Higher Order Transformers: Efficient Attention Mechanism for Tensor Structured Data

Transformers are now ubiquitous for sequence modeling tasks, but their extension to multi-dimensional data remains a challenge due to the quadratic cost of the attention mechanism. In this paper, we propose Higher-Order Transformers (HOT), a novel architecture designed to efficiently process data with more than two axes, i.e. higher-order tensors. To address the computational challenges associated with high-order tensor attention, we introduce a novel Kronecker factorized attention mechanism that reduces the attention cost to quadratic in each axis' dimension, rather than quadratic in the total size of the input tensor. To further enhance efficiency, HOT leverages kernelized attention, reducing the complexity to linear. This strategy maintains the model's expressiveness while enabling scalable attention computation. We validate the effectiveness of HOT on two high-dimensional tasks, including multivariate time series forecasting, and 3D medical image classification. Experimental results demonstrate that HOT achieves competitive performance while significantly improving computational efficiency, showcasing its potential for tackling a wide range of complex, multi-dimensional data.

GFlowNets for Hamiltonian decomposition in groups of compatible operators

Quantum computing presents a promising alternative for the direct simulation of quantum systems with the potential to explore chemical problems beyond the capabilities of classical methods. However, current quantum algorithms are constrained by hardware limitations and the increased number of measurements required to achieve chemical accuracy. To address the measurement challenge, techniques for grouping commuting and anti-commuting terms, driven by heuristics, have been developed to reduce the number of measurements needed in quantum algorithms on near-term quantum devices. In this work, we propose a probabilistic framework using GFlowNets to group fully (FC) or qubit-wise commuting (QWC) terms within a given Hamiltonian. The significance of this approach is demonstrated by the reduced number of measurements for the found groupings; 51% and 67% reduction factors respectively for FC and QWC partitionings with respect to greedy coloring algorithms, highlighting the potential of GFlowNets for future applications in the measurement problem. Furthermore, the flexibility of our algorithm extends its applicability to other resource optimization problems in Hamiltonian simulation, such as circuit design.

UTG: Towards a Unified View of Snapshot and Event Based Models for Temporal Graphs

Temporal graphs have gained increasing importance due to their ability to model dynamically evolving relationships. These graphs can be represented through either a stream of edge events or a sequence of graph snapshots. Until now, the development of machine learning methods for both types has occurred largely in isolation, resulting in limited experimental comparison and theoretical crosspollination between the two. In this paper, we introduce Unified Temporal Graph (UTG), a framework that unifies snapshot-based and event-based machine learning models under a single umbrella, enabling models developed for one representation to be applied effectively to datasets of the other. We also propose a novel UTG training procedure to boost the performance of snapshot-based models in the streaming setting. We comprehensively evaluate both snapshot and event-based models across both types of temporal graphs on the temporal link prediction task. Our main findings are threefold: first, when combined with UTG training, snapshotbased models can perform competitively with event-based models such as TGN and GraphMixer even on event datasets. Second, snapshot-based models are at least an order of magnitude faster than most event-based models during inference. Third, while event-based methods such as NAT and DyGFormer outperforms snapshotbased methods on both types of temporal graphs, this is because they leverage joint neighborhood structural features thus emphasizing the potential to incorporate these features into snapshot-based models as well. These findings highlight the importance of comparing model architectures independent of the data format and suggest the potential of combining the efficiency of snapshot-based models with the performance of event-based models in the future.

ROSA: Random Subspace Adaptation for Efficient Fine-Tuning

Model training requires significantly more memory, compared with inference. Parameter efficient fine-tuning (PEFT) methods provide a means of adapting large models to downstream tasks using less memory. However, existing methods such as adapters, prompt tuning or low-rank adaptation (LoRA) either introduce latency overhead at inference time or achieve subpar downstream performance compared with full fine-tuning. In this work we propose Random Subspace Adaptation (ROSA), a method that outperforms previous PEFT methods by a significant margin, while maintaining a zero latency overhead during inference time. In contrast to previous methods, ROSA is able to adapt subspaces of arbitrarily large dimension, better approximating full-finetuning. We demonstrate both theoretically and experimentally that this makes ROSA strictly more expressive than LoRA, without consuming additional memory during runtime. As PEFT methods are especially useful in the natural language processing domain, where models operate on scales that make full fine-tuning very expensive, we evaluate ROSA in two common NLP scenarios: natural language generation (NLG) and natural language understanding (NLU) with GPT-2 and RoBERTa, respectively. We show that on almost every GLUE task ROSA outperforms LoRA by a significant margin, while also outperforming LoRA on NLG tasks. Our code is available at https://github.com/rosa-paper/rosa

Towards Neural Scaling Laws for Foundation Models on Temporal Graphs

The field of temporal graph learning aims to learn from evolving network data to forecast future interactions. Given a collection of observed temporal graphs, is it possible to predict the evolution of an unseen network from the same domain? To answer this question, we first present the Temporal Graph Scaling (TGS) dataset, a large collection of temporal graphs consisting of eighty-four ERC20 token transaction networks collected from 2017 to 2023. Next, we evaluate the transferability of Temporal Graph Neural Networks (TGNNs) for the temporal graph property prediction task by pre-training on a collection of up to sixty-four token transaction networks and then evaluating the downstream performance on twenty unseen token networks. We find that the neural scaling law observed in NLP and Computer Vision also applies in temporal graph learning, where pre-training on greater number of networks leads to improved downstream performance. To the best of our knowledge, this is the first empirical demonstration of the transferability of temporal graphs learning. On downstream token networks, the largest pre-trained model outperforms single model TGNNs on thirteen unseen test networks. Therefore, we believe that this is a promising first step towards building foundation models for temporal graphs.

