definite data. We show that the (semi)-orthogonality constraint commonly imposed on $W$ limits the expressivity of these layers: for certain activation functions, the resulting architecture collapses to a one-hidden-layer equivalent. This lack of expressivity follows from a loss of spectral diversity in congruence-like layers for semi-orthogonal $W$ and is a direct consequence of Poincar\'e's separation theorem. We then examine the choice of the final classifier, comparing several Riemannian classifiers and discussing their compatibility with the feature maps produced by congruence-like layers.
arXiv:2504.05033v3 Announce Type: replace
Abstract: Cloth manipulation is a difficult problem mainly because of the non-rigid nature of cloth, which makes a good representation of deformation essential. We present a new representation for the deformation-state of clothes. First, we propose the dGLI disk representation based on topological indices computed for edge segments of the cloth border that are arranged on a circular grid. The heat-map of the dGLI disk uncovers patterns that correspond to features of the cloth state that are consistent for different shapes, sizes or orientation of the cloth. We then abstract these important features from the dGLI disk into a circle, calling it the Cloth StatE representation (CloSE). This representation is compact, continuous, and general for different shapes. We show that this representation is able to accurately predict the fold locations for several simulation clothing datasets. Finally, we also show the strengths of this representation in two relevant applications: semantic labeling and high- and low-level planning. The code and the dataset can be accessed from: https://close-representation.github.io/
arXiv:2505.24069v4 Announce Type: replace
Abstract: Large language models (LLMs) are deployed on increasingly complex tasks that require multi-step decision-making. Understanding their algorithmic reasoning abilities is therefore crucial. However, we lack a diagnostic benchmark for evaluating these capabilities. We propose to use data structures as a principled lens: as fundamental building blocks of algorithms, they naturally probe structural reasoning - the ability to understand and manipulate relationships such as order, hierarchy, and connectivity that underpin algorithmic reasoning. We introduce DSR-Bench (Data Structure Reasoning Benchmark), spanning 20 data structures, 35 operations, and 4,140 problem instances. DSR-Bench features hierarchical task organization, fully automated generation and evaluation, and fine-grained diagnostics. Evaluating 13 state-of-the-art LLMs reveals critical limitations: the top-performing model achieves only 0.46/1 on challenging instances. Three auxiliary probes targeting more realistic usages expose further weaknesses: models perform poorly on spatial data and context-rich scenarios, and they struggle to reason over their own code.
arXiv:2505.24621v3 Announce Type: replace
Abstract: Recent advancements in large language models (LLMs) have transformed natural language understanding and generation, leading to extensive benchmarking across diverse tasks. However, cryptanalysis - a critical area for data security and its connection to LLMs' generalization abilities - remains underexplored in LLM evaluations. To address this gap, we evaluate the cryptanalytic potential of state-of-the-art LLMs on ciphertexts produced by a range of cryptographic algorithms. We introduce a benchmark dataset of diverse plaintexts, spanning multiple domains, lengths, writing styles, and topics, paired with their encrypted versions. Using zero-shot and few-shot settings along with chain-of-thought prompting, we assess LLMs' decryption success rate and discuss their comprehension abilities. Our findings reveal key insights into LLMs' strengths and limitations in side-channel scenarios and raise concerns about their susceptibility to under-generalization-related attacks. This research highlights the dual-use nature of LLMs in security contexts and contributes to the ongoing discussion on AI safety and security.
arXiv:2506.05412v4 Announce Type: replace
Abstract: Where someone looks is a nonverbal communication cue that children and adults readily use. How well can Vision-Language Models (VLMs) infer gaze targets? To construct evaluation stimuli, we captured 1,360 real-world photos of scenes in which a person gazes at one of several objects on a table. Importantly, we also controlled the gazer's head orientation: sometimes it was directed toward the gaze target, sometimes toward a distractor object, and sometimes left unconstrained. We found a substantial performance gap between VLMs and humans, ruled out alternative explanations such as resolution and object-naming skills, and identified the main reason for the gap as VLMs inferring gaze direction using head orientation rather than eye appearance. Such a bias is likely due to data rather than architecture, as suggested by a proof-of-concept experiment finetuning a transformer-based vision model. Future work should investigate whether these findings hold broadly across various deep learning methods trained on existing data, and whether better data mitigates this problem for all architectures. Pinpointing the reason sets the stage for technologies that can interpret gaze targets to have more efficient interactions with humans.
arXiv:2504.21291v3 Announce Type: replace
Abstract: Logic rules allow analysis of complex relationships to be expressed easily, especially for transitive relations in critical applications. However, understanding and predicting the efficiency of different inference methods remain challenging, even for simplest rules given different kinds of input data.
