Recently, self-supervised learning for graph neural networks (GNNs) has attracted considerable attention because of their notable successes in learning the representation of graph-structure data. However, the formation of a real-world graph typically arises from the highly complex interaction of many latent factors. The existing self-supervised learning methods for GNNs are inherently holistic and neglect the entanglement of the latent factors, resulting in the learned representations suboptimal for downstream tasks and difficult to be interpreted. Learning disentangled graph representations with self-supervised learning poses great challenges and remains largely ignored by the existing literature. In this paper, we introduce the Disentangled Graph Contrastive Learning (DGCL) method, which is able to learn disentangled graph-level representations with self-supervision. In particular, we first identify the latent factors of the input graph and derive its factorized representations. Each of the factorized representations describes a latent and disentangled aspect pertinent to a specific latent factor of the graph. Then we propose a novel factor-wise discrimination objective in a contrastive learning manner, which can force the factorized representations to independently reflect the expressive information from different latent factors. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of our method against several state-of-the-art baselines.

Language models employ a very large number of trainable parameters. Despite being highly overparameterized, these networks often achieve good out-of-sample test performance on the original task and easily fine-tune to related tasks. Recent observations involving, for example, intrinsic dimension of the objective landscape and the lottery ticket hypothesis, indicate that often training actively involves only a small fraction of the parameter space. Thus, a question remains how large a parameter space needs to be in the first place -- the evidence from recent work on model compression, parameter sharing, factorized representations, and knowledge distillation increasingly shows that models can be made much smaller and still perform well. Here, we focus on factorized representations of matrices that underpin dense, embedding, and self-attention layers. We use low-rank factorized representation of a reshaped and rearranged original matrix to achieve space efficient and expressive linear layers. We prove that stacking such low-rank layers increases their expressiveness, providing theoretical understanding for their effectiveness in deep networks. In Transformer models, our approach leads to more than ten-fold reduction in the number of total trainable parameters, including embedding, attention, and feed-forward layers, with little degradation in on-task performance. The approach operates out-of-the-box, replacing each parameter matrix with its compact equivalent while maintaining the architecture of the network.

Learning models over factorized joins avoids redundant computations by identifying and pre-computing shared cofactors. Previous work has investigated the performance gain when computing cofactors on traditional disk-based database systems. Due to the absence of published code, the experiments could not be reproduced on in-memory database systems. This work describes the implementation when using cofactors for in-database factorized learning. We benchmark our open-source implementation for learning linear regression on factorized joins with PostgreSQL -- as a disk-based database system -- and HyPer -- as an in-memory engine. The evaluation shows a performance gain of factorized learning on in-memory database systems by 70\% to non-factorized learning and by a factor of 100 compared to disk-based database systems. Thus, modern database engines can contribute to the machine learning pipeline by pre-computing aggregates prior to data extraction to accelerate training.

Language models employ a very large number of trainable parameters.

Generating simulations to train intelligent agents in game-playing and robotics from natural language input, user input, or task documentation remains an open-ended challenge. Existing approaches focus on parts of this challenge, such as generating reward functions or task hyperparameters. Unlike previous work, we introduce FACTORSIM that generates full simulations in code from language input that can be used to train agents. Exploiting the structural modularity specific to coded simulations, we propose to use a factored partially observable Markov decision process representation that allows us to reduce context dependence during each step of the generation. For evaluation, we introduce a generative simulation benchmark that assesses the generated simulation code's accuracy and effectiveness in facilitating zero-shot transfers in reinforcement learning settings.

Recently, self-supervised learning for graph neural networks (GNNs) has attracted considerable attention because of their notable successes in learning the representation of graph-structure data. However, the formation of a real-world graph typically arises from the highly complex interaction of many latent factors. The existing self-supervised learning methods for GNNs are inherently holistic and neglect the entanglement of the latent factors, resulting in the learned representations suboptimal for downstream tasks and difficult to be interpreted. Learning disentangled graph representations with self-supervised learning poses great challenges and remains largely ignored by the existing literature. In this paper, we introduce the Disentangled Graph Contrastive Learning (DGCL) method, which is able to learn disentangled graph-level representations with self-supervision.

Language models employ a very large number of trainable parameters. Despite being highly overparameterized, these networks often achieve good out-of-sample test performance on the original task and easily fine-tune to related tasks. Recent observations involving, for example, intrinsic dimension of the objective landscape and the lottery ticket hypothesis, indicate that often training actively involves only a small fraction of the parameter space. Thus, a question remains how large a parameter space needs to be in the first place –- the evidence from recent work on model compression, parameter sharing, factorized representations, and knowledge distillation increasingly shows that models can be made much smaller and still perform well. Here, we focus on factorized representations of matrices that underpin dense, embedding, and self-attention layers.

The human cognitive system exhibits remarkable flexibility and generalization capabilities, partly due to its ability to form low-dimensional, compositional representations of the environment. In contrast, standard neural network architectures often struggle with abstract reasoning tasks, overfitting, and requiring extensive data for training. This paper investigates the impact of the relational bottleneck -- a mechanism that focuses processing on relations among inputs -- on the learning of factorized representations conducive to compositional coding and the attendant flexibility of processing. We demonstrate that such a bottleneck not only improves generalization and learning efficiency, but also aligns network performance with human-like behavioral biases. Networks trained with the relational bottleneck developed orthogonal representations of feature dimensions latent in the dataset, reflecting the factorized structure thought to underlie human cognitive flexibility. Moreover, the relational network mimics human biases towards regularity without pre-specified symbolic primitives, suggesting that the bottleneck fosters the emergence of abstract representations that confer flexibility akin to symbols.

We present a model for exact recursive Bayesian filtering based on lifted multiset states. Combining multisets with lifting makes it possible to simultaneously exploit multiple strategies for reducing inference complexity when compared to list-based grounded state representations. The core idea is to borrow the concept of Maximally Parallel Multiset Rewriting Systems and to enhance it by concepts from Rao-Blackwellization and Lifted Inference, giving a representation of state distributions that enables efficient inference. In worlds where the random variables that define the system state are exchangeable -- where the identity of entities does not matter -- it automatically uses a representation that abstracts from ordering (achieving an exponential reduction in complexity) -- and it automatically adapts when observations or system dynamics destroy exchangeability by breaking symmetry.