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arXiv

Optimal Unambiguous DNFs and Alon-Saks-Seymour

Chirag Pabbaraju

We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity. This leads to an optimal refutation of the Alon-Saks-Seymour conjecture, as well as an optimal communication lower bound for the Clique versus Independent Set problem, improving the previous results of Balodis, Ben-David, Göös, Jain and Kothari (FOCS 2021, SICOMP 2023) by several doubly logarithmic factors. As further applications of our construction to query complexity and learning theory, we exhibit: (a) a family of Boolean functions that has an optimal quartic separation between certificate complexity and approximate degree, and (b) a sample compression lower bound of $Ω(\sqrt{\log c})$ for multiclass concept classes over $c$ labels.

arXiv

Uncertainty Is Not Enough: Value-of-Information Routing for Mixtures of LoRA Experts

Tom Saliencro, Rohan Desai, Priya Nair, Maya Lindqvist, Daniel Whitmore

Mixtures of low-rank adaptation experts increase parameter-efficient capacity by routing each input through a subset of adapters. Recent dynamic routers activate more experts when the router or prediction is uncertain. This rule silently equates uncertainty with useful additional computation: an uncertain example may contain complementary, unqueried expert evidence, but it may instead remain ambiguous after every expert agrees. We formulate routing as certified value-of-information allocation. VI-MoLE learns the counterfactual risk remaining after each expert prefix, converts these predictions into simultaneous upper-risk certificates on held-out calibration data, and spends a global adapter budget on the token--layer action with the largest certified marginal risk reduction per unit cost. A terminal certificate then decides whether to answer or abstain. Unlike an uncertainty gate, this procedure distinguishes present ambiguity from recoverable and residual risk. We prove simultaneous certificate validity, optimal greedy allocation under diminishing certified gains, and allocation regret under value-estimation error. The evaluation protocol tests matched-compute accuracy, certificate coverage, risk--coverage, distribution shift, and tail latency against fixed and dynamic MoE-LoRA routers.

arXiv

Analytic Planning under Uncertainty with Moment Closure

Shishir Sharma, Doina Precup

Effective model-based reinforcement learning in stochastic environments requires planning that accounts for predictive uncertainty. Propagating full state distributions analytically offers a principled way to do this, but has traditionally required restrictive policy or reward structures to remain tractable. Consequently, modern deep reinforcement learning has largely retreated to either stochastic sampling, which introduces significant target variance, or deterministic point estimates that ignore predictive covariance entirely. We investigate whether distribution-aware planning is possible without these constraints. Using a quadratic action-value parameterization, we first reduce the Bellman backup to an expectation over the state-value function alone; the key idea is then a compatibility principle between the predictive transition distribution and the value function class, under which this expectation is analytic in the distribution's moments. We instantiate this principle with a Gaussian transition model paired with a radial-basis value function, yielding a closed-form backup that propagates both predictive mean and covariance. Empirically, our approach reduces target variance and yields well-calibrated predictive uncertainty under stochastic observations in continuous control, providing a principled framework for planning with learned distribution models.

arXiv

Optimizing Minimax Regret in Uncertain MDPs with Small Sets of Policies

Sterre Lutz, Daniël Vos, Matthijs T. J. Spaan, Anna Lukina

Sequential decision-making in real-world applications often involves uncertainty about the environment's model. Uncertain Markov decision processes (UMDPs) represent the possible environments as a set of MDPs with shared states and actions but potentially different transition probabilities and rewards. Optimizing a single policy across all possible MDPs may sacrifice performance, while preparing an individually optimized policy for every MDP may violate operational, regulatory, or interpretability constraints on the number of policies that can be prepared and deployed. We consider settings in which model uncertainty is resolved shortly before execution, allowing the most suitable policy to be selected from a limited set prepared in advance. We introduce $k$-adaptable policy synthesis, which optimizes such a set of $k$ policies under a minimax-regret objective. We prove that the problem is NP-hard and develop KAPS, an exact nested branch-and-bound algorithm with problem-specific bounds and heuristics. KAPS jointly optimizes which MDPs share a policy and the policies themselves. Experiments across various UMDP benchmarks show that the largest reduction in regret consistently occurs when increasing from one to two policies. In the single-policy setting, KAPS is competitive with existing methods in solution quality and proves optimality substantially more often.

