Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed such structures more accurately, these methods are confined under the message-passing paradigm, making the models vulnerable against side-effects such as oversmoothing and oversquashing. More recent work have proposed global attention-based graph Transformers that can easily model long-range interactions, but their extensions towards non-Euclidean geometry are yet unexplored. To bridge this gap, we propose Fully Product-Stereographic Transformer, a generalization of Transformers towards operating entirely on the product of constant curvature spaces. When combined with tokenized graph Transformers, our model can learn the curvature appropriate for the input graph in an end-to-end fashion, without the need of additional tuning on different curvature initializations. We also provide a kernelized approach to non-Euclidean attention, which enables our model to run in time and memory cost linear to the number of nodes and edges while respecting the underlying geometry. Experiments on graph reconstruction and node classification demonstrate the benefits of generalizing Transformers to the non-Euclidean domain.Comment: 19 pages, 7 figure

Discriminator-Guided Multi-step Reasoning with Language Models

In the context of multi-step reasoning, language models (LMs) probabilities are often miscalibrated -- solutions with high probabilities are not always correct. Therefore, greedy decoding, which is the standard decoding method for reasoning tasks, often yields incorrect solutions. In addition, methods such as self-consistency and verifiers rely on sampling from the LM distribution and do not tackle the underlying issue. To address this, we introduce Guiding Multi-step ReAsoning with a CorrectnEss Discriminator (GRACE), a stepwise decoding approach that nudges the model towards producing correct reasoning steps. GRACE employs a discriminator model, which is trained to differentiate correct steps from invalid ones, to adjust decoding preferences based on the correctness of each reasoning step. Importantly, GRACE does not require fine-tuning or re-training the LMs. When compared with conventional decoding strategies over four popular math reasoning benchmarks, GRACE exhibits significant improvements in both final answer accuracy and step correctness, outperforming both greedy decoding and self-consistency.\footnote{Our code can be found at \url{https://github.com/mukhal/grace.}}Comment: 19 pages, 7 figures, and 8 table

Exploring Demonstration Ensembling for In-context Learning

In-context learning (ICL) operates by showing language models (LMs) examples of input-output pairs for a given task, i.e., demonstrations. The standard approach for ICL is to prompt the LM with concatenated demonstrations followed by the test input. This approach suffers from some issues. First, concatenation offers almost no control over the contribution of each demo to the model prediction. This can be sub-optimal when some demonstrations are irrelevant to the test example. Second, due to the input length limit of some transformer models, it might be infeasible to fit many examples into the context, especially when dealing with long-input tasks. In this work, we explore Demonstration Ensembling (DENSE) as an alternative to simple concatenation. DENSE predicts outputs using subsets (i.e., buckets) of the demonstrations and then combines the output probabilities resulting from each subset to produce the final prediction. We study different ensembling methods using GPT-j and experiment on 12 language tasks. Our experiments show weighted max ensembling to outperform vanilla concatenation by as large as 2.4 average points. Code available at https://github.com/mukhal/icl-ensembling.Comment: Published at ME-FoMo workshop at ICLR 2023. Arxiv version includes evaluation on 5 more task

Merging Generated and Retrieved Knowledge for Open-Domain QA

Open-domain question answering (QA) systems are often built with retrieval modules. However, retrieving passages from a given source is known to suffer from insufficient knowledge coverage. Alternatively, prompting large language models (LLMs) to generate contextual passages based on their parametric knowledge has been shown to improve QA performance. Yet, LLMs tend to "hallucinate" content that conflicts with the retrieved knowledge. Based on the intuition that answers supported by both sources are more likely to be correct, we propose COMBO, a Compatibility-Oriented knowledge Merging for Better Open-domain QA framework, to effectively leverage the two sources of information. Concretely, we match LLM-generated passages with retrieved counterparts into compatible pairs, based on discriminators trained with silver compatibility labels. Then a Fusion-in-Decoder-based reader model handles passage pairs to arrive at the final answer. Experiments show that COMBO outperforms competitive baselines on three out of four tested open-domain QA benchmarks. Further analysis reveals that our proposed framework demonstrates greater efficacy in scenarios with a higher degree of knowledge conflicts.Comment: EMNLP 2023 - Camera Read

Transformers meet Stochastic Block Models: Attention with Data-Adaptive Sparsity and Cost

To overcome the quadratic cost of self-attention, recent works have proposed various sparse attention modules, most of which fall under one of two groups: 1) sparse attention under a hand-crafted patterns and 2) full attention followed by a sparse variant of softmax such as $\alpha$-entmax. Unfortunately, the first group lacks adaptability to data while the second still requires quadratic cost in training. In this work, we propose SBM-Transformer, a model that resolves both problems by endowing each attention head with a mixed-membership Stochastic Block Model (SBM). Then, each attention head data-adaptively samples a bipartite graph, the adjacency of which is used as an attention mask for each input. During backpropagation, a straight-through estimator is used to flow gradients beyond the discrete sampling step and adjust the probabilities of sampled edges based on the predictive loss. The forward and backward cost are thus linear to the number of edges, which each attention head can also choose flexibly based on the input. By assessing the distribution of graphs, we theoretically show that SBM-Transformer is a universal approximator for arbitrary sequence-to-sequence functions in expectation. Empirical evaluations under the LRA and GLUE benchmarks demonstrate that our model outperforms previous efficient variants as well as the original Transformer with full attention. Our implementation can be found in https://github.com/sc782/SBM-Transformer .Comment: 19 pages, 8 figure

Grouping-matrix based Graph Pooling with Adaptive Number of Clusters

Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional methods ask users to specify an appropriate number of clusters as a hyperparameter, then assume that all input graphs share the same number of clusters. In inductive settings where the number of clusters can vary, however, the model should be able to represent this variation in its pooling layers in order to learn suitable clusters. Thus we propose GMPool, a novel differentiable graph pooling architecture that automatically determines the appropriate number of clusters based on the input data. The main intuition involves a grouping matrix defined as a quadratic form of the pooling operator, which induces use of binary classification probabilities of pairwise combinations of nodes. GMPool obtains the pooling operator by first computing the grouping matrix, then decomposing it. Extensive evaluations on molecular property prediction tasks demonstrate that our method outperforms conventional methods.Comment: 10 pages, 3 figure

From Heuristic to Analytic: Cognitively Motivated Strategies for Coherent Physical Commonsense Reasoning

Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify decisions with formalized, coherent reasoning chains, but this challenge remains under-explored. Cognitive psychology theorizes that humans are capable of utilizing fast and intuitive heuristic thinking to make decisions based on past experience, then rationalizing the decisions through slower and deliberative analytic reasoning. We incorporate these interlinked dual processes in fine-tuning and in-context learning with PLMs, applying them to two language understanding tasks that require coherent physical commonsense reasoning. We show that our proposed Heuristic-Analytic Reasoning (HAR) strategies drastically improve the coherence of rationalizations for model decisions, yielding state-of-the-art results on Tiered Reasoning for Intuitive Physics (TRIP). We also find that this improved coherence is a direct result of more faithful attention to relevant language context in each step of reasoning. Our findings suggest that human-like reasoning strategies can effectively improve the coherence and reliability of PLM reasoning.Comment: EMNLP 2023 Main Conferenc