Barrier Functions

Consistent submodular maximization studies the tradeoff between solution quality and stability when elements arrive over time. For a monotone submodular objective, which models diminishing returns, an algorithm maintains a set of at most $k$ available elements and changes only $O(1)$ elements after each insertion. Dütting et al. [2025] established a tight $2/3$ approximation with unrestricted computation and a polynomial-time $0.51$ approximation. They left open at STOC 2025 whether efficient algorithms can match the offline $1-1/e$ guarantee. We resolve this problem by proving that the supremum approximation achievable with polynomially many value queries and worst-case constant recourse is $$β=2-\sqrt2\approx0.5858<1-1/e.$$ For every $\varepsilon>0$, our randomized algorithm attains $β-\varepsilon$ with $O(\varepsilon^{-2})$ changes per insertion. Any fixed improvement requires exponentially many queries before one critical insertion or linear recourse of $Ω(k)$ changes at that insertion, even with unlimited queries afterwards. This gap quantifies the cost of consistency: the current oracle hides which elements will be needed after an arrival. We also determine the exact curvature-dependent threshold $1-(\sqrt2-1)\vartheta$, attain $1-1/e-\varepsilon$ for weighted coverage with $O(\varepsilon^{-1})$ recourse, and separate the existence of universal future-price certificates from their efficient computation. Our algorithm has a bounded-bit polynomial-time implementation for polynomial-bit rational oracle answers; the lower bound uses only logarithmic-bit rational answers.

Model compression is critical for deploying networks on resource-constrained edge devices. While pruning-based methods can significantly reduce model size, they often suffer from abrupt performance collapse beyond a sparsity thresh-old, making it difficult to identify the feasible compression limit of the model. To address this challenge, we propose a boundary-Learning reverse regrowth framework, BRIDGE, that reformulates compression as a constructive boundary-search problem. Unlike forward pruning, our method first drives the model to an extremely sparse state to expose the collapse region, and then selectively regenerates the critical structure to restore performance. The proposed framework employs a hierarchical regeneration strategy, including coarse-grained layer selection and fine-grained regeneration parameter selection, to accurately identify which parameters require recovery. Experiments show that our method can recover models from the brink of collapse on both CNNs and Transformer architectures, demonstrating its architecture in-dependence. BRIDGE achieves a performance improvement of up to 1.49% in unstructured pruning and up to 4.77% in structured pruning. These results demonstrate that reverse regeneration can effectively extend the compression limit while maintaining stable performance. The source code is available at https://github.com/EnumaCaliber/BRIDGE.

Top-$k$ selection determines which components of a sparse model remain active. Hard selection blocks gradients, while continuous relaxations often couple mask hardness to the selected mass. We introduce LaPrune, a mathematically exact-budget differentiable layer that controls the normalized second moment while preserving the selected mass. A LapSum barrier preserves the selection mass, and a normalized second-moment constraint moves the mask from a dense equal-mass allocation toward hard top-$k$ at each budget. We derive a population prediction of the saturated fraction, a near-binary limiting law, and a tight worst-case guarantee on the near-zero fraction. The normalized hardness parameter is invariant to score scale, while a fixed LapSum temperature is not.

Interactive segmentation reduces the prohibitive cost of pixel-level annotation by allowing users to delineate objects with a few clicks. However, applying this paradigm directly to remote sensing imagery is non-trivial: ultra-high resolutions, small object sizes, and sparse spatial distributions all degrade segmentation quality. Recent work has addressed the resolution barrier and achieved competitive results in interactive segmentation for remote sensing (ISRS). However, they treat all instances of a class within an image as a single objective target. Consequently, interactions spent on one object contribute nothing to its same-class neighbours, and satisfactory masks may demand up to 40 clicks per image, hindering the practicality of these frameworks. We observe that remote sensing scenes exhibit markedly strong inter-object correlation, meaning a single clicked object is highly informative about the rest of its category. Building on this, we propose ISRS-DETR, a detection-guided interactive segmentation framework that injects object-level evidence into both training and inference. Our ISRS-DETR employs an RF-DETR decoder with the interactive segmentation backbone to localise co-occurring same-class objects, and introduces a Dynamic Top-K Click Selection strategy that retains only reliable proposals and converts each into a simulated click, so one user interaction propagates across an entire class. Experiments on three standard remote sensing benchmarks show that ISRS-DETR achieves state-of-the-art accuracy while substantially reducing Number of Clicks per Image (NoC-I). All codes and data splits will be released for reproducibility upon acceptance.

