Recent theoretical results show transformers cannot express sequential reasoning problems over long input lengths, intuitively because their computational depth is bounded. However, prior work treats the depth as a constant, leaving it unclear to what degree bounded depth may suffice for solving problems over short inputs, or how increasing the transformer's depth affects its expressive power. We address these questions by analyzing the expressive power of transformers whose depth can grow minimally with context length $n$. We show even highly uniform transformers with depth $\Theta(\log n)$ can express two important problems: recognizing regular languages, which captures state tracking abilities, and graph connectivity, which underlies multi-step reasoning. Notably, both of these problems cannot be expressed by fixed-depth transformers under standard complexity conjectures, demonstrating the expressivity benefit of growing depth. Moreover, our theory quantitatively predicts how depth must grow with input length to express these problems, showing that depth scaling is more efficient than scaling width or chain-of-thought steps. Empirically, we find our theoretical depth requirements for regular language recognition match the practical depth requirements of transformers remarkably well. Thus, our results clarify precisely how depth affects transformers' reasoning capabilities, providing potential practical insights for designing models that are better at sequential reasoning.

We investigate the logical reasoning capabilities of large language models (LLMs) and their scalability in complex non-monotonic reasoning. To this end, we introduce ZebraLogic, a comprehensive evaluation framework for assessing LLM reasoning performance on logic grid puzzles derived from constraint satisfaction problems (CSPs). ZebraLogic enables the generation of puzzles with controllable and quantifiable complexity, facilitating a systematic study of the scaling limits of models such as Llama, o1 models, and DeepSeek-R1. By encompassing a broad range of search space complexities and diverse logical constraints, ZebraLogic provides a structured environment to evaluate reasoning under increasing difficulty. Our results reveal a significant decline in accuracy as problem complexity grows -- a phenomenon we term the curse of complexity. This limitation persists even with larger models and increased inference-time computation, suggesting inherent constraints in current LLM reasoning capabilities. Additionally, we explore strategies to enhance logical reasoning, including Best-of-N sampling, backtracking mechanisms, and self-verification prompts. Our findings offer critical insights into the scalability of LLM reasoning, highlight fundamental limitations, and outline potential directions for improvement.

Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss, understanding the differences between these recent proposals, as well as developing new DPA loss functions, remains difficult given the lack of a technical and conceptual framework for reasoning about the underlying semantics of these algorithms. In this paper, we attempt to remedy this by formalizing DPA losses in terms of discrete reasoning problems. Specifically, we ask: Given an existing DPA loss, can we systematically derive a symbolic expression that characterizes its semantics? How do the semantics of two losses relate to each other? We propose a novel formalism for characterizing preference losses for single model and reference model based approaches, and identify symbolic forms for a number of commonly used DPA variants. Further, we show how this formal view of preference learning sheds new light on both the size and structure of the DPA loss landscape, making it possible to not only rigorously characterize the relationships between recent loss proposals but also to systematically explore the landscape and derive new loss functions from first principles. We hope our framework and findings will help provide useful guidance to those working on human AI alignment.

Can the rapid advances in code generation, function calling, and data analysis using large language models (LLMs) help automate the search and verification of hypotheses purely from a set of provided datasets? To evaluate this question, we present DiscoveryBench, the first comprehensive benchmark that formalizes the multi-step process of data-driven discovery. The benchmark is designed to systematically assess current model capabilities in discovery tasks and provide a useful resource for improving them. Our benchmark contains 264 tasks collected across 6 diverse domains, such as sociology and engineering, by manually deriving discovery workflows from published papers to approximate the real-world challenges faced by researchers, where each task is defined by a dataset, its metadata, and a discovery goal in natural language. We additionally provide 903 synthetic tasks to conduct controlled evaluations across task complexity. Furthermore, our structured formalism of data-driven discovery enables a facet-based evaluation that provides useful insights into different failure modes. We evaluate several popular LLM-based reasoning frameworks using both open and closed LLMs as baselines on DiscoveryBench and find that even the best system scores only 25%. Our benchmark, thus, illustrates the challenges in autonomous data-driven discovery and serves as a valuable resource for the community to make progress.

State-space models (SSMs) have emerged as a potential alternative architecture for building large language models (LLMs) compared to the previously ubiquitous transformer architecture. One theoretical weakness of transformers is that they cannot express certain kinds of sequential computation and state tracking (Merrill & Sabharwal, 2023), which SSMs are explicitly designed to address via their close architectural similarity to recurrent neural networks (RNNs). But do SSMs truly have an advantage (over transformers) in expressive power for state tracking? Surprisingly, the answer is no. Our analysis reveals that the expressive power of SSMs is limited very similarly to transformers: SSMs cannot express computation outside the complexity class $\mathsf{TC}^0$. In particular, this means they cannot solve simple state-tracking problems like permutation composition. It follows that SSMs are provably unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. To supplement our formal analysis, we report experiments showing that Mamba-style SSMs indeed struggle with state tracking. Thus, despite its recurrent formulation, the "state" in an SSM is an illusion: SSMs have similar expressiveness limitations to non-recurrent models like transformers, which may fundamentally limit their ability to solve real-world state-tracking problems.

