分析了无限维函数空间之间地图的深层替代物的近似速率，例如作为线性和非线性偏微分方程的数据到解决图。具体而言，我们研究了深神经操作员和广义多项式混乱（GPC）操作员的近似速率，用于无线性，可分开的希尔伯特空间之间的非线性，全态图。假定功能空间的运算符和输出通过稳定的仿射表示系统进行参数化。可接受的表示系统包括正常基础，RIESZ底座或所考虑的空间的合适的紧密框架。建立了代数表达速率界限，为具有有限的Sobolev或BESOV规律性的范围内的深层神经和GPC操作员替代物都作用于可分离的Hilbert空间和拟合图表的范围。我们通过表达速率界限来说明抽象速率界限的系数到测序图，用于圆环上线性椭圆形PDE。

Deep learning models are known to put the privacy of their training data at risk, which poses challenges for their safe and ethical release to the public. Differentially private stochastic gradient descent is the de facto standard for training neural networks without leaking sensitive information about the training data. However, applying it to models for graph-structured data poses a novel challenge: unlike with i.i.d. data, sensitive information about a node in a graph cannot only leak through its gradients, but also through the gradients of all nodes within a larger neighborhood. In practice, this limits privacy-preserving deep learning on graphs to very shallow graph neural networks. We propose to solve this issue by training graph neural networks on disjoint subgraphs of a given training graph. We develop three random-walk-based methods for generating such disjoint subgraphs and perform a careful analysis of the data-generating distributions to provide strong privacy guarantees. Through extensive experiments, we show that our method greatly outperforms the state-of-the-art baseline on three large graphs, and matches or outperforms it on four smaller ones.

Explainable AI transforms opaque decision strategies of ML models into explanations that are interpretable by the user, for example, identifying the contribution of each input feature to the prediction at hand. Such explanations, however, entangle the potentially multiple factors that enter into the overall complex decision strategy. We propose to disentangle explanations by finding relevant subspaces in activation space that can be mapped to more abstract human-understandable concepts and enable a joint attribution on concepts and input features. To automatically extract the desired representation, we propose new subspace analysis formulations that extend the principle of PCA and subspace analysis to explanations. These novel analyses, which we call principal relevant component analysis (PRCA) and disentangled relevant subspace analysis (DRSA), optimize relevance of projected activations rather than the more traditional variance or kurtosis. This enables a much stronger focus on subspaces that are truly relevant for the prediction and the explanation, in particular, ignoring activations or concepts to which the prediction model is invariant. Our approach is general enough to work alongside common attribution techniques such as Shapley Value, Integrated Gradients, or LRP. Our proposed methods show to be practically useful and compare favorably to the state of the art as demonstrated on benchmarks and three use cases.

A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir functional associated with a state-space representation of the Volterra series expansion available for any analytic fading memory filter. It is hence called the Volterra reservoir kernel. Even though the state-space representation and the corresponding reservoir feature map are defined on an infinite-dimensional tensor algebra space, the kernel map is characterized by explicit recursions that are readily computable for specific data sets when employed in estimation problems using the representer theorem. We showcase the performance of the Volterra reservoir kernel in a popular data science application in relation to bitcoin price prediction.

There are two important things in science: (A) Finding answers to given questions, and (B) Coming up with good questions. Our artificial scientists not only learn to answer given questions, but also continually invent new questions, by proposing hypotheses to be verified or falsified through potentially complex and time-consuming experiments, including thought experiments akin to those of mathematicians. While an artificial scientist expands its knowledge, it remains biased towards the simplest, least costly experiments that still have surprising outcomes, until they become boring. We present an empirical analysis of the automatic generation of interesting experiments. In the first setting, we investigate self-invented experiments in a reinforcement-providing environment and show that they lead to effective exploration. In the second setting, pure thought experiments are implemented as the weights of recurrent neural networks generated by a neural experiment generator. Initially interesting thought experiments may become boring over time.

Heating in private households is a major contributor to the emissions generated today. Heat pumps are a promising alternative for heat generation and are a key technology in achieving our goals of the German energy transformation and to become less dependent on fossil fuels. Today, the majority of heat pumps in the field are controlled by a simple heating curve, which is a naive mapping of the current outdoor temperature to a control action. A more advanced control approach is model predictive control (MPC) which was applied in multiple research works to heat pump control. However, MPC is heavily dependent on the building model, which has several disadvantages. Motivated by this and by recent breakthroughs in the field, this work applies deep reinforcement learning (DRL) to heat pump control in a simulated environment. Through a comparison to MPC, it could be shown that it is possible to apply DRL in a model-free manner to achieve MPC-like performance. This work extends other works which have already applied DRL to building heating operation by performing an in-depth analysis of the learned control strategies and by giving a detailed comparison of the two state-of-the-art control methods.