This paper analyzes the efficiency of all three types of well-known inference methods -- query-driven, ground-and-solve, and fact-driven -- along with their respective optimizations, and compares with optimal complexities for the first time, for analyzing transitive graph relations. We also experiment with rule systems widely considered to have the best performance. We analyze all well-known rule variants and widely varying input graphs. The results include precisely calculated optimal time complexities; comparative analysis across different inference methods, rule variants, and graph types; confirmation with performance experiments; as well as discovery of a performance bug.
arXiv:2505.05362v2 Announce Type: replace
Abstract: Formal verification has become increasingly important because of the kinds of guarantees that it can provide for software systems. Verification of models of biological and medical systems is a promising application of formal verification. Human neural networks have recently been emulated and studied as a biological system. In this paper, we provide a model of some crucial neuronal circuits, called "archetypes", in the Coq Proof Assistant and prove properties concerning their dynamic behavior. Understanding the behavior of these modules is crucial because they constitute the elementary building blocks of bigger neuronal circuits. We consider seven fundamental archetypes (simple series, series with multiple outputs, parallel composition, positive loop, negative loop, inhibition of a behavior, and contralateral inhibition), and prove an important representative property for six of them. In building up to our model of archetypes, we also provide a general model of "neuronal circuits", and prove a variety of general properties about neurons and circuits. In addition, we have defined our model with a longer term goal of modelling the composition of basic archetypes into larger networks, and structured our libraries with definitions and lemmas useful for proving the properties in this paper as well as those to be proved as future work.
arXiv:2506.06228v2 Announce Type: replace
Abstract: We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal robustness, which robustifies the Lyapunov and zeroing barrier certificates of data-driven dynamical systems against model prediction uncertainties using conformal prediction. It quantifies these uncertainties by leveraging rank statistics of prediction scores over system trajectories, without assuming any specific underlying structure of the prediction model or distribution of the uncertainties. With the quantified uncertainty information, we further construct the conformally robust control Lyapunov function (CR-CLF) and control barrier function (CR-CBF), data-driven counterparts of the CLF and CBF, for fully data-driven control with statistical guarantees of finite-horizon exponential stability and safety. The performance of the proposed concept is validated in numerical simulations with four benchmark nonlinear control problems.
arXiv:2012.02110v2 Announce Type: replace
Abstract: Pre-trained language models have significantly advanced natural language processing (NLP), especially with the introduction of BERT and its optimized version, RoBERTa. While initial research focused on English, single-language models can be advantageous compared to multilingual ones in terms of pre-training effort, overall resource efficiency or downstream task performance. Despite the growing popularity of prompt-based LLMs, more compute-efficient BERT-like models remain highly relevant. In this work, we present the first German single-language RoBERTa model, GottBERT, pre-trained exclusively on the German portion of the OSCAR dataset. Additionally, we investigated the impact of filtering the OSCAR corpus. GottBERT was pre-trained using fairseq and standard hyperparameters. We evaluated its performance on two Named Entity Recognition (NER) tasks (Conll 2003 and GermEval 2014) and three text classification tasks (GermEval 2018 fine and coarse, and 10kGNAD) against existing German BERT models and two multilingual models. Performance was measured using the $F_{1}$ score and accuracy. The GottBERT base and large models showed competitive performance, with GottBERT leading among the base models in 4 of 6 tasks. Contrary to our expectation, the applied filtering did not significantly affect the results. To support the German NLP research community, we are releasing the GottBERT models under the MIT license.
arXiv:2208.00335v5 Announce Type: replace
Abstract: Rule extraction is a central problem in interpretable machine learning because it seeks to convert opaque predictive behavior into human-readable symbolic structure. This paper presents Chat Incremental Pattern Constructor (ChatIPC), a lightweight incremental symbolic learning system that extracts ordered token-transition rules from text, enriches them with definition-based expansion, and constructs responses by similarity-guided candidate selection. The system may be viewed as a rule extractor operating over a token graph rather than a conventional classifier. I formalize the knowledge base, definition expansion, candidate scoring, repetition control, English-rule heuristics, and response construction mechanisms used by ChatIPC. I further situate the method within the literature on rule extraction, decision tree induction, association rules, interpretable machine learning, and sequence construction. The updated implementation is also reviewed in detail: it parses an embedded dictionary, normalizes lexical keys, caches definition tokens and part-of-speech tags, computes Jaccard scores on bitsets, applies heuristic linguistic bonuses, and persists the knowledge base with a versioned binary format. The paper emphasizes mathematical formulation and algorithmic clarity, and it provides pseudocode for the learning, scoring, and construction algorithms.