arXiv

Beyond Modern Asymptotics for Log-Likelihood Ratios in Logistic Regression

Hugo Chardon, Reese Pathak, Nikita Zhivotovskiy

We characterize the finite sample behavior of the log-likelihood ratio statistic in binary logistic regression, uniformly over both the design and the target parameter. For $n\geq d\geq 3$, we determine, up to universal constants, its worst case $(1-δ)$ quantile over all fixed collections of design vectors and all target parameters: \[ d\log\left(\frac{e n}{d}\right)+\log\left(\frac{1}δ\right). \] This is a nonasymptotic analogue of the Wilks $χ^2_d$ phenomenon and requires no regularity assumptions on the design. The low dimensional cases exhibit unusual behavior. The worst case quantile in dimension $d=2$ is sharply of order \[ \log\log\log n+\log\left(\frac{1}δ\right). \] The worst case quantile in dimension $d=1$ is of order $\log(1/δ)$, with no dependence on $n$. Finally, i.i.d. Gaussian design vectors recover the classical Wilks scale. In the regime $n\gtrsim d+\log(1/δ)$, we prove the sharp bound \[ d+\log\left(\frac{1}δ\right). \] Unlike existing asymptotic results, our bounds are uniform over the target parameter, which may depend on $n$, $d$, and $δ$.

arXiv

Computational and Statistical Guarantees of the \textit{c}-Rectified flow

Leda Wang, Zhehao Xu, Qiang Liu, Harrison H. Zhou

Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.1 and Stable Diffusion 3. Despite its remarkable empirical success, the computational and statistical guarantees of iterative rectified flow have remained largely unexplored. We address this problem by studying \textit{c}-rectified flow, a cost-aware class of rectified flow that projects velocity fields onto a gradient class while preserving endpoint marginals. The ordinary rectified flow can fail to recover the optimal transport coupling: in a Gaussian case study, the iteration converges to the optimal coupling if and only if the source and target covariance matrices commute. In contrast, under suitable compactness and uniform-integrability assumptions, iterative \textit{c}-rectified flow always converges to the optimal transport coupling. We further establish quantitative one-step contraction and exponential convergence guarantees under projection-stability assumptions for both quadratic and strongly convex displacement costs. Finally, under a Hölder ball assumption, we develop new minimax-optimal score estimation rates and show that, when combined with iterative \textit{c}-rectified flow, they yield a rate-optimal estimator of the optimal transport for the dimension \(d \ge 3\) and a nearly parametric rate for \(d=1,2\).

arXiv

Private Generative Bootstrap via Blocking

Jinwon Sohn, Veronika Ročková

With AI systems gaining more access to individuals' information, it is important to protect privacy when reporting statistical answers. Equally important is to privatize the reporting of uncertainty in such answers. To this end, we adopt a Bayesian likelihood-free framework and make simulation from the posterior private. In particular, we propose a new private instantiation of the Bayesian bootstrap using a blocking strategy. Rather than assigning idiosyncratic random weights to each individual, we randomly group individuals and assign a single weight to each group. By concealing individuals' contributions within a group, we fortify differential privacy gates. We harness amortized inference that decouples private learning from posterior sampling. A push-forward map from observation weights to posterior samples is learned privately by adding calibrated noise during training. Subsequent posterior draws require no additional privacy and computation budget. We call the resulting method the Private Generative Bayesian Bootstrap (PGBB). We establish a differential privacy guarantee, analyze convergence to the non-private blocked-bootstrap target, and quantify the discrepancy between the ordinary and blocked Bayesian-bootstrap posteriors. In addition, we derive data-free tuning of the block Dirichlet concentration parameter that restores posterior dispersion asymptotically. We also show a single fit of PGBB can support a family of loss-based decision rules simultaneously without additional privacy cost. In simulations and in applications to U.S. Census returns to schooling and U.S. natality birthweight quantiles, PGBB gives competitive private uncertainty quantification and improves over private Bayesian alternatives that require a specified data-generating model in common settings.

