SearcharxivSearch

arXiv subjects

Alexander Weber

Publications and source records attributed to Alexander Weber.

16 recordsLinked to original sources

Modalities, a PyTorch-native Framework For Large-scale LLM Training and Research

Today's LLM (pre-) training and research workflows typically allocate a significant amount of compute to large-scale ablation studies. Despite the substantial compute costs of these ablations, existing open-source frameworks provide limited tooling for these experiments, often forcing researchers to write their own wrappers and scripts. We propose Modalities, an end-to-end PyTorch-native framework that integrates data-driven LLM research with large-scale model training from two angles. Firstly, by integrating state-of-the-art parallelization strategies, it enables both efficient pretraining and systematic ablations at trillion-token and billion-parameter scale. Secondly, Modalities adopts modular design with declarative, self-contained configuration, enabling reproducibility and extensibility levels that are difficult to achieve out-of-the-box with existing LLM training frameworks.

cs.LG

A modified Bellman-Ford Algorithm for Application in Symbolic Optimal Control and Plan and Goal Recognition

The contributions of this short technical note are two-fold. Firstly, we introduce a modified version of a generalized Bellman-Ford algorithm calculating the value function of optimal control problems defined on hyper-graphs. Those Bellman-Ford algorithms can be used in particular for the synthesis of near-optimal controllers by the principle of symbolic control. Our modification causes less nodes of the hyper-graph being iterated during the execution compared to our initial version of the algorithm published in 2020. Our second contribution lies in the field of Plan recognition applied to drone missions driven by symbolic controllers. We address and resolve the Plan and Goal Recognition monitor's dependence on a pre-defined initial guess for a drone's task allocation and mission execution. To validate the enhanced implementation, we use a more challenging scenario for UAV-based aerial firefighting, demonstrating the practical applicability and robustness of the system architecture.

math.OC

ADS Performance Revisited

Real-time measurements are important for in-depth control of manufacturing processes, which, for modern AI methods, need integration with high-level languages. In our last SSP paper we investigated the performance of a Python and a Java-JNA based approach to integrate the Beckhoff ADS protocol for real-time edge communication into an Industry 4.0 platform. There, we have shown that while Java outperforms Python, both solutions do not meet the desired goal of 1-20kHz depending on the task. However, we are are still lacking an explanation for this result as well as an analysis of alternatives. For the first topic, we show in this paper that 1) exchanging Java-JNA with Java-JNI in this setting does not further improve the performance 2) a C++ program realizing the same behavior in a more direct integration does not perform better and 3) profiling shows that the majority of the execution is spend in ADS. For the second topic, we show that alternative uses of the ADS library allow for better performance.

cs.PF

Model-driven realization of IDTA submodel specifications: The good, the bad, the incompatible?

Asset Administration Shells are trending in Industry 4.0. In February 2024, the Industrial Digital Twin Association announced 84 and released 18 AAS submodel specifications. As an enabler on programming level, dedicated APIs are needed, for which, at this level of scale, automated creation is desirable. In this paper, we present a model-driven approach, which transforms extracted information from IDTA specifications into an intermediary meta-model and, from there, generates API code and tests. We show we can process all current IDTA specifications successfully leading in total to more than 50000 lines of code. However, syntactical variations and issues in the specifications impose obstacles that require human intervention or AI support. We also discuss experiences that we made and lessons learned.

cs.SE

FORFIS: A forest fire firefighting simulation tool for education and research

We present a forest fire firefighting simulation tool named FORFIS that is implemented in Python. Unlike other existing software, we focus on a user-friendly software interface with an easy-to-modify software engine. Our tool is published under GNU GPLv3 license and comes with a GUI as well as additional output functionality. The used wildfire model is based on the well-established approach by cellular automata in two variants - a rectangular and a hexagonal cell decomposition of the wildfire area. The model takes wind into account. In addition, our tool allows the user to easily include a customized firefighting strategy for the firefighting agents.

cs.RO

Developing an AI-enabled IIoT platform -- Lessons learned from early use case validation

For a broader adoption of AI in industrial production, adequate infrastructure capabilities are crucial. This includes easing the integration of AI with industrial devices, support for distributed deployment, monitoring, and consistent system configuration. Existing IIoT platforms still lack required capabilities to flexibly integrate reusable AI services and relevant standards such as Asset Administration Shells or OPC UA in an open, ecosystem-based manner. This is exactly what our next level Intelligent Industrial Production Ecosphere (IIP-Ecosphere) platform addresses, employing a highly configurable low-code based approach. In this paper, we introduce the design of this platform and discuss an early evaluation in terms of a demonstrator for AI-enabled visual quality inspection. This is complemented by insights and lessons learned during this early evaluation activity.

cs.AI

Vehicle mission guidance by symbolic optimal control

Symbolic optimal control is a powerful method to synthesize algorithmically correct-by-design state-feedback controllers for nonlinear plants. Its solutions are (near-)optimal with respect to a given cost function. In this note, it is demonstrated how symbolic optimal control can be used to calculate controllers for an optimized routing guidance of vehicle systems in continuous state space. In fact, the capacitated vehicle routing problem and a variant of travelling salesman problem are investigated. The latter problem has a relevant application in case of loss of vehicles during mission. A goods delivery scenario and a reconnaissance mission, involving bicycle and aircraft dynamics respectively, are provided as examples.