arXiv:2505.12741v3 Announce Type: replace
Abstract: Language models are increasingly used not only as standalone predictors but also as components in larger inference systems, from test-time scaling to multi-agent collaboration. We study language model networks, where pre-trained language models serve as reusable nodes and intelligence emerges from their topology, communication, and optimization. Existing systems mostly communicate through natural language: easy to deploy, but discrete, inefficient, and hard to optimize from end-task supervision. We propose LMNet, a dense and differentiable realization of this paradigm. LMNet uses stripped LLMs as vertex modules and trainable seq2seq modules as communication edges, enabling intermediate nodes to exchange dense vectors while preserving natural-language input and output at the system boundary. By bypassing intermediate embedding and de-embedding, LMNet enables efficient information transfer, end-to-end gradient optimization, and learned communication beyond hand-designed protocols. Experiments show performance with small additional training cost and effective adaptation under limited supervision.
arXiv:2506.06572v3 Announce Type: replace
Abstract: Due to possible devastating consequences, counteracting sensor data attacks is an extremely impor- tant topic, which has not seen sufficient study. To the best of our knowledge, this paper develops the first meth- ods that accurately identify/eliminate only the problem- atic attacked sensor data presented to a sequence es- timation/regression algorithm under any attack from our attack model. The approach does not assume a known form for the statistical model of the sensor data, allow- ing data-driven and machine learning sequence estima- tion/regression algorithms to be protected. A simple pro- tection approach for attackers not endowed with knowledge of the details of our protection approach is first developed, followed by additional processing for attacks based on pro- tection system knowledge. Experimental results show that the simple approach achieves performance indistinguish- able from that for an approach which knows which sensors are attacked. For cases where the attacker has knowledge of the protection approach, experimental results indicate the additional processing can be configured so that the worst-case degradation under the additional processing and a large number of sensors attacked can be made signif- icantly smaller than the worst-case degradation of the sim- ple approach, and close to an approach which knows which sensors are attacked, with just a slight degradation under no attacks. Mathematical descriptions of the worst-case attacks are used to demonstrate the additional processing will provide similar advantages for cases for which we do not have numerical results. All the data-driven/machine learning processing used in our approaches employ only unattacked training data.
arXiv:2506.11083v3 Announce Type: replace
Abstract: We introduce RedDebate, a novel multi-agent debate framework that provides the foundation for Large Language Models (LLMs) to identify and mitigate their unsafe behaviours. AI safety approaches often rely on costly human evaluation or isolated single-model assessment, both constrained by scalability and prone to oversight failures. RedDebate employs collaborative argumentation among multiple LLMs across diverse debate scenarios, enabling them to critically evaluate one another's reasoning and systematically uncover unsafe failure modes through fully automated red-teaming. To support this, we propose designing distinct long-term memory modules that preserve safety-relevant insights from debate interactions and leverage them during subsequent inference, facilitating continuous refinement of model behaviour. Empirical evaluation on safety benchmarks across a diverse set of models demonstrates that RedDebate substantially reduces unsafe outputs. While debate alone allows LLMs to refine their behaviour, the addition of memory yields further error reductions. To the best of our knowledge, RedDebate is the first fully automated framework to unify multi-agent debate and red-teaming to progressively enhance LLM safety without human intervention.
arXiv:2506.11903v5 Announce Type: replace
Abstract: Advances in transformer-based language models have highlighted the benefits of language-specific pre-training on high-quality corpora. In this context, German NLP stands to gain from updated architectures and modern datasets tailored to the linguistic characteristics of the German language. GeistBERT seeks to improve German language processing by incrementally training on a diverse corpus and optimizing model performance across various NLP tasks. We pre-trained GeistBERT using fairseq, following the RoBERTa base configuration with Whole Word Masking (WWM), and initialized from GottBERT weights. The model was trained on a 1.3 TB German corpus with dynamic masking and a fixed sequence length of 512 tokens. For evaluation, we fine-tuned the model on standard downstream tasks, including NER (CoNLL 2003, GermEval 2014), text classification (GermEval 2018 coarse/fine, 10kGNAD), and NLI (German XNLI), using $F_1$ score and accuracy as evaluation metrics. GeistBERT achieved strong results across all tasks, leading among base models and setting a new state-of-the-art (SOTA) in GermEval 2018 fine text classification. It also outperformed several larger models, particularly in classification benchmarks. To support research in German NLP, we release GeistBERT under the MIT license.
arXiv:2506.13702v4 Announce Type: replace
Abstract: Single-trajectory preference optimization methods learn from datasets of ((prompt, response, reward)) tuples, offering a practical alternative to pairwise preference learning by directly leveraging scalar feedback. Existing approaches such as Direct Reward Optimization (DRO) have demonstrated promising results but rely on value function estimation, introducing additional variance, optimization complexity, and sensitivity to off-policy data. We introduce Reward Partition Optimization (RPO), a simple and scalable reward-driven objective that eliminates the need for value function learning. RPO normalizes rewards through a partition-based formulation estimated directly from prompt-level reward distributions, yielding a stable supervised optimization objective without auxiliary models or reinforcement learning loops. We evaluate RPO across multiple encoder-decoder and decoder-only language models using automatic metrics, LLM-as-a-judge evaluations, and optimization stability analyses. Experimental results show that RPO consistently outperforms strong baselines, including SFT, KTO, and DRO, while producing more aligned, diverse, and less toxic generations.