arXiv

Real-Time Detection and Repair of LLM Agent Failures

Sunny Dubey

LLM agents fail mid-episode -- they loop, cascade tool errors, drift off goal, fabricate results, or silently absorb corrupted content -- and the standard remedy, judging every step with a second LLM, costs more than the agent itself. We ask how much detection is achievable from observable step telemetry alone, using monitors costing microseconds per step and trained only on healthy runs. On 2,823 committed agent episodes across three frameworks, three local models (qwen2.5 7b/3b, llama3.1 8b) and a commercial API (gemini-2.5-flash), a one-class echo-state-network ensemble with CUSUM alarms detects 0.71 of failures at a 5% false-alarm budget (AUROC 0.872). Its advantage over a memoryless baseline is a monotone function of post-onset horizon (+0.09 at <=3 steps, +0.40 at >=9), predicting its own failure region out of sample on AFTraj-2K. Ranking transfers with no retraining to two corpora from other groups (AFTraj-2K 0.745, ATBench 0.779). Monitors carry two burdens: a per-deployment healthy null (they do not transfer -- AUROC 0.527 cold against 0.885 recalibrated) and a residual false-alarm rate. We add a layer carrying neither: deterministic verification, which recomputes a run's stated total from the tool results it actually received and confirms every required call was made. Head-to-head it catches 60% of failures (96% with the coverage check) at 0 of 63 false positives against the monitor's 54% at 17%, transfers unchanged to llama3.1:8b (110 of 110 at 0 of 10), and trips on 0 of 1825 healthy episodes. Detection is then closed into repair: each flagged run is rolled back and re-run live, recovering 45% of failures against a 16% resampling control (p=0.0005) and lifting task success from 52% to 73% for about one extra model call per run. The system runs at ~200 microseconds per step, three orders of magnitude below a judge call. Code, traces and results are released.

arXiv

Aggregate-then-Calibrate for Human-centered Assessment with Theoretical Guarantees

Zejun Xie, Xintong Li, Guang Wang, Desheng Zhang

Human-centered assessment tasks, which are essential for systematic decision-making, rely heavily on human judgment and typically lack verifiable ground truth. Existing approaches face a dilemma: methods using only human judgments suffer from heterogeneous expertise and inconsistent rating scales, while methods using only model-generated scores must learn from imperfect proxies or incomplete features. We propose Aggregate-then-Calibrate (AtC), a two-stage framework that combines these complementary sources. Stage-1 aggregates heterogeneous comparative judgments into a consensus ranking using a rank-aggregation model that accounts for annotator reliability. Stage-2 calibrates any predictive model's scores by an isotonic projection onto the order, enforcing ordinal consistency while preserving as much of the model's quantitative information as possible. Theoretically, we show: (1) modeling annotator heterogeneity yields strictly more efficient consensus estimation than homogeneity; (2) isotonic calibration enjoys risk bounds even when the consensus ranking is misspecified; and (3) AtC asymptotically outperforms model-only assessment. Across semi-synthetic and real-world datasets, AtC consistently improves accuracy and robustness over human-only or model-only assessments. Our results bridge judgment aggregation with model-free calibration, providing a principled recipe for human-centered assessment when ground truth is costly, scarce, or unverifiable.

arXiv

Advancing Relevance Measurement with Vision-Language Models for Web-Scale Search

Han Wang, Alex Whitworth, Pak Ming Cheung, Zhenjie Zhang, Krishna Kamath, Xi Chen, Roberto Konow, Kurchi Subhra Hazra

Relevance evaluation plays a crucial role in personalized search systems, serving as a guardrail alongside user engagement metrics to ensure that search results align with user queries and intent. While human annotation is the traditional method for relevance evaluation, its high cost and long turnaround time limit its scalability. In this work, we present a VLM-based automated relevance evaluation pipeline deployed within Pinterest Search for online A/B experiments. We rigorously validate the alignment between VLM-generated judgments and human annotations, demonstrating that VLMs can provide reliable relevance measurement for experiments while greatly improving the evaluation efficiency. Leveraging VLM-based labeling further unlocks opportunities to expand the query set, optimize sampling design, and efficiently assess a wider range of search experiences at scale. This approach leads to higher-quality relevance metrics and significantly reduces the Minimum Detectable Effects (MDEs) in online experiment measurements.

arXiv

Intention Inference Under Execution Noise: Separating Aleatoric and Epistemic Uncertainty in Social Dilemmas

