Abstract: Large Language Models (LLMs) drive significant advancements in AI, yet understanding their internal workings remains a challenge. This paper introduces a novel geometric perspective to characterize LLMs, offering practical insights into their functionality. By analyzing the intrinsic dimension of Multi-Head Attention (MHA) embeddings and the affine mappings within layer feed-forward networks, we unlock new ways to manipulate and interpret LLMs. Our findings enable bypassing restrictions like RLHF in models such as Llama2, and we introduce seven interpretable spline features extracted from any LLM layer. These features, tested on models like Mistral-7B and Llama2, prove highly effective in toxicity detection, domain inference, and addressing the Jigsaw challenge, showcasing the practical utility of our geometric characterization.
LLMs, a subset of Deep Neural Networks (DNNs), have transformed various domains with their unparalleled capabilities. Despite their success, the black-box nature of these models hampers a clear understanding of their internal representations. Current methods to probe these models either rely on engineered prompts or sparse classifiers, both of which have significant limitations. Our research proposes a geometric approach to dissect LLMs, offering a more tangible understanding of their internal mechanisms.
Our analysis begins with the MHA component, where we demonstrate that the output of MHA resides within a specific geometric construct - the Minkowski sum of convex hulls formed by token embeddings. This insight reveals the role of token interrelations in determining the embedding space's dimensionality. Further, we delve into the MLP (Multilayer Perceptron) component, illustrating its operation as a piecewise affine mapping, which partitions the input space in a manner dependent on the preceding MHA output. These geometric characteristics are pivotal in understanding the expressivity and limitations of LLMs.
Building on our geometric insights, we propose seven spline features that capture the essence of an LLM layer's functionality. These features are not just theoretical constructs but have practical implications. They enable tasks such as toxicity detection, domain classification, and more, with minimal computational overhead. The efficacy of these features is validated through extensive experiments across various models and tasks, underscoring the value of our geometric perspective.
The practical applications of our work are vast. We demonstrate how manipulating the intrinsic dimension of embeddings can bypass safeguards like RLHF, raising important questions about model security. Our spline features facilitate high-accuracy toxicity detection, outperforming existing methods significantly. These applications highlight the potential of geometric insights in enhancing the interpretability, usability, and safety of LLMs.
The application of spline theory to Feed-Forward Networks (FFNs) within Large Language Models (LLMs) offers a novel perspective for understanding these complex systems. Spline theory, a well-established mathematical framework, is used to model FFNs as Continuous Piecewise Affine (CPA) operators. This approach allows for a decomposition of FFNs into a series of linear functions, each applicable to specific regions of the input space.
The spline theory provides a foundation for extracting meaningful features from LLMs, bridging the gap between complex model behaviors and practical applications such as toxicity detection. This geometric approach enhances our ability to interpret, manipulate, and ultimately trust the outputs of these powerful models.
The paper focuses on geometric modeling of LLMs to provide a structured and intuitive understanding of how these models process and transform input data. This approach sheds light on the internal mechanisms of LLMs, moving beyond the traditional black-box perspective.
Modeling the geometry of LLMs opens new avenues for exploring, understanding, and applying these models in various domains. The geometric perspective, particularly when combined with spline theory, equips researchers and practitioners with powerful tools to analyze and leverage the capabilities of LLMs for tasks ranging from natural language understanding to ensuring the ethical use of AI.
Toxicity detection is a critical component of maintaining a positive and respectful online environment. It involves identifying content that may be harmful, offensive, or inappropriate, which can range from explicit insults to more subtle forms of negative communication. In the realm of AI and NLP, this task requires sophisticated models that can discern the nuanced differences between toxic and non-toxic expressions.
A cornerstone of the paper's methodology is the derivation of seven spline features from the LLM's feed-forward networks. These features capture the essence of how the model interprets and transforms input text, offering a window into the underlying decision-making process. For example, features that measure the distance of input tokens to the partition boundaries within the model can indicate how 'extreme' or 'outlying' the model perceives the input, which could correlate with toxic content.
To illustrate, consider a comment on a social media platform: "I hope you realize how utterly incompetent you are." An LLM equipped with the spline-based geometric framework would analyze this sentence, extracting features that reflect the aggressive tone and personal attack present. These features might include an increased distance to partition boundaries, indicating that the input falls outside the 'normal' range the model has been trained on, suggesting toxicity.
Conversely, a constructive criticism such as "Your argument could be stronger if you provided more evidence," would generate different spline feature values. These would likely indicate a closer alignment with non-toxic, regular discourse, leading the model to classify this input as non-toxic.
Incorporating this geometric approach into LLMs for toxicity detection can significantly enhance content moderation tools. By providing a more nuanced understanding of text, these models can more accurately identify harmful content, reducing false positives and negatives. This, in turn, supports healthier online interactions, fostering spaces where users feel safe to engage in open and respectful dialogue.
In summary, the paper's geometric perspective on LLMs not only advances our understanding of these complex models but also offers practical applications in crucial areas such as toxicity detection. This innovative approach holds promise for creating more inclusive and positive digital environments.
Created 2024-03-18T07:49:16-07:00 · Edit