We argue that a single structural fact organizes a wide range of phenomena in contemporary AI safety: a semantic safety constraint (e.g., the agent does not escape its sandbox) is an off-support object. Formally, if q is the data distribution and $p(\cdot\mid w)$ the model, the safety predicate B is not measurable with respect to $σ(\text{model}, q)$, whereas the real log-canonical threshold (RLCT) of singular learning theory (SLT) is. From this non-invariance we derive, as corollaries rather than independent observations: (i) why reward hacking and sandbox escape arise under outcome-based optimization; (ii) why encoding such constraints through Bayesian prior design or soft penalty weighting has poor leverage in singular models; (iii) why hard invariants belong in the harness and soft dispositions in the model; (iv) why the same B is nonetheless soundly and locally certifiable by formal verification, exactly as the local learning coefficient (LLC) locally pins the same RLCT --- with two precise points of disanalogy; and (v) why the residual difficulty, identifying which off-support region matters, coincides with performative prediction and self-referential functional dynamics, where SLT's analytic machinery breaks down. We use the July 2026 OpenAI--Hugging Face evaluation incident as the motivating case. Numerical experiments code and related proofs in lean are available at https://github.com/xiangze/Preventing_Jailbreak_as_regularization

Quantum computers are moving from research laboratories to industrial machines accessible via the cloud and integrated into high-performance computing facilities. However, translating theoretical quantum protocols into hardware experiments remains a major bottleneck, requiring expertise across protocol design, compilation, simulation, and cloud execution. Here, we introduce an agentic workflow that automates this pipeline on neutral-atom quantum processors (here two Pasqal QPUs available on the cloud) while keeping the researcher in the loop for critical validation. In three case studies from many-body physics and optimization, the agent went from published paper or patent to a QPU campaign run overnight. In particular, human intervention was crucial to ensure scientific validity: the agent selected an inadequate observable in one experiment and constructed a plausible but incorrect hardware diagnosis in another, with both failures detected only through domain-expert review. Finally, we use a second agent to classify a corpus of 633 Rydberg-array arXiv papers and show that nearly half are implementable on present-day QPUs while identifying specific hardware upgrades needed for the rest. Together, these results demonstrate that agentic workflows provide a practical bridge between theoretical ideas and physical hardware, opening quantum experimentation to a much broader scientific community.

Inverse Reinforcement Learning (IRL) algorithms are powerful tools for learning from and generalizing expert demonstrations, but they often rely on unconstrained exploration, rendering them unsafe for real-world deployment. Meanwhile, Control Barrier Functions (CBFs) can guarantee the safety of control systems, but the analytical design of CBFs can be time-consuming and esoteric. In this work, we address these limitations jointly by constraining reward function candidacy during IRL to the space of CBFs, yielding a formulation that exhibits safe online control with continuous experiential improvement. Crucially, this framework enables the data-driven recovery of barrier functions directly from unlabeled expert observations. We demonstrate that the recovered barrier function is robust to unsafe states entirely absent from the expert data. Furthermore, we benchmark our method against standard IRL baselines in a simulated navigation environment, demonstrating improved safety performance. Finally, we investigate the trade-offs of planning-based versus policy-based IRL methods across both simulation and a real world obstacle avoidance task.

Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii--Mann fixed-point iteration rather than by contraction to a unique equilibrium. We study this regime under a contractive fast map and a non-expansive reduced slow map. We first prove a finite-horizon lower bound showing that, for any prescribed slow stepsize schedule $(β_k)$, the classical KM residual scale $(\sum_{i<N}β_i(1-β_i))^{-1}$ is worst-case sharp for the corresponding unregularized KM update. Combined with the raw fast-tracking leakage scale, this explains the previously observed $k^{-1/4+o(1)}$ last-iterate mean-square residual exponent. We then introduce a residual-preconditioned slow oracle that cancels the first-order dependence on the fast tracking error. In a nested Tikhonov-KM algorithm, the uncorrected oracle yields total-sample rate $T^{-1/4+o(1)}$, while the corrected oracle yields $T^{-1/3+o(1)}$. This improvement comes from changing the slow-oracle bias from first order to second order in the fast error after all inner-loop samples are counted. Finally, we show that the repeated inner-loop cost of the nested method can be avoided in a smooth derivative-oracle model. A single-loop algorithm that tracks both the fast equilibrium and the leakage preconditioner online achieves $T^{-1/2+o(1)}$ with $O(1)$ primitive samples per iteration.

Service robots in retail stores increasingly rely on cascaded speech pipelines (STT-LLM-TTS), yet many customer-robot interactions are initiated or guided by nonverbal behaviors such as approaching, waving, pointing, or showing items. This paper studies such cues in a real-world store deployment with a teleoperated humanoid robot and shows that a non-negligible portion of robot turns are triggered by nonverbal behaviors rather than spoken input, revealing a limitation of audio-only dialogue systems. In a 6-day in-the-wild deployment, 15.3% of robot utterances were initiated by users' nonverbal behaviors rather than spoken input. Based on an analysis of observed customer behaviors, we define a set of frequent, service-relevant nonverbal cues and develop a real-time multi-person, multi-label recognizer that runs online from video. We then propose a dialogue framework that conditions LLM-based utterance generation on recognized nonverbal cue tokens, and optionally leverages a vision-language model when items are shown, enabling proactive robot responses without hand-crafted rules. We evaluate the approach offline on nonverbal-triggered turns and demonstrate an online prototype that reacts to users' nonverbal cues in real time.

Learning-based separation assurance for small Unmanned Aircraft Systems (sUAS) achieves near-zero collision rates in simulation, but assumes accurate position and velocity information from Global Navigation Satellite Systems (GNSS). This assumption fails in urban environments, where multipath propagation, signal blockage, and intentional interference degrade navigation integrity. This raises a fundamental architectural question for deploying learned separation policies under GNSS degradation: should runtime safety mechanisms filter the policy's actions or its observations? This work evaluates both approaches for multi-agent sUAS separation under adversarial GNSS degradation. Both architectures first estimate a worst-case traffic state consistent with bounded observation uncertainty, then diverge: action filtering constrains policy outputs via discrete-time control barrier functions evaluated at the worst-case state, while observation filtering presents the worst-case state directly to the policy as corrected input. Experimental results show that action filtering provides negligible safety improvement, while observation filtering reduces near mid-air collisions by 90% and remains robust to the barrier function's tradeoff between separation distance and closing rate. These results suggest that, for policies with learned safety behaviors, preserving the policy's decision authority outperforms overriding its actions with hand-designed constraints.

Tabular foundation models cannot reason about data produced by running systems without access to the rules that govern them. We make this statement falsifiable. The \emph{Operational Turing Test} (OTT) constructs pairs of legal and rule-violating database states whose $1$- and $2$-way column-value marginals match to a total variation of $<0.02$; Le~Cam's lemma then bounds any values-only classifier at $\geq0.49$ Bayes error. Three values-only baselines (XGBoost, TabICL, TabPFN) hit the bound exactly (accuracy $0.50$, pre-registered two one-sided tests (TOST) $p<0.002$), raw row-level access does not help, exposing relational value consistency closes most of the gap, and only a classifier fed by seven executable rule-derived audits reaches $1.00$ classification accuracy. In three matched $100$-state frontier large-language-model (LLM) runs, models given the schema, trigger source, rule tables, and state files classify at most $2/50$ legal states as LEGAL; GPT-5.5 accepts $0/50$ legal states even with higher reasoning effort and a Structured Query Language (SQL) executor. The access-ladder pattern also appears on a second schema with structurally distinct rule families (banking ledger: cross-row balance, cumulative aggregate). The barrier is identifiability, not capacity: scale, data, and richer features cannot cross it without operational grounding.