We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language designed to help people "think like transformers," as an intermediate representation. We extend the existing Boolean variant B-RASP to sequence-to-sequence functions and show that it computes exactly the first-order rational functions (such as string rotation). Then, we introduce two new extensions. B-RASP[pos] enables calculations on positions (such as copying the first half of a string) and contains all first-order regular functions. S-RASP adds prefix sum, which enables additional arithmetic operations (such as squaring a string) and contains all first-order polyregular functions. Finally, we show that masked average-hard attention transformers can simulate S-RASP. A corollary of our results is a new proof that transformer decoders are Turing-complete.

With the accumulation of data at an unprecedented rate, its potential to fuel scientific discovery is growing exponentially. This position paper urges the Machine Learning (ML) community to exploit the capabilities of large generative models (LGMs) to develop automated systems for end-to-end data-driven discovery -- a paradigm encompassing the search and verification of hypotheses purely from a set of provided datasets, without the need for additional data collection or physical experiments. We first outline several desiderata for an ideal data-driven discovery system. Then, through DATAVOYAGER, a proof-of-concept utilizing GPT-4, we demonstrate how LGMs fulfill several of these desiderata -- a feat previously unattainable -- while also highlighting important limitations in the current system that open up opportunities for novel ML research. We contend that achieving accurate, reliable, and robust end-to-end discovery systems solely through the current capabilities of LGMs is challenging. We instead advocate for fail-proof tool integration, along with active user moderation through feedback mechanisms, to foster data-driven scientific discoveries with efficiency and reproducibility.

Recent works have showcased the ability of LLMs to embody diverse personas in their responses, exemplified by prompts like 'You are Yoda. Explain the Theory of Relativity.' While this ability allows personalization of LLMs and enables human behavior simulation, its effect on LLMs' capabilities remains unclear. To fill this gap, we present the first extensive study of the unintended side-effects of persona assignment on the ability of LLMs to perform basic reasoning tasks. Our study covers 24 reasoning datasets, 4 LLMs, and 19 diverse personas (e.g. an Asian person) spanning 5 socio-demographic groups. Our experiments unveil that LLMs harbor deep rooted bias against various socio-demographics underneath a veneer of fairness. While they overtly reject stereotypes when explicitly asked ('Are Black people less skilled at mathematics?'), they manifest stereotypical and erroneous presumptions when asked to answer questions while adopting a persona. These can be observed as abstentions in responses, e.g., 'As a Black person, I can't answer this question as it requires math knowledge', and generally result in a substantial performance drop. Our experiments with ChatGPT-3.5 show that this bias is ubiquitous - 80% of our personas demonstrate bias; it is significant - some datasets show performance drops of 70%+; and can be especially harmful for certain groups - some personas suffer statistically significant drops on 80%+ of the datasets. Overall, all 4 LLMs exhibit this bias to varying extents, with GPT-4-Turbo showing the least but still a problematic amount of bias (evident in 42% of the personas). Further analysis shows that these persona-induced errors can be hard-to-discern and hard-to-avoid. Our findings serve as a cautionary tale that the practice of assigning personas to LLMs - a trend on the rise - can surface their deep-rooted biases and have unforeseeable and detrimental side-effects.

In-context learning (ICL) is an appealing approach for semantic parsing due to its few-shot nature and improved generalization. However, learning to parse to rare domain-specific languages (DSLs) from just a few demonstrations is challenging, limiting the performance of even the most capable LLMs. In this work, we improve the effectiveness of ICL for semantic parsing by (1) using general-purpose programming languages such as Python instead of DSLs, and (2) augmenting prompts with a structured domain description that includes, e.g., the available classes and functions. We show that both these changes significantly improve accuracy across three popular datasets. Combined, they lead to dramatic improvements (e.g. 7.9% to 66.5% on SMCalFlow compositional split), nearly closing the performance gap between easier i.i.d.\ and harder compositional splits when used with a strong model, and reducing the need for a large number of demonstrations. We find that the resemblance of the target parse language to general-purpose code is a more important factor than the language's popularity in pre-training corpora. Our findings provide an improved methodology for building semantic parsers in the modern context of ICL with LLMs.

Large Language Models (LLMs) are increasingly being used for interactive decision-making tasks requiring planning and adapting to the environment. Recent works employ LLMs-as-agents in broadly two ways: iteratively determining the next action (iterative executors) or generating plans and executing sub-tasks using LLMs (plan-and-execute). However, these methods struggle with task complexity, as the inability to execute any sub-task may lead to task failure. To address these shortcomings, we introduce As-Needed Decomposition and Planning for complex Tasks (ADaPT), an approach that explicitly plans and decomposes complex sub-tasks as-needed, i.e., when the LLM is unable to execute them. ADaPT recursively decomposes sub-tasks to adapt to both task complexity and LLM capability. Our results demonstrate that ADaPT substantially outperforms established strong baselines, achieving success rates up to 28.3% higher in ALFWorld, 27% in WebShop, and 33% in TextCraft -- a novel compositional dataset that we introduce. Through extensive analysis, we illustrate the importance of multilevel decomposition and establish that ADaPT dynamically adjusts to the capabilities of the executor LLM as well as to task complexity.