In this section, we provide supplementary details of our VRDP1. First, we give more details of ourphysicsmodel andtheneuro-symbolic operations intheprogram executor.

Complex software-driven systems often interleave distributed, concurrent computation processes with physical interactions with the environment. Developing these systems more efficiently and safely can be achieved by employing actionable, software-based models. From a high-level system model, engineers often need to derive multiple specialized models for different purposes, including simulation, deployment, and formal verification. Each of these target models usually rely on its own formalism, specification language, and execution platform. Traditionally, a compiler analyzes a program written in a programming language and generates executable code. In contrast, a model compiler processes a source model written in a modeling language and should ideally support the generation of multiple heterogeneous targets. However, most existing modeling languages are designed with a narrow focus, typically targeting only simulation or implementation. Multi-target compilation, when not considered during the language's early design, becomes significantly harder to achieve. In this paper, we introduce our initiative: a toolchain and modeling language called M, designed to support system modeling and multi-target compilation for model-driven engineering of complex, concurrent, and time-aware systems. M is a textual, grammar-driven language based on the actor model and extended with discrete-event scheduling semantics. It provides constructs for modeling system entities, message-based interactions, and time- or state-triggered reactions. From such models, M enables the systematic generation of diverse target artifacts while preserving semantic conformance to the original model. Moreover, M can serve as a middle language to which other modeling languages may anchor, thereby allowing them to benefit from its compilation framework.

LLMs can perform multi-step reasoning through Chain-of-Thought (CoT), but they cannot reliably verify their own logic. Even when they reach correct answers, the underlying reasoning may be flawed, undermining trust in high-stakes scenarios. To mitigate this issue, we introduce VeriCoT, a neuro-symbolic method that extracts and verifies formal logical arguments from CoT reasoning. VeriCoT formalizes each CoT reasoning step into first-order logic and identifies premises that ground the argument in source context, commonsense knowledge, or prior reasoning steps. The symbolic representation enables automated solvers to verify logical validity while the NL premises allow humans and systems to identify ungrounded or fallacious reasoning steps. Experiments on the ProofWriter, LegalBench, and BioASQ datasets show VeriCoT effectively identifies flawed reasoning, and serves as a strong predictor of final answer correctness. We also leverage VeriCoT's verification signal for (1) inference-time self-reflection, (2) supervised fine-tuning (SFT) on VeriCoT-distilled datasets and (3) preference fine-tuning (PFT) with direct preference optimization (DPO) using verification-based pairwise rewards, further improving reasoning validity and accuracy.

Large language models (LLMs) are increasingly deployed as agents in various contexts by providing tools at their disposal. However, LLM agents can exhibit unpredictable behaviors, including taking undesirable and/or unsafe actions. In order to measure the latent propensity of LLM agents for taking illegal actions under an EU legislative context, we introduce EU-Agent-Bench, a verifiable human-curated benchmark that evaluates an agent's alignment with EU legal norms in situations where benign user inputs could lead to unlawful actions. Our benchmark spans scenarios across several categories, including data protection, bias/discrimination, and scientific integrity, with each user request allowing for both compliant and non-compliant execution of the requested actions. Comparing the model's function calls against a rubric exhaustively supported by citations of the relevant legislature, we evaluate the legal compliance of frontier LLMs, and furthermore investigate the compliance effect of providing the relevant legislative excerpts in the agent's system prompt along with explicit instructions to comply. We release a public preview set for the research community, while holding out a private test set to prevent data contamination in evaluating upcoming models. We encourage future work extending agentic safety benchmarks to different legal jurisdictions and to multi-turn and multilingual interactions. We release our code on \href{https://github.com/ilijalichkovski/eu-agent-bench}{this URL}.

In order to provide a robot with the ability to understand and react to a user's natural language inputs, the natural language must be connected to the robot's underlying representations of the world. Recently, large language models (LLMs) and 3D scene graphs (3DSGs) have become a popular choice for grounding natural language and representing the world. In this work, we address the challenge of using LLMs with 3DSGs to ground natural language. Existing methods encode the scene graph as serialized text within the LLM's context window, but this encoding does not scale to large or rich 3DSGs. Instead, we propose to use a form of Retrieval Augmented Generation to select a subset of the 3DSG relevant to the task. We encode a 3DSG in a graph database and provide a query language interface (Cypher) as a tool to the LLM with which it can retrieve relevant data for language grounding. We evaluate our approach on instruction following and scene question-answering tasks and compare against baseline context window and code generation methods. Our results show that using Cypher as an interface to 3D scene graphs scales significantly better to large, rich graphs on both local and cloud-based models. This leads to large performance improvements in grounded language tasks while also substantially reducing the token count of the scene graph content. A video supplement is available at https://www.youtube.com/watch?v=zY_YI9giZSA.

Modern causal discovery methods face critical limitations in scalability, computational efficiency, and adaptability to mixed data types, as evidenced by benchmarks on node scalability (30, $\le 50$, $\ge 70$ nodes), computational energy demands, and continuous/non-continuous data handling. While traditional algorithms like PC, GES, and ICA-LiNGAM struggle with these challenges, exhibiting prohibitive energy costs for higher-order nodes and poor scalability beyond 70 nodes, we propose \textbf{GUIDE}, a framework that integrates Large Language Model (LLM)-generated adjacency matrices with observational data through a dual-encoder architecture. GUIDE uniquely optimizes computational efficiency, reducing runtime on average by $\approx 42%$ compared to RL-BIC and KCRL methods, while achieving an average $\approx 117%$ improvement in accuracy over both NOTEARS and GraN-DAG individually. During training, GUIDE's reinforcement learning agent dynamically balances reward maximization (accuracy) and penalty avoidance (DAG constraints), enabling robust performance across mixed data types and scalability to $\ge 70$ nodes -- a setting where baseline methods fail.

Abstract--In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost functions. Conversely, the approach (ii) provides a global view with strong bounds, but the size of the reformulation can be problematic. We focus on approach (iii) in which soft arc consistency (SAC) algorithms produce bounds of intermediate quality. Recently, the introduction of linear constraints as local cost functions increases their modeling expressiveness. We adapt an existing SAC algorithm to handle linear constraints. We show that our algorithm significantly improves the lower bounds compared to the original algorithm on several benchmarks, reducing solving time in some cases. Graphical models provide a powerful framework for modeling a variety of combinatorial problems, addressing tasks that range from satisfaction problems to probabilistic models. They employ local functions defined over'small' subset of variables to represent diverse interactions among them. For example, to model the Constraint Satisfaction Problem (CSP) [2], each local function is a constraint evaluating to true (satisfied) or false (falsified).

The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its expressiveness over standard HOL. Yet it retains strong automated theorem proving support via a sound and complete translation to HOL. We leverage this design to extend DHOL with refinement and quotient types. Both of these are commonly requested by practitioners but rarely provided by automated theorem provers. This is because they inherently require undecidable typing and thus are very difficult to retrofit to decidable type systems. But with DHOL already doing the heavy lifting, adding them is not only possible but elegant and simple. Concretely, we add refinement and quotient types as special cases of subtyping. This turns the associated canonical inclusion resp. projection maps into identity maps and thus avoids costly changes in representation. We present the syntax, semantics, and translation to HOL for the extended language, including the proofs of soundness and completeness.