Understanding the expressive power of transformers has recently attracted attention, as it offers insights into their abilities and limitations. Many studies analyze unique hard attention transformers, where attention selects a single position that maximizes the attention scores. When multiple positions achieve the maximum score, either the rightmost or the leftmost of those is chosen. In this paper, we highlight the importance of this seeming triviality. Recently, finite-precision transformers with both leftmost- and rightmost-hard attention were shown to be equivalent to Linear Temporal Logic (LTL). We show that this no longer holds with only leftmost-hard attention -- in that case, they correspond to a \emph{strictly weaker} fragment of LTL. Furthermore, we show that models with leftmost-hard attention are equivalent to \emph{soft} attention, suggesting they may better approximate real-world transformers than right-attention models. These findings refine the landscape of transformer expressivity and underscore the role of attention directionality.

Large language models (LLMs) exhibit an intriguing ability to learn a novel task from in-context examples presented in a demonstration, termed in-context learning (ICL). Understandably, a swath of research has been dedicated to uncovering the theories underpinning ICL. One popular hypothesis explains ICL by task selection. LLMs identify the task based on the demonstration and generalize it to the prompt. Another popular hypothesis is that ICL is a form of meta-learning, i.e., the models learn a learning algorithm at pre-training time and apply it to the demonstration. Finally, a third hypothesis argues that LLMs use the demonstration to select a composition of tasks learned during pre-training to perform ICL. In this paper, we empirically explore these three hypotheses that explain LLMs' ability to learn in context with a suite of experiments derived from common text classification tasks. We invalidate the first two hypotheses with counterexamples and provide evidence in support of the last hypothesis. Our results suggest an LLM could learn a novel task in context via composing tasks learned during pre-training.

Natural languages are believed to be (mildly) context-sensitive. Despite underpinning remarkably capable large language models, transformers are unable to model many context-free language tasks. In an attempt to address this limitation in the modeling power of transformer-based language models, we propose augmenting them with a differentiable, stack-based attention mechanism. Our stack-based attention mechanism can be incorporated into any transformer-based language model and adds a level of interpretability to the model. We show that the addition of our stack-based attention mechanism enables the transformer to model some, but not all, deterministic context-free languages.

Recent work has shown that language models (LMs) have strong multi-step (i.e., procedural) reasoning capabilities. However, it is unclear whether LMs perform these tasks by cheating with answers memorized from pretraining corpus, or, via a multi-step reasoning mechanism. In this paper, we try to answer this question by exploring a mechanistic interpretation of LMs for multi-step reasoning tasks. Concretely, we hypothesize that the LM implicitly embeds a reasoning tree resembling the correct reasoning process within it. We test this hypothesis by introducing a new probing approach (called MechanisticProbe) that recovers the reasoning tree from the model's attention patterns. We use our probe to analyze two LMs: GPT-2 on a synthetic task (k-th smallest element), and LLaMA on two simple language-based reasoning tasks (ProofWriter & AI2 Reasoning Challenge). We show that MechanisticProbe is able to detect the information of the reasoning tree from the model's attentions for most examples, suggesting that the LM indeed is going through a process of multi-step reasoning within its architecture in many cases.

Multi-head attention, a collection of several attention mechanisms that independently attend to different parts of the input, is the key ingredient in the Transformer. Recent work has shown, however, that a large proportion of the heads in a Transformer's multi-head attention mechanism can be safely pruned away without significantly harming the performance of the model; such pruning leads to models that are noticeably smaller and faster in practice. Our work introduces a new head pruning technique that we term differentiable subset pruning. Intuitively, our method learns per-head importance variables and then enforces a user-specified hard constraint on the number of unpruned heads. The importance variables are learned via stochastic gradient descent. We conduct experiments on natural language inference and machine translation; we show that differentiable subset pruning performs comparably or better than previous works while offering precise control of the sparsity level.