Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations?In an attempt to demystify transformer LLMs, we investigate the limits of these models across three representative compositional tasks---multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that transformer LLMs solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how autoregressive generations' performance can rapidly decay with increased task complexity.

Many real-world problems are compositional - solving them requires completing interdependent sub-tasks, either in series or in parallel, that can be represented as a dependency graph. Deep reinforcement learning (RL) agents often struggle to learn such complex tasks due to the long time horizons and sparse rewards. To address this problem, we present Compositional Design of Environments (CoDE), which trains a Generator agent to automatically build a series of compositional tasks tailored to the RL agent's current skill level. This automatic curriculum not only enables the agent to learn more complex tasks than it could have otherwise, but also selects tasks where the agent's performance is weak, enhancing its robustness and ability to generalize zero-shot to unseen tasks at test-time. We analyze why current environment generation techniques are insufficient for the problem of generating compositional tasks, and propose a new algorithm that addresses these issues. Our results assess learning and generalization across multiple compositional tasks, including the real-world problem of learning to navigate and interact with web pages. We learn to generate environments composed of multiple pages or rooms, and train RL agents capable of completing wide-range of complex tasks in those environments. We contribute two new benchmark frameworks for generating compositional tasks, compositional MiniGrid and gMiniWoB for web navigation. CoDE yields 4x higher success rate than the strongest baseline, and demonstrates strong performance of real websites learned on 3500 primitive tasks.

Despite impressive capabilities, LLMs' successes often rely on pattern-matching behaviors, yet these are also linked to OOD generalization failures in compositional tasks. However, behavioral studies commonly employ task setups that allow multiple generalization sources (e.g., algebraic invariances, structural repetition), obscuring a precise and testable account of how well LLMs perform generalization through pattern matching and their limitations. To address this ambiguity, we first formalize pattern matching as functional equivalence, i.e., identifying pairs of subsequences of inputs that consistently lead to identical results when the rest of the input is held constant. Then, we systematically study how decoder-only Transformer and Mamba behave in controlled tasks with compositional structures that isolate this mechanism. Our formalism yields predictive and quantitative insights: (1) Instance-wise success of pattern matching is well predicted by the number of contexts witnessing the relevant functional equivalence. (2) We prove a tight sample complexity bound of learning a two-hop structure by identifying the exponent of the data scaling law for perfect in-domain generalization. Our empirical results align with the theoretical prediction, under 20x parameter scaling and across architectures. (3) Path ambiguity is a structural barrier: when a variable influences the output via multiple paths, models fail to form unified intermediate state representations, impairing accuracy and interpretability. (4) Chain-of-Thought reduces data requirements yet does not resolve path ambiguity. Hence, we provide a predictive, falsifiable boundary for pattern matching and a foundational diagnostic for disentangling mixed generalization mechanisms.