Challenge: Existing studies have shown that word embeddings do not occupy a narrow cone, but rather drift in common directions.
Approach: They show that anisotropy can be restored using a simple transformation of word embeddings.
Outcome: The proposed model can restore anisotropy using a simple transformation.

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Anisotropy is Not Inherent to Transformers (2024.naacl-long)

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Challenge: Existing work has shown that Transformer embeddings are anisotropic, which is called the representation degradation problem.
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Outcome: The proposed model sets show that isotropic models do not develop as previously theorized.
How to Dissect a Muppet: The Structure of Transformer Embedding Spaces (2022.tacl-1)

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Challenge: Pretrained embeddings based on the Transformer architecture have taken the NLP community by storm . a novel decomposition of Transformer output embeddables is demonstrated .
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Do Transformer Modifications Transfer Across Implementations and Applications? (2021.emnlp-main)

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Challenge: Currently, the Transformer is the de facto architecture of choice for processing sequential data.
Approach: They evaluate the Transformer architecture and its modifications in a shared experimental setting . they conjecture that performance improvements may strongly depend on implementation details .
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Transformer Grammars: Augmenting Transformer Language Models with Syntactic Inductive Biases at Scale (2022.tacl-1)

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Challenge: a novel class of Transformer language models that combine expressive power, scalability, and strong performance of Transformers and recursive syntactic compositions.
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A Meta-Learning Perspective on Transformers for Causal Language Modeling (2024.findings-acl)

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Challenge: Mechanisms of the Transformer architecture for causal language modeling are not well understood.
Approach: They propose a meta-learning view of the Transformer architecture when trained for a causal language modeling task by explicating an inner optimization process that may happen within the Transformer.
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The Shape of Learning: Anisotropy and Intrinsic Dimensions in Transformer-Based Models (2024.findings-eacl)

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Challenge: Embeddings in transformers encode vast amounts of linguistic nuances and patterns.
Approach: They investigate the anisotropy dynamics and intrinsic dimension of embeddings in transformers . they found that transformer decoders exhibit a bell-shaped anisotropie profile .
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Latent Positional Information is in the Self-Attention Variance of Transformer Language Models Without Positional Embeddings (2023.acl-short)

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Challenge: Recent research has called into question the necessity of positional embeddings in transformer language models.
Approach: They propose to discard positional embeddings in transformer language models to facilitate more efficient pretraining.
Outcome: The proposed model encodes strong positional information through shrinkage of self-attention variance.
Beyond Position: the emergence of wavelet-like properties in Transformers (2025.acl-long)

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Challenge: Despite its widespread adoption, theoretical limitations in positional encodings are resolved by developing emergent, wavelet-like processing strategies.
Approach: They propose to use Rotary Position Embeddings to develop emergent, wavelet-like properties that compensate for the positional encoding’s theoretical limitations.
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Can Transformers Learn n-gram Language Models? (2024.emnlp-main)

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Challenge: Existing work has tested transformers' ability to represent formal languages, but language models are not classifiers of strings but rather distributions over them.
Approach: They relate transformers' ability to learn random n-gram language models to ngram language model (LM) they find add- smoothing outperforms transformers on the former, while transformers perform better on the latter .
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The Hidden Space of Transformer Language Adapters (2024.acl-long)

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Challenge: Adapters are small modules trained on top of a frozen language model to adapt predictions to new target languages.
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