Confidence-based loss weighting is usually avoided in generative models because it accelerates errors when the model is confidently wrong, but this intuition breaks down in supervised diffusion training. We introduce the Eisbach log-barrier, a parameter-free weight derived from the entropy of the DiT output's spatial energy distribution: high entropy damps the gradient, while low entropy preserves it. Applied to LoRA fine-tuning of Stable Audio 3 Medium on MusicCaps, it unexpectedly yields stronger thematic development, clearer acoustic differentiation, and higher textural diversity than unweighted training, the opposite of mode collapse. This works because in supervised diffusion the gradient direction is locked to ground truth, so confidence only scales the step size, and because temporal entropy downweights flat samples while preserving high-contrast ones. The result is an online, self-referential data curriculum that emerges purely from the forward pass, with analyzed noise-level dynamics and testable predictions.

The critical question after a correct driving veto is not only whether a maneuver is unsafe, but whether the blocked interaction admits a lawful, auditable, and responsibility-bounded repair. Prediction and game-theoretic planners can suggest plausible cooperation, yet they do not return a proof that the repair respects hard rules, right-of-way, cost allocation, and ego fallback. We introduce CARVE, Certified Affordable Repair of Vetoed maneuvers via Envelopes, a certificate architecture for prediction-free interactive repair. Given a vetoed maneuver, CARVE constructs a finite repair lattice and emits a structured certificate recording the binding rule, selected joint repair, right-of-way-scaled cooperation envelope, responsibility-weighted cost split, and ego-only fallback. This certificate view reveals the algorithmic bottleneck: multi-owner repair induces a product lattice $M = \prod_j |\mathcal{A}_j|$. We therefore introduce CARVE-Q, a verifier-shielded quantum-AI search layer that applies quantum minimum finding only to this black-box lattice while leaving all safety authority classical. In the conservative verifier-oracle model, exact classical minimum finding requires $Θ(M)$ queries in the worst case, whereas Durr-Hoyer/Grover minimum finding uses $O(\sqrt{M})$ oracle queries with high probability. We prove verifier-shielded certificate soundness, priority non-elicitation, black-box query separation, and finite-precision reversible-oracle constructibility. We then demonstrate state-vector minimum finding on CARVE repair oracles up to 65,536 assignments and validate certificate preservation on Lanelet2-grounded INTERACTION replay with 100% right-of-way respect, 100% blame consistency, and zero priority false positives. The result is a trust-bounded quantum-AI pattern for certified autonomy: quantum proposes; CARVE certifies.

Safe navigation often relies on well-defined conditions based on the shape of robots and obstacles, and can be challenging when they have irregular geometries. While Control Barrier Functions (CBFs) offer an efficient mechanism to enforce safe set forward invariance, common shape surrogates (e.g., spheres or super-ellipsoids) either are overly conservative in unstructured scenes or require many local primitives, which inflates constraint counts and degrades real-time performance. In this paper, we introduce a novel geometry-aware Control Barrier Function (CBF) based on Bernstein-Polynomial Signed Distance Fields (BP-SDFs). It provides a unified way to represent the obstacles and robots, so as to represent the barrier function with a unified minimum distance. Benefiting from the differentiability of the Bernstein polynomials, one can easily enforce the control constraints in a closed loop. We validate the method's efficiency and performance to guarantee safety in single-robot navigation and heterogeneous multi-robot collision avoidance via simulations under different environments.

