Daily Papers

Catastrophic forgetting remains a major challenge when adapting large language models (LLMs) to new tasks or domains. Conventional fine-tuning often overwrites existing knowledge, causing performance degradation on original tasks. We introduce Superposition in Transformers, a novel architecture that leverages autoencoders to superimpose the hidden representations of a base model and a fine-tuned model within a shared parameter space. By using B-spline-based blending coefficients and autoencoders that adaptively reconstruct hidden states based on the input data distribution, our method effectively mitigates catastrophic forgetting and enables a new paradigm of "in-model" superposition. This approach preserves original model capabilities while allowing compact domain-specific expertise to be added, and it supports dynamic switching between model states during inference.

We show how to "compile" human-readable programs into standard decoder-only transformer models. Our compiler, Tracr, generates models with known structure. This structure can be used to design experiments. For example, we use it to study "superposition" in transformers that execute multi-step algorithms. Additionally, the known structure of Tracr-compiled models can serve as ground-truth for evaluating interpretability methods. Commonly, because the "programs" learned by transformers are unknown it is unclear whether an interpretation succeeded. We demonstrate our approach by implementing and examining programs including computing token frequencies, sorting, and parenthesis checking. We provide an open-source implementation of Tracr at https://github.com/google-deepmind/tracr.

Large Language Models (LLMs) have demonstrated remarkable performance in many applications, including challenging reasoning problems via chain-of-thoughts (CoTs) techniques that generate ``thinking tokens'' before answering the questions. While existing theoretical works demonstrate that CoTs with discrete tokens boost the capability of LLMs, recent work on continuous CoTs lacks a theoretical understanding of why it outperforms discrete counterparts in various reasoning tasks such as directed graph reachability, a fundamental graph reasoning problem that includes many practical domain applications as special cases. In this paper, we prove that a two-layer transformer with D steps of continuous CoTs can solve the directed graph reachability problem, where D is the diameter of the graph, while the best known result of constant-depth transformers with discrete CoTs requires O(n^2) decoding steps where n is the number of vertices (D<n). In our construction, each continuous thought vector is a superposition state that encodes multiple search frontiers simultaneously (i.e., parallel breadth-first search (BFS)), while discrete CoTs must choose a single path sampled from the superposition state, which leads to sequential search that requires many more steps and may be trapped into local solutions. We also performed extensive experiments to verify that our theoretical construction aligns well with the empirical solution obtained via training dynamics. Notably, encoding of multiple search frontiers as a superposition state automatically emerges in training continuous CoTs, without explicit supervision to guide the model to explore multiple paths simultaneously.

Large Language Models (LLMs) have demonstrated remarkable in-context learning (ICL) capabilities. In this study, we explore a surprising phenomenon related to ICL: LLMs can perform multiple, computationally distinct ICL tasks simultaneously, during a single inference call, a capability we term "task superposition". We provide empirical evidence of this phenomenon across various LLM families and scales and show that this phenomenon emerges even if we train the model to in-context learn one task at a time. We offer theoretical explanations that this capability is well within the expressive power of transformers. We also explore how LLMs internally compose task vectors during superposition. Furthermore, we show that larger models can solve more ICL tasks in parallel, and better calibrate their output distribution. Our findings offer insights into the latent capabilities of LLMs, further substantiate the perspective of "LLMs as superposition of simulators", and raise questions about the mechanisms enabling simultaneous task execution.