nandan523
Abstract
The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive information. While PI offers a promising solution, its practical deployment is hindered by substantial communication and latency overheads, primarily stemming from nonlinear operations. To address this, we introduce an information-theoretic framework to characterize the role of nonlinearities in decoder-only language models, laying a principled foundation for optimizing transformer-architectures tailored to the demands of PI. By leveraging Shannon's entropy as a quantitative measure, we uncover the previously unexplored dual significance of nonlinearities: beyond ensuring training stability, they are crucial for maintaining attention head diversity. Specifically, we find that their removal triggers two critical failure modes: {\em entropy collapse} in deeper layers that destabilizes training, and {\em entropic overload} in earlier layers that leads to under-utilization of Multi-Head Attention's (MHA) representational capacity. We propose an entropy-guided attention mechanism paired with a novel entropy regularization technique to mitigate entropic overload. Additionally, we explore PI-friendly alternatives to layer normalization for preventing entropy collapse and stabilizing the training of LLMs with reduced-nonlinearities. Our study bridges the gap between information theory and architectural design, establishing entropy dynamics as a principled guide for developing efficient PI architectures. The code and implementation are available at https://github.com/Nandan91/entropy-guided-attention-llm{entropy-guided-llm}.
Community
In the realm of Private Language Models, the high computational cost of nonlinear operations poses a significant challenge, and to address this, our work introduces an information-theoretic framework for designing nonlinearity-reduced LLMs, aiming to balance efficiency and performance.
We discover the dual role of nonlinearities in LLMs: they stabilize training and preserve functional diversity across attention heads. Leveraging this understanding, we propose an adaptive entropy regularization technique that mitigates entropic overload—a phenomenon where a disproportionately higher number of attention heads in nonlinearity-reduced LLMs are trapped in persistently high entropy states during training. By dynamically adjusting regularization strength to head-specific roles, our method significantly reduces the reliance on expensive nonlinear operations.
This work aspires to bridge the gap between information theory and architectural design, offering a principled framework that leverages entropy dynamics to guide the development of efficient architectures for private LLMs.
Great work! We had very related observations in our paper "Your Transformer is Secretly Linear". Seems that the role of nonlinear operations in transformers isn't so significant as previously assumed.
https://huggingface.co/papers/2405.12250
Thanks for sharing your interesting work!
The paper "Your Transformer is Secretly Linear," studied the transformation introduced by sequential layers in the embedding space. In our work, we focused on two critical failure modes: entropy collapse (associated with training instability) and entropic overload (associated with the under-utilization of the representational capacity of MHA).
Indeed, we can get rid of nonlinearities like GELU and LayerNorm through careful architectural optimizations (for training stability in the absence of nonlinearities ) and algorithmic innovations (such as entropy-regularization to foster attention-head diversity in functional space) in transformer-based LLMs.
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I recall that a recent(ish) result out of mech. interpretability and the various attempts at linearizing attention was the observation that ICL suffers catastrophically without nonlinearity in MHA (e.g. I recall this was one of the main findings of the Zoology program, which they interpreted using the induction heads view of MHA a la Anthropic). Does entropic regularization of the attention affect the model's ICL abilities or how long it takes for ICL to emerge? I understand that this paper mainly focuses on training dynamics, but I'm curious how reducing nonlinearity affects downstream performance as well.
Thank you for your thoughtful comment and for bringing up the connection between attention nonlinearity and ICL performance! You’re right! Nonlinearity is critical in enabling ICL, especially through mechanisms like induction heads.
A quick clarification: when we talk about LINEARIZATION in our work, we’re not addressing the common approach of linearizing the softmax attention mechanism to reduce quadratic complexity (e.g., attention transfer in [1]). Instead, our focus is on linearizing the overall transformer architecture by removing GELU and LayerNorms. While the softmax-based attention remains intact, we incorporate a learnable softmax temperature and apply entropy regularization during training to maintain a well-behaved entropy distribution. Thus, our architectural goals and challenges differ significantly from those in works targeting softmax linearization.
To your point about ICL: reducing nonlinearities (GELU and LNs) can affect ICL, as these elements are shown to negatively impact the inductive biases required for ICL (e.g., inductive heads) to emerge effectively. That said, entropy regularization can be tuned to promote the emergence of inductive heads, which is required for ICL and downstream task performance, during the pre-training (since we've seen the effectiveness of entropy regularization for fostering attention head diversity and specialization in the absence of conventional nonlinearities: GELU and LNs)
To summarize, a deeper characterization of the entropic behavior of induction heads is essential to understanding their dynamics. If these heads exhibit consistent and predictable patterns, entropy regularization could be further refined to actively promote their emergence. Exploring this, along with the broader impact of entropy regularization on ICL emergence and performance, is a fascinating direction for follow-up work!
[1] Zhang et al., LoLCATs: On Low-Rank Linearizing of Large Language Models, 2024.
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