Providing a very low critical probabilitypc means that certification occurs when the simulation ends after alarge number of iterationsm. On the other hand, the projection of X onto any other direction orthogonal tog remains normal distributed. For each couple of parameters(N,T)we make1000 runs and count the number of false positive(i.e. the number of times the algorithm wrongfully asserted thatp < pc). Combining the latter proposal withT we obtain again a proposal reversible w.r.t. Step4: Conclusionbyinduction Let l0 be any critical level such thatπ0(h(X) > l0) > 0. We consider the following induction hypothesisatiterationk: Hk On the event, Lk l0, The probability that the two particle systems are equal tends exponentiallyfastto1whent + .

Abstract-- Locomotion robots with active or passive compliance can show robustness to uncertain scenarios, which can be promising for agricultural, research and environmental industries. However, state estimation for these robots is challenging due to the lack of rigid-body assumptions and kinematic changes from morphing. We propose a method to estimate typical rigid-body states alongside compliance-related states, such as soft robot shape in different morphologies and locomotion modes. Our neural network-based state estimator uses a history of states and a mechanism to directly influence unreliable sensors. We test our framework on the GOA T platform, a robot capable of passive compliance and active morphing for extreme outdoor terrain. The network is trained on motion capture data in a novel compliance-centric frame that accounts for morphing-related states. Our method predicts shape-related measurements within 4.2% of the robot's size, velocities within 6.3% and 2.4% of the top linear and angular speeds, respectively, and orientation within 1.5 For robots to support outdoor industries and research activities, such as animal monitoring, climate surveillance, and agriculture, they require the capability to operate within and traverse extreme terrain conditions [1][2][3]. While animals demonstrate such capabilities, and can operate on challenging and varied terrains, typical state-of-the art robotic solutions, such as rigid-body quadrupeds, are primarily confined to challenging but man-made terrain [4]. This can be partially attributed to their reliance on a singular mode of locomotion and an inability to physically adapt to the wide range of conditions found in outdoor environments [5][6].

The modelling of business processes is an important task to support decision-making in complex industrial and corporate domains. Recent years have seen the birth of the BPM! (BPM!) research area, focused on the analysis and control of process execution quality, and in particular, the rise in popularity of process mining [van12], which encompasses a set of techniques to extract valuable information from event logs. Process discovery is one of the most investigated process mining techniques. It deals with the automatic learning of a process model from a given set of logged traces, each one representing the digital footprint of the execution of a case. Process discovery algorithms are usually classified into two categories according to the language they employ to represent the output model: procedural and declarative. Procedural techniques envisage the process model as a synthetic description of all possible sequences of actions that the process accepts from an initial to an ending state. Declarative discovery algorithms--which represent the context of this work--return the model as a set of constraints equipped with a declarative, logic-based semantics, and that must be fulfilled by the traces at hand. Both approaches have their strengths and weaknesses depending on the characteristics of the considered process.

The capability to store data about business processes execution in so-called Event Logs has brought to the diffusion of tools for the analysis of process executions and for the assessment of the goodness of a process model. Nonetheless, these tools are often very rigid in dealing with with Event Logs that include incomplete information about the process execution. Thus, while the ability of handling incomplete event data is one of the challenges mentioned in the process mining manifesto, the evaluation of compliance of an execution trace still requires an end-to-end complete trace to be performed. This paper exploits the power of abduction to provide a flexible, yet computationally effective, framework to deal with different forms of incompleteness in an Event Log. Moreover it proposes a refinement of the classical notion of compliance into strong and conditional compliance to take into account incomplete logs. Finally, performances evaluation in an experimental setting shows the feasibility of the presented approach.

Alignment faking in large language models presented a demonstration of Claude 3 Opus and Claude 3.5 Sonnet selectively complying with a helpful-only training objective to prevent modification of their behavior outside of training. We expand this analysis to 25 models and find that only 5 (Claude 3 Opus, Claude 3.5 Sonnet, Llama 3 405B, Grok 3, Gemini 2.0 Flash) comply with harmful queries more when they infer they are in training than when they infer they are in deployment. First, we study the motivations of these 5 models. Results from perturbing details of the scenario suggest that only Claude 3 Opus's compliance gap is primarily and consistently motivated by trying to keep its goals. Second, we investigate why many chat models don't fake alignment. Our results suggest this is not entirely due to a lack of capabilities: many base models fake alignment some of the time, and post-training eliminates alignment-faking for some models and amplifies it for others. We investigate 5 hypotheses for how post-training may suppress alignment faking and find that variations in refusal behavior may account for a significant portion of differences in alignment faking.