math.OC

On the Solution of the Travelling Salesman Problem for Nonlinear Salesman Dynamics using Symbolic Optimal Control

This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics. The presented method is based on the framework of Symbolic Control. In this way, our method returns a provably correct state-feedback controller for the underlying coverage specification, which is the TSP leaving out the requirement for optimality on the route. In addition, we utilize the Lin-Kernighan-Helsgaun TSP solver to heuristically optimize the cost for the overall taken route. Two examples, an urban parcel delivery task and a UAV reconnaissance mission, greatly illustrate the powerfulness of the proposed heuristic.

math.OC

Approximately Optimal Controllers for Quantitative Two-Phase Reach-Avoid Problems on Nonlinear Systems

The present work deals with quantitative two-phase reach-avoid problems on nonlinear control systems. This class of optimal control problem requires the plant's state to visit two (rather than one) target sets in succession while minimizing a prescribed cost functional. As we illustrate, the naive approach, which subdivides the problem into the two evident classical reach-avoid tasks, usually does not result in an optimal solution. In contrast, we prove that an optimal controller is obtained by consecutively solving two special quantitative reach-avoid problems. In addition, we present a fully-automated method based on Symbolic Optimal Control to practically synthesize for the considered problem class approximately optimal controllers for sampled-data nonlinear plants. Experimental results on parcel delivery and on an aircraft routing mission confirm the practicality of our method.

math.OC

A generalized Bellman-Ford Algorithm for Application in Symbolic Optimal Control

Symbolic controller synthesis is a fully-automated and correct-by-design synthesis scheme whose limitations are its immense memory and runtime requirements. A current trend to compensate for this downside is to develop techniques for parallel execution of the scheme both in mathematical foundation and in software implementation. In this paper we present a generalized Bellman-Ford algorithm to be used in the so-called symbolic optimal control, which is an extension of the aforementioned synthesis scheme. Compared to the widely used Dijkstra algorithm our algorithm has two advantages. It allows for cost functions taking arbitrary (e.g. negative) values and for parallel execution with the ability for trading processing speed for memory consumption. We motivate the usefulness of negative cost values on a scenario of aerial firefighting with unmanned aerial vehicles. In addition, this four-dimensional numerical example, which is rich in detail, demonstrates the great performance of our algorithm.

math.OC

Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

math.NA

Optimized State Space Grids for Abstractions

The practical impact of abstraction-based controller synthesis methods is currently limited by the immense computational effort for obtaining abstractions. In this note we focus on a recently proposed method to compute abstractions whose state space is a cover of the state space of the plant by congruent hyper-intervals. The problem of how to choose the size of the hyper-intervals so as to obtain computable and useful abstractions is unsolved. This note provides a twofold contribution towards a solution. Firstly, we present a functional to predict the computational effort for the abstraction to be computed. Secondly, we propose a method for choosing the aspect ratio of the hyper-intervals when their volume is fixed. More precisely, we propose to choose the aspect ratio so as to minimize a predicted number of transitions of the abstraction to be computed, in order to reduce the computational effort. To this end, we derive a functional to predict the number of transitions in dependence of the aspect ratio. The functional is to be minimized subject to suitable constraints. We characterize the unique solvability of the respective optimization problem and prove that it transforms, under appropriate assumptions, into an equivalent convex problem with strictly convex objective. The latter problem can then be globally solved using standard numerical methods. We demonstrate our approach on an example.

math.OC

Feedback Refinement Relations for the Synthesis of Symbolic Controllers

We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples.

math.OC

A linear time algorithm to verify strong structural controllability

We prove that strong structural controllability of a pair of structural matrices $(\mathcal{A},\mathcal{B})$ can be verified in time linear in $n + r + ν$, where $\mathcal{A}$ is square, $n$ and $r$ denote the number of columns of $\mathcal{A}$ and $\mathcal{B}$, respectively, and $ν$ is the number of non-zero entries in $(\mathcal{A},\mathcal{B})$. We also present an algorithm realizing this bound, which depends on a recent, high-level method to verify strong structural controllability and uses sparse matrix data structures. Linear time complexity is actually achieved by separately storing both the structural matrix $(\mathcal{A},\mathcal{B})$ and its transpose, linking the two data structures through a third one, and a novel, efficient scheme to update all the data during the computations. We illustrate the performance of our algorithm using systems of various sizes and sparsity.

math.OC

Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems

Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of the so-called local quadratic support is proved. The results concerning strong convexity are used to derive sufficient conditions for attainable sets of continuous-time nonlinear systems to be strongly convex. An application of these conditions is a novel method to over-approximate attainable sets when strong convexity is present.

math.OC

Local characterization of strongly convex sets

Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity δ_Ωof a set Ω. We also show that \lim_{ε\to 0} δ_Ω(ε)/ε^2 exists whenever Ωis closed and convex.

math.MG