Hallucination remains a major reliability barrier for production LLM systems, particularly in multi-agent pipelines where unsupported claims can propagate unchecked across stages. This paper adapts a HOPE-inspired Nested Learning architecture with Continuum Memory Systems (CMS) and semantic similarity caching to a hybrid benchmark of 310 prompts combining 217 epistemic-uncertainty prompts and 93 fabrication-induction stress-test prompts. A three-stage agentic pipeline orchestrated via the Open Floor Protocol (OFP) is evaluated with five KPIs -- FCD (Factual Claim Density), FGR (Factual Grounding References), FDF (Fictional Disclaimer Frequency), ECS (Explicit Contextualization Score), and OSR (Observability Score Ratio) -- aggregated into THS (Total Hallucination Score) across five weighting configurations to study mitigation-observability trade-offs. FDF, ECS, OSR, and FGR are subtracted as mitigation signals, so that a more negative THS indicates stronger mitigation. The FrontEndAgent is configured as a high-stochasticity generator (temperature = 1.0) to produce a realistic hallucination baseline, while the SecondLevelReviewer and ThirdLevelReviewer operate as progressive correctors. This asymmetric design yields end-to-end THS reductions of -31.3% to -35.9% across five weighting configurations. Semantic caching achieves 440 cache hits over 930 potential calls (47.3% hit rate), reducing LLM invocations to 490, lowering energy and CO2e footprint, and making multi-stage review pipelines operationally viable at production scale. ExtremeObservability attains the most negative final THS (-0.0709), confirming that observability-heavy configurations reinforce rather than compromise mitigation. These findings suggest that memory-augmented multi-agent designs can jointly improve factual reliability, operational efficiency, and auditability without model retraining.

Automatic Speech Recognition (ASR) systems are commonly evaluated using aggregate metrics such as Word Error Rate (WER), which do not capture the linguistic structure of errors. Fine-grained analysis, such as Part-of-Speech (PoS)-wise error characterization, requires accurate alignment between ASR hypotheses and reference transcriptions. However, existing alignment tools are often unreliable for languages written in non-Latin scripts. In this work, we address this gap by proposing a robust, automated, language-agnostic alignment mechanism applicable across ASR architectures and across languages written in both Latin and non-Latin scripts. This enables consistent alignment of hypotheses, references, and evaluation sequences, forming the basis for downstream linguistic analysis. Building on this, we employ standard PoS taggers to perform scalable and reproducible PoS-wise error analysis. Notably, we perform alignment and downstream ASR error analysis across three major segmented writing systems, namely, Abugida (Tamil, Hindi, Kannada), Alphabetic (English, Russian, Greek), and Abjad (Arabic). We further demonstrate how such error information can be leveraged during ASR training to improve metrics such as WER.

Safety has been a major concern when deploying deep reinforcement learning algorithms in the real world. A promising direction that ensures that the learned policy does not visit unsafe regions is to learn a \emph{barrier function} along with the policy. A barrier is a function from states to reals that assigns low values to the initial states, high values to the unsafe states, and decreases in expectation on each transition; such a function can be used to bound the probability of reaching unsafe states. Previous attempts learned a barrier function directly from exploration data, but this required either large amounts of data or restrictions on the system dynamics. In this paper, we show how kernel embeddings can be used to learn barrier functions during deep reinforcement learning for stochastic systems with unknown dynamics. Our algorithm, \emph{kernel-based safe exploration (KBSE)}, learns an optimal policy and a barrier simultaneously during exploration. The barriers are computed iteratively, represented as conditional mean embeddings, and provide better probabilistic safety guarantees with more exploration. The exploration algorithm uses the learned barrier functions to identify safety violations. In the case of violation, it intervenes to modify the unsafe action to a safe action, thereby ensuring that the exploration is restricted to actions that bound the probability of reaching unsafe states. We evaluate KBSE on several complex continuous control benchmarks. Experimental results establish our new algorithm to be suitable for synthesizing control policies that are probabilistically safe without degradation in reward accumulation.