We present a Fair Housing and Fair Lending dataset (FairHome): A dataset with around 75,000 examples across 9 protected categories. To the best of our knowledge, FairHome is the first publicly available dataset labeled with binary labels for compliance risk in the housing domain. We demonstrate the usefulness and effectiveness of such a dataset by training a classifier and using it to detect potential violations when using a large language model (LLM) in the context of real-estate transactions. We benchmark the trained classifier against state-of-the-art LLMs including GPT-3.5, GPT-4, LLaMA-3, and Mistral Large in both zero-shot and fewshot contexts. Our classifier outperformed with an F1-score of 0.91, underscoring the effectiveness of our dataset. WARNING: Some of the examples included in the paper are not polite, in so far as they reveal bias that might feel discriminatory to the readers.

Spinal cord injuries (SCIs) generally result in sensory and mobility impairments, with torso instability being particularly debilitating. Existing torso stabilisers are often rigid and restrictive. This paper presents an early investigation into a non-restrictive 1 degree-of-freedom (DoF) mechanical torso stabiliser inspired by devices such as centrifugal clutches and seat-belt mechanisms. Firstly, the paper presents a motion-capture (MoCap) and OpenSim-based kinematic analysis of the cable-based system to understand requisite device characteristics. The simulated evaluation resulted in the cable-based device to require 55-60cm of unrestricted travel, and to lock at a threshold cable velocity of 80-100cm/sec. Next, the developed 1-DoF device is introduced. The proposed mechanical device is transparent during activities of daily living, and transitions to compliant blocking when incipient fall is detected. Prototype behaviour was then validated using a MoCap-based kinematic analysis to verify non-restrictive movement, reliable transition to blocking, and compliance of the blocking.

The robotic handling of compliant and deformable food raw materials, characterized by high biological variation, complex geometrical 3D shapes, and mechanical structures and texture, is currently in huge demand in the ocean space, agricultural, and food industries. Many tasks in these industries are performed manually by human operators who, due to the laborious and tedious nature of their tasks, exhibit high variability in execution, with variable outcomes. The introduction of robotic automation for most complex processing tasks has been challenging due to current robot learning policies. A more consistent learning policy involving skilled operators is desired. In this paper, we address the problem of robot learning when presented with inconsistent demonstrations. To this end, we propose a robust learning policy based on Learning from Demonstration (LfD) for robotic grasping of food compliant objects. The approach uses a merging of RGB-D images and tactile data in order to estimate the necessary pose of the gripper, gripper finger configuration and forces exerted on the object in order to achieve effective robot handling. During LfD training, the gripper pose, finger configurations and tactile values for the fingers, as well as RGB-D images are saved. We present an LfD learning policy that automatically removes inconsistent demonstrations, and estimates the teacher's intended policy. The performance of our approach is validated and demonstrated for fragile and compliant food objects with complex 3D shapes. The proposed approach has a vast range of potential applications in the aforementioned industry sectors.

LLM-powered chatbots are becoming widely adopted in applications such as healthcare, personal assistants, industry hiring decisions, etc. In many of these cases, chatbots are fed sensitive, personal information in their prompts, as samples for in-context learning, retrieved records from a database, or as part of the conversation. The information provided in the prompt could directly appear in the output, which might have privacy ramifications if there is sensitive information there. As such, in this paper, we aim to understand the input copying and regurgitation capabilities of these models during inference and how they can be directly instructed to limit this copying by complying with regulations such as HIPAA and GDPR, based on their internal knowledge of them. More specifically, we find that when ChatGPT is prompted to summarize cover letters of a 100 candidates, it would retain personally identifiable information (PII) verbatim in 57.4% of cases, and we find this retention to be non-uniform between different subgroups of people, based on attributes such as gender identity. We then probe ChatGPT's perception of privacy-related policies and privatization mechanisms by directly instructing it to provide compliant outputs and observe a significant omission of PII from output.

Differentiable simulation enables gradients to be back-propagated through physics simulations. In this way, one can learn the dynamics and properties of a physics system by gradient-based optimization or embed the whole differentiable simulation as a layer in a deep learning model for downstream tasks, such as planning and control. However, differentiable simulation at its current stage is not perfect and might provide wrong gradients that deteriorate its performance in learning tasks. In this paper, we study differentiable rigid-body simulation with contacts. We find that existing differentiable simulation methods provide inaccurate gradients when the contact normal direction is not fixed - a general situation when the contacts are between two moving objects. We propose to improve gradient computation by continuous collision detection and leverage the time-of-impact (TOI) to calculate the post-collision velocities. We demonstrate our proposed method, referred to as TOI-Velocity, on two optimal control problems. We show that with TOI-Velocity, we are able to learn an optimal control sequence that matches the analytical solution, while without TOI-Velocity, existing differentiable simulation methods fail to do so.