TGB 2.0: A Benchmark for Learning on Temporal Knowledge Graphs and Heterogeneous Graphs

Multi-relational temporal graphs are powerful tools for modeling real-world data, capturing the evolving and interconnected nature of entities over time. Recently, many novel models are proposed for ML on such graphs intensifying the need for robust evaluation and standardized benchmark datasets. However, the availability of such resources remains scarce and evaluation faces added complexity due to reproducibility issues in experimental protocols. To address these challenges, we introduce Temporal Graph Benchmark 2.0 (TGB 2.0), a novel benchmarking framework tailored for evaluating methods for predicting future links on Temporal Knowledge Graphs and Temporal Heterogeneous Graphs with a focus on large-scale datasets, extending the Temporal Graph Benchmark. TGB 2.0 facilitates comprehensive evaluations by presenting eight novel datasets spanning five domains with up to 53 million edges. TGB 2.0 datasets are significantly larger than existing datasets in terms of number of nodes, edges, or timestamps. In addition, TGB 2.0 provides a reproducible and realistic evaluation pipeline for multi-relational temporal graphs. Through extensive experimentation, we observe that 1) leveraging edge-type information is crucial to obtain high performance, 2) simple heuristic baselines are often competitive with more complex methods, 3) most methods fail to run on our largest datasets, highlighting the need for research on more scalable methods.

A Tensor Decomposition Perspective on Second-order RNNs

Second-order Recurrent Neural Networks (2RNNs) extend RNNs by leveraging second-order interactions for sequence modelling. These models are provably more expressive than their first-order counterparts and have connections to well-studied models from formal language theory. However, their large parameter tensor makes computations intractable. To circumvent this issue, one approach known as MIRNN consists in limiting the type of interactions used by the model. Another is to leverage tensor decomposition to diminish the parameter count. In this work, we study the model resulting from parameterizing 2RNNs using the CP decomposition, which we call CPRNN. Intuitively, the rank of the decomposition should reduce expressivity. We analyze how rank and hidden size affect model capacity and show the relationships between RNNs, 2RNNs, MIRNNs, and CPRNNs based on these parameters. We support these results empirically with experiments on the Penn Treebank dataset which demonstrate that, with a fixed parameter budget, CPRNNs outperforms RNNs, 2RNNs, and MIRNNs with the right choice of rank and hidden size.

Simulating Weighted Automata over Sequences and Trees with Transformers

Transformers are ubiquitous models in the natural language processing (NLP) community and have shown impressive empirical successes in the past few years. However, little is understood about how they reason and the limits of their computational capabilities. These models do not process data sequentially, and yet outperform sequential neural models such as RNNs. Recent work has shown that these models can compactly simulate the sequential reasoning abilities of deterministic finite automata (DFAs). This leads to the following question: can transformers simulate the reasoning of more complex finite state machines? In this work, we show that transformers can simulate weighted finite automata (WFAs), a class of models which subsumes DFAs, as well as weighted tree automata (WTA), a generalization of weighted automata to tree structured inputs. We prove these claims formally and provide upper bounds on the sizes of the transformer models needed as a function of the number of states the target automata. Empirically, we perform synthetic experiments showing that transformers are able to learn these compact solutions via standard gradient-based training.

Generative Learning of Continuous Data by Tensor Networks

Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable features arising from their quantum-inspired nature, tensor network generative models have previously been largely restricted to binary or categorical data, limiting their utility in real-world modeling problems. We overcome this by introducing a new family of tensor network generative models for continuous data, which are capable of learning from distributions containing continuous random variables. We develop our method in the setting of matrix product states, first deriving a universal expressivity theorem proving the ability of this model family to approximate any reasonably smooth probability density function with arbitrary precision. We then benchmark the performance of this model on several synthetic and real-world datasets, finding that the model learns and generalizes well on distributions of continuous and discrete variables. We develop methods for modeling different data domains, and introduce a trainable compression layer which is found to increase model performance given limited memory or computational resources. Overall, our methods give important theoretical and empirical evidence of the efficacy of quantum-inspired methods for the rapidly growing field of generative learning.

Towards Foundational Models for Molecular Learning on Large-Scale Multi-Task Datasets

Recently, pre-trained foundation models have enabled significant advancements in multiple fields. In molecular machine learning, however, where datasets are often hand-curated, and hence typically small, the lack of datasets with labeled features, and codebases to manage those datasets, has hindered the development of foundation models. In this work, we present seven novel datasets categorized by size into three distinct categories: ToyMix, LargeMix and UltraLarge. These datasets push the boundaries in both the scale and the diversity of supervised labels for molecular learning. They cover nearly 100 million molecules and over 3000 sparsely defined tasks, totaling more than 13 billion individual labels of both quantum and biological nature. In comparison, our datasets contain 300 times more data points than the widely used OGB-LSC PCQM4Mv2 dataset, and 13 times more than the quantum-only QM1B dataset. In addition, to support the development of foundational models based on our proposed datasets, we present the Graphium graph machine learning library which simplifies the process of building and training molecular machine learning models for multi-task and multi-level molecular datasets. Finally, we present a range of baseline results as a starting point of multi-task and multi-level training on these datasets. Empirically, we observe that performance on low-resource biological datasets show improvement by also training on large amounts of quantum data. This indicates that there may be potential in multi-task and multi-level training of a foundation model and fine-tuning it to resource-constrained downstream tasks.