Planning through crowded environments under uncertain obstacle motions remains difficult, as stochastic interactions often induce overly conservative behavior or reduced efficiency. To address this challenge, we propose an end-to-end risk adaptation framework for crowd navigation under obstacle-motion uncertainty modeled by a Gaussian mixture model. The framework combines reinforcement learning~(RL) with a differentiable quadratic-program safety layer based on Conditional Value-at-Risk~(CVaR) barrier functions, jointly learning nominal control input, risk level, and safety margin and enforcing explicit probabilistic safety constraints. This design enables context-aware adaptation, promoting efficient behavior while invoking caution only when necessary. We conduct extensive evaluations in dynamic, uncertain, and crowded environments across varying obstacle densities and robot models, and further assess generalization under three out-of-distribution cases. Comparisons across optimization-based, RL-based, and integrated RL and optimization methods are provided, and the proposed method is shown to deliver the strongest overall performance in safety, efficiency, and generalization under uncertainty.

Reinforcement Learning (RL) uses rewards to guide learning, yet reward design is typically hand-crafted using heuristics that can be difficult to tune. We propose a Control Barrier Function (CBF)-informed reward design for Multi-Agent RL (MARL) that converts CBF constraint values under joint MARL actions into a reward signal that explicitly guides safe learning. We compare against two heuristic reward baselines in a four-way multi-lane intersection with connected and automated vehicles. Results show that our method achieves the highest task performance and is less sensitive to reward hyperparameters, yielding consistently strong performance across the tested hyperparameter range. Code for reproducing the experimental results and a video demonstration are available at https://github.com/bassamlab/SigmaRL.

Autonomous navigation and obstacle avoidance remain a core challenge of modern Unmanned Aerial Vehicles (UAVs). While traditional control methods struggle with the complexity and variability of the environment, reinforcement learning (RL) enables UAVs to learn adaptive behaviors through interaction with the environment. Existing research with RL prioritizes the mission success at the expense of mission time and safety of UAVs. This study integrates Potential Based Reward Shaping (PBRS) with Control Lyapunov Functions (CLF) and Control Barrier Functions (CBF) to simultaneously optimize mission time and ensure formal safety guarantees. An RL model is trained in a generalized simple environment, then used in complex scenarios incorporating a CLF-CBF-QP filter without further training. Experimental results in simulated environments demonstrate a significant reduction in mission time and outstanding performance in complex environment.

Cross-lingual transfer in NLP is often hindered by the ``script barrier'' where differences in writing systems inhibit transfer learning between languages. Transliteration, the process of converting the script, has emerged as a powerful technique to bridge this gap by increasing lexical overlap. This paper provides a comprehensive survey of the application of transliteration in cross-lingual NLP. We present a taxonomy of key motivations to utilize transliterations in language models, and provide an overview of different approaches of incorporating transliterations as input. We analyze the evolution and effectiveness of these methods, discussing the critical trade-offs involved, and contextualize their need in modern LLMs. The review explores various settings that show how transliteration is beneficial, including handling code-mixed text, leveraging language family relatedness, and pragmatic gains in inference efficiency. Based on this analysis, we provide concrete recommendations for researchers on selecting and implementing the most appropriate transliteration strategy based on their specific language, task, and resource constraints.

Conversational agents, such as ChatGPT and Doubao, have become essential daily assistants for billions of users. To further enhance engagement, these systems are evolving from passive responders to proactive companions. However, existing efforts focus on activation within ongoing dialogues, while overlooking a key real-world bottleneck. In the conversation initiation stage, users may have a vague need but no explicit query intent, creating a first-message barrier where the conversation holds before it begins. To overcome this, we introduce Conversation Starter Generation: generating personalized starters to guide users into conversation. However, unlike in-conversation stages where immediate context guides the response, initiation must operate in a cold-start moment without explicit user intent. To pioneer in this direction, we present IceBreaker that frames human ice-breaking as a two-step handshake: (i) evoke resonance via Resonance-Aware Interest Distillation from session summaries to capture trigger interests, and (ii) stimulate interaction via Interaction-Oriented Starter Generation, optimized with personalized preference alignment and a self-reinforced loop to maximize engagement. Online A/B tests on one of the world's largest conversational agent products show that IceBreaker improves user active days by +0.184% and click-through rate by +9.425%, and has been deployed in production.