Cuspidal机器人是具有至少两种逆运动溶液的机器人，可以通过无奇异路径连接。过去已经研究了普通3R机器人的尖锐性，但是将研究扩展到六度自由的机器人可能是一个具有挑战性的问题。许多机器人可以与真实代数集一起建模为多项式图，以便将尖的概念扩展到这些数据。在本文中，我们设计了一种算法，该算法在输入$ n $不确定的多项式地图上，而$ s $多项式在相同的不确定的情况下描述了一个真实的代数$ d $，请确定地图限制的限制性正在考虑的实际代数设定。此外，如果$ d $和$ \ \ tau $分别是输入多项式系数的最高学位和界限，则该算法在$ \ tau $中以$ \ tau $和$（$（ （s+d）d）^{o（n^2）} $。它依赖于计算机代数中的许多高级算法，这些算法在真实代数集和多项式图的关键基因座上使用高级方法。据我们所知，这是第一种从一般角度解决尖锐性问题的算法。

This report summarizes the work carried out by the authors during the Twelfth Montreal Industrial Problem Solving Workshop, held at Universit\'e de Montr\'eal in August 2022. The team tackled a problem submitted by CBC/Radio-Canada on the theme of Automatic Text Simplification (ATS).

Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $\epsilon$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\mathcal{O}(H(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\mathcal{X}}$ and $B_{\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regularize leader (FTRL) algorithms for this setting: Balanced-FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive-FTRL which needs $\mathcal{O}(H^2(A_{\mathcal{X}}+B_{\mathcal{Y}})/\epsilon^2)$ plays without this requirement by progressively adapting the regularization to the observations.

Line segments are ubiquitous in our human-made world and are increasingly used in vision tasks. They are complementary to feature points thanks to their spatial extent and the structural information they provide. Traditional line detectors based on the image gradient are extremely fast and accurate, but lack robustness in noisy images and challenging conditions. Their learned counterparts are more repeatable and can handle challenging images, but at the cost of a lower accuracy and a bias towards wireframe lines. We propose to combine traditional and learned approaches to get the best of both worlds: an accurate and robust line detector that can be trained in the wild without ground truth lines. Our new line segment detector, DeepLSD, processes images with a deep network to generate a line attraction field, before converting it to a surrogate image gradient magnitude and angle, which is then fed to any existing handcrafted line detector. Additionally, we propose a new optimization tool to refine line segments based on the attraction field and vanishing points. This refinement improves the accuracy of current deep detectors by a large margin. We demonstrate the performance of our method on low-level line detection metrics, as well as on several downstream tasks using multiple challenging datasets. The source code and models are available at https://github.com/cvg/DeepLSD.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

The increasing complexity of gameplay mechanisms in modern video games is leading to the emergence of a wider range of ways to play games. The variety of possible play-styles needs to be anticipated by designers, through automated tests. Reinforcement Learning is a promising answer to the need of automating video game testing. To that effect one needs to train an agent to play the game, while ensuring this agent will generate the same play-styles as the players in order to give meaningful feedback to the designers. We present CARMI: a Configurable Agent with Relative Metrics as Input. An agent able to emulate the players play-styles, even on previously unseen levels. Unlike current methods it does not rely on having full trajectories, but only summary data. Moreover it only requires little human data, thus compatible with the constraints of modern video game production. This novel agent could be used to investigate behaviors and balancing during the production of a video game with a realistic amount of training time.

Modern video games are becoming richer and more complex in terms of game mechanics. This complexity allows for the emergence of a wide variety of ways to play the game across the players. From the point of view of the game designer, this means that one needs to anticipate a lot of different ways the game could be played. Machine Learning (ML) could help address this issue. More precisely, Reinforcement Learning is a promising answer to the need of automating video game testing. In this paper we present a video game environment which lets us define multiple play-styles. We then introduce CARI: a Configurable Agent with Reward as Input. An agent able to simulate a wide continuum range of play-styles. It is not constrained to extreme archetypal behaviors like current methods using reward shaping. In addition it achieves this through a single training loop, instead of the usual one loop per play-style. We compare this novel training approach with the more classic reward shaping approach and conclude that CARI can also outperform the baseline on archetypes generation. This novel agent could be used to investigate behaviors and balancing during the production of a video game with a realistic amount of training time.

Diffusion models have quickly become the go-to paradigm for generative modelling of perceptual signals (such as images and sound) through iterative refinement. Their success hinges on the fact that the underlying physical phenomena are continuous. For inherently discrete and categorical data such as language, various diffusion-inspired alternatives have been proposed. However, the continuous nature of diffusion models conveys many benefits, and in this work we endeavour to preserve it. We propose CDCD, a framework for modelling categorical data with diffusion models that are continuous both in time and input space. We demonstrate its efficacy on several language modelling tasks.

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License.

Can continuous diffusion models bring the same performance breakthrough on natural language they did for image generation? To circumvent the discrete nature of text data, we can simply project tokens in a continuous space of embeddings, as is standard in language modeling. We propose Self-conditioned Embedding Diffusion, a continuous diffusion mechanism that operates on token embeddings and allows to learn flexible and scalable diffusion models for both conditional and unconditional text generation. Through qualitative and quantitative evaluation, we show that our text diffusion models generate samples comparable with those produced by standard autoregressive language models - while being in theory more efficient on accelerator hardware at inference time. Our work paves the way for scaling up diffusion models for text, similarly to autoregressive models, and for improving performance with recent refinements to continuous diffusion.