arXiv:2506.14003v5 Announce Type: replace
Abstract: Machine unlearning (MU) for large language models (LLMs), commonly referred to as LLM unlearning, seeks to remove specific undesirable data or knowledge from a trained model, while maintaining its performance on standard tasks. While unlearning plays a vital role in protecting data privacy, enforcing copyright, and mitigating sociotechnical harms in LLMs, we identify a new vulnerability post-unlearning: unlearning trace detection. We discover that unlearning leaves behind persistent "fingerprints" in LLMs, detectable traces in both model behavior and internal representations. These traces can be identified from output responses, even when prompted with forget-irrelevant inputs. Specifically, even a simple supervised classifier can determine whether a model has undergone unlearning, using only its prediction logits or even its textual outputs. Further analysis shows that these traces are embedded in intermediate activations and propagate nonlinearly to the final layer, forming low-dimensional, learnable manifolds in activation space. Through extensive experiments, we demonstrate that unlearning traces can be detected with over 90% accuracy even under forget-irrelevant inputs, and that larger LLMs exhibit stronger detectability. These findings reveal that unlearning leaves measurable signatures, introducing a new risk of reverse-engineering forgotten information when a model is identified as unlearned, given an input query.
arXiv:2506.16114v3 Announce Type: replace
Abstract: Generative recommendations (GR), which usually include item tokenizers and generative Large Language Models (LLMs), have demonstrated remarkable success across a wide range of scenarios. The majority of existing research efforts primarily concentrate on developing powerful item tokenizers or advancing LLM decoding strategies to attain superior performance. However, the critical fine-tuning step in GR frameworks, which is essential for adapting LLMs to recommendation data, remains largely unexplored. Current approaches predominantly rely on either the next-token prediction loss of supervised fine-tuning (SFT) or recommendationspecific direct preference optimization (DPO) strategies. Both methods ignore the exploration of possible positive unobserved samples, which is commonly referred to as the exposure bias problem. To mitigate this problem, this paper treats the GR as a multi-step generation task and constructs a GFlowNets-based fine-tuning framework (GFlowGR). The proposed framework integrates collaborative knowledge from traditional recommender systems to create an adaptive trajectory sampler and a comprehensive reward model. Leveraging the diverse generation property of GFlowNets, along with sampling and heuristic weighting techniques, GFlowGR emerges as a promising approach to mitigate the exposure bias problem. Extensive empirical results on two real-world datasets and with two different GR backbones highlight the effectiveness and robustness of GFlowGR.
arXiv:2506.21025v3 Announce Type: replace
Abstract: This work develops novel energy-stable parametric finite element methods (ES-PFEM) for the Willmore flow and curvature-dependent geometric gradient flows of surfaces in three dimensions. The key to achieving the energy stability lies in the use of two novel geometric identities: (i) a reformulated variational form of the normal velocity field, and (ii) incorporation of the temporal evolution of the mean curvature into the governing equations. These identities enable the derivation of a new variational formulation. By using the parametric finite element method, an implicit fully discrete scheme is subsequently developed, which maintains the energy dissipative property at the fully discrete level. Based on the ES-PFEM, comprehensive insights into the design of ES-PFEM for general curvature-dependent geometric gradient flows and a new understanding of mesh quality improvement in PFEM are provided. In particular, we develop the first PFEM for the Gauss curvature flow of surfaces. Furthermore, a tangential velocity control methodology is applied to improve the mesh quality and enhance the robustness of the proposed numerical method. Extensive numerical experiments confirm that the proposed method preserves energy dissipation properties and maintain good mesh quality in the surface evolution under the Willmore flow.
arXiv:2506.22666v3 Announce Type: replace
Abstract: The rise of API-only access to state-of-the-art LLMs highlights the need for effective black-box jailbreak methods to identify model vulnerabilities in real-world settings. Without a principled objective for gradient-based optimization, most existing approaches rely on genetic algorithms, which are limited by their initialization and dependence on manually curated prompt pools. Furthermore, these methods require individual optimization for each prompt, failing to provide a comprehensive characterization of model vulnerabilities. To address this gap, we introduce VERA: Variational infErence fRamework for jAilbreaking. VERA casts black-box jailbreak prompting as a variational inference problem, training a small attacker LLM to approximate the target LLM's posterior over adversarial prompts. Once trained, the attacker can generate diverse, fluent jailbreak prompts for a target query without re-optimization. Experimental results show that VERA achieves strong performance across a range of target LLMs, highlighting the value of probabilistic inference for adversarial prompt generation.