The Impossibility of Inverse Permutation Learning in Transformer Models

• URL: http://arxiv.org/abs/2509.24125v1
• Date: Sun, 28 Sep 2025 23:48:11 GMT
• Title: The Impossibility of Inverse Permutation Learning in Transformer Models
• Authors: Rohan Alur, Chris Hays, Manish Raghavan, Devavrat Shah,
• Abstract summary: We study the problem of inverse permutation learning in decoder-only transformers.<n>We show that an arbitrary depth, decoder-only transformer cannot learn this task.<n>We conjecture that this may suggest an alternative mechanism by which chain-of-thought prompting or, more generally, intermediate thinking'' tokens can enable reasoning.
• Score: 15.463427361201914
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this technical note, we study the problem of inverse permutation learning in decoder-only transformers. Given a permutation and a string to which that permutation has been applied, the model is tasked with producing the original (``canonical'') string. We argue that this task models a natural robustness property across a variety of reasoning tasks, including long-context retrieval, multiple choice QA and in-context learning. Our primary contribution is an impossibility result: we show that an arbitrary depth, decoder-only transformer cannot learn this task. This result concerns the expressive capacity of decoder-only transformer models and is agnostic to training dynamics or sample complexity. We give a pair of alternative constructions under which inverse permutation learning is feasible. The first of these highlights the fundamental role of the causal attention mask, and reveals a gap between the expressivity of encoder-decoder transformers and the more popular decoder-only architecture. The latter result is more surprising: we show that simply padding the input with ``scratch tokens" yields a construction under which inverse permutation learning is possible. We conjecture that this may suggest an alternative mechanism by which chain-of-thought prompting or, more generally, intermediate ``thinking'' tokens can enable reasoning in large language models, even when these tokens encode no meaningful semantic information (e.g., the results of intermediate computations).

Related papers

• On the Existence of Universal Simulators of Attention [17.01811978811789]
  We present solutions to identically replicate attention outputs and the underlying elementary matrix and activation operations via RASP.<n>Our proofs, for the first time, show the existence of an algorithmically achievable data-agnostic solution, previously known to be approximated only by learning.
  arXiv  Detail & Related papers  (2025-06-23T15:15:25Z)
• Algorithmic Capabilities of Random Transformers [49.73113518329544]
  We investigate what functions can be learned by randomly transformers in which only the embedding layers are optimized. We find that these random transformers can perform a wide range of meaningful algorithmic tasks. Our results indicate that some algorithmic capabilities are present in transformers even before these models are trained.
  arXiv  Detail & Related papers  (2024-10-06T06:04:23Z)
• Transformers need glasses! Information over-squashing in language tasks [18.81066657470662]
  We study how information propagates in decoder-only Transformers. We show that certain sequences of inputs to the Transformer can yield arbitrarily close representations in the final token. We also show that decoder-only Transformer language models can lose sensitivity to specific tokens in the input.
  arXiv  Detail & Related papers  (2024-06-06T17:14:44Z)
• GEC-DePenD: Non-Autoregressive Grammatical Error Correction with Decoupled Permutation and Decoding [52.14832976759585]
  Grammatical error correction (GEC) is an important NLP task that is usually solved with autoregressive sequence-to-sequence models. We propose a novel non-autoregressive approach to GEC that decouples the architecture into a permutation network. We show that the resulting network improves over previously known non-autoregressive methods for GEC.
  arXiv  Detail & Related papers  (2023-11-14T14:24:36Z)
• The Expressive Power of Transformers with Chain of Thought [29.839710738657203]
  In practice, transformers can be improved by allowing them to use a "chain of thought" or "scratchpad" We show that the answer is yes, but the amount of increase depends crucially on the amount of intermediate generation. Our results also imply that linear steps keep transformer decoders within context-sensitive languages.
  arXiv  Detail & Related papers  (2023-10-11T22:35:18Z)
• Mapping of attention mechanisms to a generalized Potts model [50.91742043564049]
  We show that training a neural network is exactly equivalent to solving the inverse Potts problem by the so-called pseudo-likelihood method. We also compute the generalization error of self-attention in a model scenario analytically using the replica method.
  arXiv  Detail & Related papers  (2023-04-14T16:32:56Z)
• Discovering Non-monotonic Autoregressive Orderings with Variational Inference [67.27561153666211]
  We develop an unsupervised parallelizable learner that discovers high-quality generation orders purely from training data. We implement the encoder as a Transformer with non-causal attention that outputs permutations in one forward pass. Empirical results in language modeling tasks demonstrate that our method is context-aware and discovers orderings that are competitive with or even better than fixed orders.
  arXiv  Detail & Related papers  (2021-10-27T16:08:09Z)
• Iterative Decoding for Compositional Generalization in Transformers [5.269770493488338]
  In sequence-to-sequence learning, transformers are often unable to predict correct outputs for even marginally longer examples. This paper introduces iterative decoding, an alternative to seq2seq learning. We show that transfomers trained via iterative decoding outperform their seq2seq counterparts on the PCFG dataset.
  arXiv  Detail & Related papers  (2021-10-08T14:52:25Z)
• Thinking Like Transformers [64.96770952820691]
  We propose a computational model for the transformer-encoder in the form of a programming language. We show how RASP can be used to program solutions to tasks that could conceivably be learned by a Transformer. We provide RASP programs for histograms, sorting, and Dyck-languages.
  arXiv  Detail & Related papers  (2021-06-13T13:04:46Z)
• Autoencoding Variational Autoencoder [56.05008520271406]
  We study the implications of this behaviour on the learned representations and also the consequences of fixing it by introducing a notion of self consistency. We show that encoders trained with our self-consistency approach lead to representations that are robust (insensitive) to perturbations in the input introduced by adversarial attacks.
  arXiv  Detail & Related papers  (2020-12-07T14:16:14Z)
• Category-Learning with Context-Augmented Autoencoder [63.05016513788047]
  Finding an interpretable non-redundant representation of real-world data is one of the key problems in Machine Learning. We propose a novel method of using data augmentations when training autoencoders. We train a Variational Autoencoder in such a way, that it makes transformation outcome predictable by auxiliary network.
  arXiv  Detail & Related papers  (2020-10-10T14:04:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.