Human motion prediction is a complex task as it involves forecasting variables over time on a graph of connected sensors. This is especially true in the case of few-shot learning, where we strive to forecast motion sequences for previously unseen actions based on only a few examples. Despite this, almost all related approaches for few-shot motion prediction do not incorporate the underlying graph, while it is a common component in classical motion prediction. Furthermore, state-of-the-art methods for few-shot motion prediction are restricted to motion tasks with a fixed output space meaning these tasks are all limited to the same sensor graph. In this work, we propose to extend recent works on few-shot time-series forecasting with heterogeneous attributes with graph neural networks to introduce the first few-shot motion approach that explicitly incorporates the spatial graph while also generalizing across motion tasks with heterogeneous sensors. In our experiments on motion tasks with heterogeneous sensors, we demonstrate significant performance improvements with lifts from 10.4% up to 39.3% compared to best state-of-the-art models. Moreover, we show that our model can perform on par with the best approach so far when evaluating on tasks with a fixed output space while maintaining two magnitudes fewer parameters.

This project leverages advances in multi-agent reinforcement learning (MARL) to improve the efficiency and flexibility of order-picking systems for commercial warehouses. We envision a warehouse of the future in which dozens of mobile robots and human pickers work together to collect and deliver items within the warehouse. The fundamental problem we tackle, called the order-picking problem, is how these worker agents must coordinate their movement and actions in the warehouse to maximise performance (e.g. order throughput) under given resource constraints. Established industry methods using heuristic approaches require large engineering efforts to optimise for innately variable warehouse configurations. In contrast, the MARL framework can be flexibly applied to any warehouse configuration (e.g. size, layout, number/types of workers, item replenishment frequency) and the agents learn via a process of trial-and-error how to optimally cooperate with one another. This paper details the current status of the R&D effort initiated by Dematic and the University of Edinburgh towards a general-purpose and scalable MARL solution for the order-picking problem in realistic warehouses.

Telling stories is an integral part of human communication which can evoke emotions and influence the affective states of the audience. Automatically modelling emotional trajectories in stories has thus attracted considerable scholarly interest. However, as most existing works have been limited to unsupervised dictionary-based approaches, there is no labelled benchmark for this task. We address this gap by introducing continuous valence and arousal annotations for an existing dataset of children's stories annotated with discrete emotion categories. We collect additional annotations for this data and map the originally categorical labels to the valence and arousal space. Leveraging recent advances in Natural Language Processing, we propose a set of novel Transformer-based methods for predicting valence and arousal signals over the course of written stories. We explore several strategies for fine-tuning a pretrained ELECTRA model and study the benefits of considering a sentence's context when inferring its emotionality. Moreover, we experiment with additional LSTM and Transformer layers. The best configuration achieves a Concordance Correlation Coefficient (CCC) of .7338 for valence and .6302 for arousal on the test set, demonstrating the suitability of our proposed approach. Our code and additional annotations are made available at https://github.com/lc0197/emotion_modelling_stories.

Automatic video captioning aims for a holistic visual scene understanding. It requires a mechanism for capturing temporal context in video frames and the ability to comprehend the actions and associations of objects in a given timeframe. Such a system should additionally learn to abstract video sequences into sensible representations as well as to generate natural written language. While the majority of captioning models focus solely on the visual inputs, little attention has been paid to the audiovisual modality. To tackle this issue, we propose a novel two-fold approach. First, we implement a reward-guided KL Divergence to train a video captioning model which is resilient towards token permutations. Second, we utilise a Bi-Modal Hierarchical Reinforcement Learning (BMHRL) Transformer architecture to capture long-term temporal dependencies of the input data as a foundation for our hierarchical captioning module. Using our BMHRL, we show the suitability of the HRL agent in the generation of content-complete and grammatically sound sentences by achieving $4.91$, $2.23$, and $10.80$ in BLEU3, BLEU4, and METEOR scores, respectively on the ActivityNet Captions dataset. Finally, we make our BMHRL framework and trained models publicly available for users and developers at https://github.com/d-rothen/bmhrl.