We have listened, Technology Secretary Liz Kendall said on Wednesday, saying the government no longer favours that approach. However, the government's position is now unclear, saying it no longer has a preferred option for what to do next. Kendall said the government had engaged extensively with people in the creative and AI industries. It is attempting to balance the interests of the two sectors by giving creatives control how their work is used, while recognising AI models need to be trained on work such as writing, music and video. In a report published on Wednesday, the government said there was no consensus on how these objectives should be achieved.

Supplementary Materials for "Don't be so Monotone: Relaxing Stochastic Line Search in Over-Parameterized Models" Appendix A The Algorithm Appendix B Convergence Rates Appendix B.1 Rate of Convergence for Strongly Convex Functions Appendix B.2 Rate of Convergence for Convex Functions Appendix B.3 Rate of Convergence for Functions Satisfying the PL Condition Appendix B.4 Common Lemmas Appendix B.5 The Polyak Step Size is Bounded Appendix C Experimental details Appendix D Plots Completing the Figures in the Main Paper Appendix D.1 Comparison between PoNoS and the state-of-the-art Appendix D.2 A New Resetting Technique Appendix D.3 Time Comparison Appendix D.4 Experiments on Convex Losses Appendix D.5 Experiments on Transformers Appendix E Additional Plots Appendix E.1 Study on the Choice of c: Theory (0.5) vs Practice (0.1) Appendix E.2 Study on the Line Search Choice: V arious Nonmonotone Adaptations Appendix E.3 Zoom in on the Amount of Backtracks Appendix E.4 Study on the Choice of η In this section, we give the details of our proposed algorithm PoNoS. Training machine learning models (e.g., neural networks) entails solving the following finite sum problem: min Before that, we establish the following auxiliary result. The following Lemma shows the importance of the interpolation property. Lemma 4. W e assume interpolation and that f Let us now analyze case 2). Let us now show that b < 1. B.2 Rate of Convergence for Convex Functions In this subsection, we prove a O ( The above bound will be now proven also for case 2).

Recent works have shown that line search methods can speed up Stochastic Gradient Descent (SGD) and Adam in modern over-parameterized settings. However, existing line searches may take steps that are smaller than necessary since they require a monotone decrease of the (mini-)batch objective function.

Determining exactly which relationships to include when representing an object as agraph is not alwaysstraightforward.

Automatic test pattern generation (ATPG) is a crucial process in integrated circuit (IC) design and testing, responsible for efficiently generating test patterns. As semiconductor technology progresses, traditional ATPG struggles with long execution times to achieve the expected fault coverage, which impacts the time-to-market of chips. Recent machine learning techniques, like reinforcement learning (RL) and graph neural networks (GNNs), show promise but face issues such as reward delay in RL models and inadequate circuit representation in GNN-based methods. In this paper, we propose InF-ATPG, an intelligent FFR-driven ATPG framework that overcomes these challenges by using advanced circuit representation to guide RL. By partitioning circuits into fanout-free regions (FFRs) and incorporating ATPG-specific features into a novel QGNN architecture, InF-ATPG enhances test pattern generation efficiency. Experimental results show InF-ATPG reduces backtracks by 55.06\% on average compared to traditional methods and 38.31\% compared to the machine learning approach, while also improving fault coverage.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities when they generate step-by-step solutions, known as chain-of-thought (CoT) reasoning. When trained to using chain-of-thought reasoning examples, the resulting models (called Large Reasoning Models, or LRMs) appear to learn hierarchical thinking strategies similar to those used by humans. However, understanding LRMs emerging reasoning capabilities remains a difficult open problem, with many potential important applications including improving training and understanding robustness. In this paper, we adopt a memoryless Finite State Machine formulation to approximate LRM's emerging hierarchical reasoning dynamics as a structured, interpretable abstraction. We identify a small set of discrete reasoning states including - initialization, deduction, augmentation-strategy, uncertainty-estimation, backtracking, and final-conclusion that capture the high-level states present in the model's reasoning process. By annotating each step of a model's CoT with these states, we can represent the reasoning trajectory as a transition sequence through the state graph. This FSM formulation provides a systematic way to analyze, interpret and visualize how different models approach problems. We describe the FSM model, provide examples of CoT annotations under this scheme, and discuss how it can shed light on differences between available models in their approach to reasoning. Our results demonstrate that this FSM-based analysis reveals distinct reasoning patterns and potential shortcomings, offering a new lens to evaluate and improve LLM reasoning.

Supplementary Materials for "Don't be so Monotone: Relaxing Stochastic Line Search in Over-Parameterized Models" Appendix A The Algorithm Appendix B Convergence Rates Appendix B.1 Rate of Convergence for Strongly Convex Functions Appendix B.2 Rate of Convergence for Convex Functions Appendix B.3 Rate of Convergence for Functions Satisfying the PL Condition Appendix B.4 Common Lemmas Appendix B.5 The Polyak Step Size is Bounded Appendix C Experimental details Appendix D Plots Completing the Figures in the Main Paper Appendix D.1 Comparison between PoNoS and the state-of-the-art Appendix D.2 A New Resetting Technique Appendix D.3 Time Comparison Appendix D.4 Experiments on Convex Losses Appendix D.5 Experiments on Transformers Appendix E Additional Plots Appendix E.1 Study on the Choice of c: Theory (0.5) vs Practice (0.1) Appendix E.2 Study on the Line Search Choice: V arious Nonmonotone Adaptations Appendix E.3 Zoom in on the Amount of Backtracks Appendix E.4 Study on the Choice of η In this section, we give the details of our proposed algorithm PoNoS. Training machine learning models (e.g., neural networks) entails solving the following finite sum problem: min Before that, we establish the following auxiliary result. The following Lemma shows the importance of the interpolation property. Lemma 4. W e assume interpolation and that f Let us now analyze case 2). Let us now show that b < 1. B.2 Rate of Convergence for Convex Functions In this subsection, we prove a O ( The above bound will be now proven also for case 2).