Radu State
Publications
Feed-Forward Steering in Transformer Residual Dynamics
Attention-only dynamical theories model Transformer residual directions as particles aggregating on a sphere. We extend this framework by incorporating the feed-forward network (FFN) term as a local steering field acting on each token state. The resulting theory predicts that the tangential component of the FFN field is necessary for motion in residual-direction space, that critical residual directions correspond to nonlinear projective equilibria, and that a commutator defect determines when a finite attention--FFN block can be accurately approximated by a parallel, additive flow. Across GPT-2, Pythia, Mistral, and Llama models, the extended theory improves one-step angular prediction relative to an attention-only baseline, with the contribution of the FFN increasing from GPT-2 to Llama-3-8B. Intervention experiments show that retaining only the tangential FFN component preserves most model quality, whereas retaining only the radial component causes performance to collapse. The tangential component also preserves output diversity under aggregation pressure. As a practical application, layers with small commutator defects can be approximately parallelized with only a modest increase in loss, whereas layers with large defects degrade rapidly. These findings support the interpretation of FFN layers as directional steering fields that shape Transformer residual geometry and govern the feasibility of block-level interventions.
Agent Skill Framework: Perspectives on the Potential of Small Language Models in Industrial Environments
Agent Skill framework, now widely and officially supported by major players such as GitHub Copilot, LangChain, and OpenAI, performs especially well with proprietary models by improving context engineering, reducing hallucinations, and boosting task accuracy. Based on these observations, an investigation is conducted to determine whether the Agent Skill paradigm provides similar benefits to small language models (SLMs). This question matters in industrial scenarios where continuous reliance on public APIs is infeasible due to data-security and budget constraints requirements, and where SLMs often show limited generalization in highly customized scenarios. This work introduces a formal mathematical definition of the Agent Skill process, followed by a systematic evaluation of language models of varying sizes across multiple use cases. The evaluation encompasses two open-source tasks and a real-world insurance claims data set. The results show that tiny models struggle with reliable skill selection, while moderately sized SLMs (approximately 12B - 30B) parameters) benefit substantially from the Agent Skill approach. Moreover, code-specialized variants at around 80B parameters achieve performance comparable to closed-source baselines while improving GPU efficiency. Collectively, these findings provide a comprehensive and nuanced characterization of the capabilities and constraints of the framework, while providing actionable insights for the effective deployment of Agent Skills in SLM-centered environments.
Geometric Analysis of Token Selection in Multi-Head Attention
We present a geometric framework for analysing multi-head attention in large language models (LLMs). Without altering the mechanism, we view standard attention through a top-N selection lens and study its behaviour directly in value-state space. We define geometric metrics - Precision, Recall, and F-score - to quantify separability between selected and non-selected tokens, and derive non-asymptotic bounds with explicit dependence on dimension and margin under empirically motivated assumptions (stable value norms with a compressed sink token, exponential similarity decay, and piecewise attention weight profiles). The theory predicts a small-N operating regime of strongest non-trivial separability and clarifies how sequence length and sink similarity shape the metrics. Empirically, across LLaMA-2-7B, Gemma-7B, and Mistral-7B, measurements closely track the theoretical envelopes: top-N selection sharpens separability, sink similarity correlates with Recall. We also found that in LLaMA-2-7B heads specialize into three regimes - Retriever, Mixer, Reset - with distinct geometric signatures. Overall, attention behaves as a structured geometric classifier with measurable criteria for token selection, offering head level interpretability and informing geometry-aware sparsification and design of attention in LLMs.