Challenge: Quantized models using softpick outperform softmax on standard benchmarks . softmax is widely used in statistics and especially in machine learning .
Approach: They introduce a rectified, not sum-to-one, drop-in replacement for softmax in transformer attention mechanisms that eliminates attention sink and massive activations.
Outcome: The proposed model outperforms softmax on benchmarks with lower bit precisions.

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Self-Adjust Softmax (2025.emnlp-main)

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Challenge: Usually, tokens with larger attention scores are important for the final prediction.
Approach: They propose to modify softmax(z) to z softmax and its normalized variant to improve the Transformer attention mechanism by making minor adjustments to the softmax function.
Outcome: The proposed model provides enhanced gradient properties compared to the vanilla softmax function.
Attention Sinks Are Provably Necessary in Softmax Transformers: Evidence from Trigger-Conditional Tasks (2026.acl-short)

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Challenge: Xiao et al., 2024) show that softmax models display an attention sink . he argues that normalization over a probability simplex must force attention to collapse onto a stable anchor to realize a default state.
Approach: They show that normalization over a trigger-conditional behavior *necessarily* induces a sink in softmax self-attention models.
Outcome: The proposed model can solve a task with no sink in softmax models.
Threshold Differential Attention for Sink-Free, Ultra-Sparse, and Non-Dispersive Language Modeling (2026.acl-long)

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Challenge: a strict sum-to-one constraint forces attention sinks on irrelevant tokens, while probability mass disperses as sequence lengths increase.
Approach: They propose a sink-free attention mechanism that achieves ultra-sparsity and improved robustness at longer sequence lengths without the computational overhead of projection methods.
Outcome: The proposed mechanism produces >99 % exact zeros and eliminates attention sinks while maintaining competitive performance on standard and long-context benchmarks.
Integral Transformer: Denoising Attention, Not Too Much Not Too Little (2025.emnlp-main)

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Challenge: Existing methods to reduce attention noise by integrating signals from logit distributions are prone to attention noise.
Approach: They propose a self-attention mechanism that integrates signals from the logit distribution to denoise attention.
Outcome: The proposed model outperforms vanilla, Cog, and Differential attention variants on knowledge and reasoning benchmarks.
Sparse Attention with Linear Units (2021.emnlp-main)

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Challenge: Recent studies have suggested that sparse attention mechanisms can be made more interpretable by replacing the softmax activation with its sparser variants.
Approach: They propose a method to replace softmax activation with a ReLU to achieve sparsity in attention by layer normalization with either a specialized initialization or an additional gating function.
Outcome: The proposed model is easy to implement and more efficient than previously proposed sparse attention mechanisms.
Simulating Hard Attention Using Soft Attention (2026.tacl-1)

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Challenge: a central element of hard attention is attention, which computes a weighted average of values from all unmasked positions.
Approach: They propose transformers that can simulate hard attention by using temperature scaling and positional embeddings.
Outcome: The proposed transformers can effectively focus all attention on a subset of positions.
Sparsifying Transformer Models with Trainable Representation Pooling (2022.acl-long)

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Challenge: Existing approaches to sparsify attention in the Transformer model are based on quadratic memory complexity and a lack of information for each word.
Approach: They propose a method to sparsify attention in a Transformer model by learning to select the most-informative token representations during the training process.
Outcome: The proposed model performs better than the current SOTA model while being 1.8 faster during training, 4.5 faster inference and 13 more efficient in the decoder.
On the Distribution, Sparsity, and Inference-time Quantization of Attention Values in Transformers (2021.findings-acl)

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Challenge: Recent work shows that attention can be pruned to zeros with minimal loss in accuracy.
Approach: They propose a pruning technique which quantizes attention to a 3-bit format without retraining . they find that 80% of attention values can be pruned to zeros with minimal loss in accuracy .
Outcome: The proposed approach produces only a few unique attention values with minimal loss in accuracy.
A Mechanistic Account of Attention Sinks in GPT-2: One Circuit, Broader Implications for Mitigation (2026.acl-short)

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Challenge: Xiao et al., 2025) show a tendency to allocate disproportionate attention mass to early (often first) positions independent of semantic content.
Approach: They find that Transformers display an attention sink: disproportionate attention to the first position.
Outcome: The proposed sinks are found in GPT-2–style models with learned query biases and absolute positional embeddings.
Learning Adaptive Axis Attentions in Fine-tuning: Beyond Fixed Sparse Attention Patterns (2022.findings-acl)

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Challenge: Adaptive Axis Attention learns different attention patterns for each task and model layer . sparse attention patterns do not improve the run time of the models but they reduce model memory requirements .
Approach: They propose a method that learns different attention patterns for each Transformer layer . they propose 'adaptive axis attention' method that identifies important tokens .
Outcome: The proposed method does not require pre-training to accommodate sparse attention patterns.

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