Kival Mahadew, Jonathan Shock

In noisy social dilemmas, intended actions are stochastically corrupted before execution, so an observed defection may reflect hostile intent or action error. Standard Markov Decision Process (MDP) formulations treat executed actions as states, structurally precluding this distinction and causing systematic over-retaliation. We introduce a Partially Observable MDP (POMDP) formulation encoding opponent intentions as latent states and executed actions as noisy observations, solved within the active inference (AIF) framework with a cost function that decomposes into epistemic and pragmatic components that jointly address inferring current intent and learning how intent evolves. In the Iterated Prisoner's Dilemma with symmetric noise, we derive a critical noise threshold governing cooperation collapse, connecting it to a fixed-point condition on learned priors. Experiments reveal that the value of intention inference is context-dependent: the POMDP provides consistent advantages against conditionally cooperative opponents, but mutual intention inference under sufficient noise produces correlated belief-driven collapse. The advantage is specific to games where intent attribution is decision-relevant.

arXiv

Foundations of Reinforcement Learning and Control:Connections and New Perspectives

Claire Vernade, Onno Eberhard, Martha White, Florian Dörfler, Csaba Szepesvári, Miroslav Krstic, Michael Muehlebach

Reinforcement learning and control theory are two adjacent scientific fields that focus on optimizing the controller of unknown dynamical systems using feedback. While both fields have common roots in dynamic programming, they have evolved with distinct methodologies, goals, and cultures. Despite decades of mutual influence, a significant gap persists between the two communities. This tutorial introduces adaptive control, actor-critic reinforcement algorithms, and a new way to combine these two paradigms for data-driven decision making on a classical locomotion control problem. Our aim is to provide a foundation for understanding the core differences between the two approaches and insights to help experts in each field better understand and engage with the tools and approaches of the other.

arXiv

Wasserstein mixing time of the unadjusted Langevin algorithm

Francesco Pedrotti, Peter A. Whalley

We provide new estimates in Wasserstein distance for the asymptotic bias of the unadjusted Langevin algorithm, in the classical setting of log-smooth strongly log-concave measures. Our bound implies a Wasserstein mixing time of order $κ\sqrt{d}/\varepsilon$, where $κ$ is the condition number, $d$ is the dimension, and $\varepsilon$ is the target precision: this improves by a factor of $\sqrt{d}/\varepsilon$ over the previous state-of-the-art results.

arXiv

Why Large Language Models Fail at Tabular Prediction

Marta Garnelo, Wojciech M. Czarnecki

Large language models (LLMs) have become the default tool for a remarkable range of tasks, yet they have had conspicuously little success at one of the most common machine learning workloads: predictive analytics over tabular data. This gap is the founding premise of the fast-growing field of tabular foundation models, but the question of why generic LLMs fail has remained open. We study a frontier LLM in its purest inference regime - a single generation pass over a prompt containing the full training and test data, with no tools, no agentic scaffolding, and no fine-tuning - and systematically evaluate five hypotheses for the failure: (a) an inability to handle noisy or non-linearly-separable data; (b) the linearised CSV format obscuring column structure; (c) the tokenisation of numeric values; (d) the number of test points classified per query; and (e) the dimensionality of the input. Controlled experiments falsify (a)-(d). Dimensionality, in contrast, is decisive: sweeping random linear projections of thirty-one benchmark datasets, the LLM is the only method among nine whose accuracy decreases as dimensionality grows, while every classical baseline stays flat or improves. A behavioural comparison against 252 configured classical models finds that in two dimensions the LLM predicts like a local, distance-based method (up to 91.6% grid agreement), but in higher dimensions no classical model - even when augmented with tuned, dimension-dependent noise - reproduces its predictions. We do not claim to have identified the internal mechanism; our results show, more modestly, that the LLM's capability dissolves with dimension in a way no noise-corrupted classical learner mimics - which explains why LLMs, so capable elsewhere, keep losing to fifty-year-old baselines on tables, while leaving the mechanism of the prediction as an open question.

arXiv

Human-Centered Reflections on Care Robots: A Comparative Study of Caregiver Perspectives

Laura Londoño, Klaus Baumann, Abhinav Valada, Markus Langer

Care robots are increasingly being introduced into healthcare settings, raising important questions about their acceptance and ethical implementation. To better understand these challenges, this study investigates caregivers' perceptions of four categories of care robots: delivering supplies, helping patients into bed, monitoring vital signs, and assisting with mobility. We conducted a mixed-methods study employing a mixed-factorial design in which 298 caregivers from the United States, Mexico, and Chile evaluated all four robot categories. Quantitative measures integrated constructs from the Unified Theory of Acceptance and Use of Technology, the Cognitive-Affective-Normative model, and overall acceptance ratings. Qualitative data were collected through open-ended questions and analyzed using a literature-informed ethical framework. The results indicate that participants across countries generally evaluated care robots positively, particularly for logistical and physically demanding tasks rather than those requiring intensive interpersonal interaction. The qualitative findings provide further insight into stakeholders' views of the ethical implications of care robot use. Participants emphasized potential benefits such as reduced workload, lower risk, and greater patient autonomy, while also expressing concerns about dependability, the need for human oversight, and potential job displacement. Although many ethical concerns were shared across countries, participants differed in how they interpreted and prioritized them. These findings advance a context-sensitive and socially informed understanding of responsible design and implementation of care robots.

arXiv

Deep Learning-Based Estimation of Ground Reaction Forces in Parkinsonian Gait Using an Optimized Set of IMU Data

Run Lin, Yingtian Tang, Jiawen Xu, Dongfei Huo, Lefan Wang, Helen Dawes, Dominic J. Farris, Dong Wang, Xijin Hua

Accurate gait analysis in Parkinson's disease (PD) typically relies on laboratory-based systems to capture biomechanical data, such as ground reaction forces (GRFs). Estimating GRFs using inertial measurement units (IMUs) provides a feasible alternative. However, this approach remains challenging in pathological gait like PD due to its high variability and complexity. Moreover, existing monitoring approaches often require multiple body-mounted sensors, which limit practicality and reduce patient compliance. To date, no study has investigated the application of deep learning approaches to address this challenge. This study proposes, for the first time, a deep learning framework to estimate bilateral vertical GRFs (vGRFs) in PD using an optimized set of wearable IMUs. A hybrid CNN-BiLSTM model was trained separately on data from 61 PD patients and 65 healthy controls (HC) using 13 IMUs. The model achieved high intra-subject accuracy ($R^2$ = 0.98) and strong inter-subject generalization ($R^2$ = 0.93 for HC, $R^2$ = 0.91 for PD). Sensor configuration was found to significantly influence estimation accuracy, with optimal sensor placement varying between PD patients and HC. For PD patients, estimation accuracy dropped markedly when reducing to a single IMU. The optimal configuration for PD used four IMUs. We identified a minimal setup with only two IMUs still enabled robust estimation. This compact setup offers a practical and scalable solution. Overall, the proposed approach supports the development of wearable vGRF-based gait analysis systems for Parkinsonian gait and potentially other pathological conditions, enabling accessible clinical assessments, remote monitoring, and personalized rehabilitation.

arXiv

From fragmented data to actionable design: Physics-calibrated learning for plastic upcycling

Jingyang Bai, Zijia Wang, Xiangyi Long, Marcos Millan, Binjian Nie, Mingyue Ding

Thermochemical upgrading of plastic waste is a key upcycling pathway, yet the experimental literature is fragmented by heterogeneous conditions and incomplete reporting. Complete-case learning would retain only 10.99% of the curated experiments, while target imputation can introduce biased supervision. Here we develop a Physics-Calibrated, Missingness-Gated, and Load-Balanced Mixture-of-Experts (PC-MG-MoE) framework that converts structured missingness into an informative learning signal. PC-MG-MoE learns directly from partially observed experiments without target imputation, reconstructs physically consistent product distributions, accommodates cross-laboratory heterogeneity, and provides interpretable model behaviour rather than black-box prediction alone. Under stringent source-grouped validation, it achieved the lowest aggregate absolute error among the evaluated models, supporting engineering screening under cross-laboratory heterogeneity. Wet-lab experiments provide an external comparison, showing key composition-dependent trends. Implemented as an interactive web-based workflow, PC-MG-MoE enables forward screening, physics-grounded constrained inverse design, targeted experimental planning that supports reduced experimental workload and trial-and-error, and laboratory-specific adaptation with new platform-specific data. This work establishes a transferable framework for converting fragmented literature data into experimentally actionable guidance for model-guided plastic upcycling and broader thermochemical systems.

arXiv

Network Information Enhances Unreliable News Domain Detection

Raphaela Keßler, Roman David Ventzke, Viola Priesemann, Giordano De Marzo

Content-based detection of unreliable news is increasingly difficult, as low-reliability sources mimic credible journalism and generative AI makes fabricated content harder to flag. We ask whether network structure can improve news reliability classification, taking a domain-level approach that shifts the focus from individual articles to source reliability. From URL-sharing patterns in Telegram chats, we build a statistically validated domain co-sharing network and find assortative mixing by reliability: low-reliability domains group together, as do reliable ones. Exploiting this structure, we compare Graph Neural Networks against network-unaware baselines using both content-aware features (multilingual text embeddings) and content-agnostic features (spreading dynamics). GNNs consistently outperform Multi-Layer Perceptrons on identical features, with GraphSAGE best in both settings (accuracy 0.63 with content, 0.53 without), a 13-14% relative gain over the network-unaware baseline. Network topology thus systematically improves domain reliability assessment, and remains effective even when content analysis is infeasible.

arXiv

Cooperative Coevolution for Resource-Constrained Agentic LLM Post-Training

Zhiyuan Wang, Shengcai Liu, Jiahao Wu, Ning Lu, Hui Ouyang, Shaofeng Zhang, Haoze Lv, Ke Tang

Tool-using large language model (LLM) agents produce long, multi-turn trajectories, making gradient-based post-training memory-intensive. Evolution strategies (ES) enable memory-efficient full-parameter post-training without backpropagation and can eventually match the performance of gradient-based reinforcement learning (RL). However, resource-constrained settings typically offer only a few GPUs, so the high GPU-hour requirements of ES translate into prohibitively long training times. To address this, we introduce Cooperative Parameter-subspace Evolution Strategy (CoPES), a cooperative coevolutionary method that decomposes the full parameter space into lower-dimensional subspaces and searches over them cooperatively to improve optimization efficiency. We post-train a Qwen3.5-4B tool-using agent for the math task and evaluate it on five benchmarks of varying difficulty. Under the GPU-hour budget of full-parameter GRPO's best validation checkpoint, CoPES recovers 92% of GRPO's validation-accuracy gain, versus 67% for standard ES, while its theoretical GPU memory requirement is less than one-eighth that of full-parameter GRPO. It consistently outperforms standard ES and LoRA-based GRPO on all evaluated pass@k metrics across the five benchmarks. Additional experiments further show the advantage of CoPES on the question-answering task. These results demonstrate an improved trade-off between memory requirements and training time for agentic LLM post-training under resource constraints. The code is open-sourced in https://github.com/MetaronWang/CoPES

arXiv

Gecko: Fast Private Inference via Secure Public Encoder Offloading

Cheng'an Wei, Kai Chen, Yue Zhao, Congyi Li, Shenchen Zhu

Private inference protects both user inputs and server models during neural network inference, but existing solutions remain too slow for practical deployment. This motivates recent efforts to run a public encoder, such as a pretrained backbone, outside the protection boundary and evaluate only a small private predictor cryptographically. While appealing for efficiency, this design is not inherently secure: naively offloading a public encoder may create a feature-space shortcut: an extraction adversary may learn the remaining private predictor's feature-to-output mapping more easily than the original model's input-to-output behavior. We present Gecko, designed to limit this additional risk while retaining a compact encrypted predictor. We leverage a frozen backbone that contributes hierarchical features, fixed Fastfood projections that compress them, and private feature gating that prepares them for prediction. We formalize ideal independence and information-preservation conditions as design guidance, then separately evaluate component-reuse extraction attacks. Across image and audio tasks, Gecko achieves 0.4-2.2 second inference with at most 10.8 MB communication and accuracy comparable to transfer-learning baselines. Under the evaluated attacks, reusing the offloaded public encoder provides no significant advantage to model-extraction adversaries. Source code and a demo are available at https://github.com/CassiniHuy/gecko-infer.

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