Felipe Urrutia
Cargo: Ingeniero de investigación
Licenciado en ciencias de la ingeniería, mención matemáticas, alumno de doble titulación en ingeniería civil matemática y magister en ciencias de la computación de la Universidad de Chile. Investigador asistente en el Centro de Investigación Avanzada en Educación. Anteriormente se desempeñó como investigador asistente en Center of Research in Learning and Teaching, University of Jyväskylä, Finlandia.
PUBLICACIONES
Understanding how Transformers work and how they process information is key to the theoretical and empirical advancement of these machines. In this work, we demonstrate the existence of two phenomena in Transformers, namely isolation and continuity. Both of these phenomena hinder Transformers to learn even simple pattern sequences. Isolation expresses that any learnable sequence must be isolated from another learnable sequence, and hence some sequences cannot be learned by a single Transformer at the same time. Continuity entails that an attractor basin forms around a learned sequence, such that any sequence falling in that basin will collapse towards the learned sequence. Here, we mathematically prove these phenomena emerge in all Transformers that use compact positional encoding, and design rigorous experiments, demonstrating that the theoretical limitations we shed light on occur on the practical scale.
An important aspect subtending language understanding and production is the ability to independently encode positional and symbolic information of the words within a sentence. In Transformers, positional information is typically encoded using Positional Encodings (PEs). One such popular PE, namely Rotary PE (RoPE), has been widely used due to its empirical success. Recently, it has been argued that part of RoPE's success emerges from its ability to encode robust positional and semantic information using large and small frequencies, respectively. In this work, we perform a deeper dive into the positional versus symbolic dichotomy of attention heads behavior, both at the theoretical and empirical level. We provide general definitions of what it means for a head to behave positionally or symbolically, prove that these are two mutually exclusive behaviors and develop a metric to quantify them. We apply our framework to analyze Transformer-based LLMs using RoPE and find that all heads exhibit a strong correspondence between behavior and frequency use. Finally, we introduce canonical tasks designed to be either purely positional or symbolic, and demonstrate that the Transformer performance causally relates to the ability of attention heads to leverage the appropriate frequencies. In particular, we show that we can control the Transformer performance by controlling which frequencies the attention heads can access. Altogether, our work provides a detailed understanding of RoPE, and how its properties relate to model behavior.
We propose the first method to show theoretical limitations for one-layer softmax transformers with arbitrarily many precision bits (even infinite). We establish those limitations for three tasks that require advanced reasoning. The first task, Match 3 (Sanford et al., 2023), requires looking at all possible token triplets in an input sequence. The second and third tasks address compositionality-based reasoning: function composition (Peng et al., 2024) and binary relations composition, respectively. We formally prove the inability of one-layer softmax Transformers to solve any of these tasks. To overcome these limitations, we introduce Strassen attention and prove that, equipped with this mechanism, a one-layer transformer can in principle solve all these tasks. Importantly, we show that it enjoys sub-cubic running-time complexity, making it more scalable than similar previously proposed mechanisms, such as higher-order attention (Sanford et al., 2023). To complement our theoretical findings, we experimentally studied Strassen attention and compared it against standard (Vaswani et al, 2017), higher-order attention (Sanford et al., 2023), and triangular attention (Bergen et al. 2021). Our results help to disentangle all these attention mechanisms, highlighting their strengths and limitations. In particular, Strassen attention outperforms standard attention significantly on all the tasks. Altogether, understanding the theoretical limitations can guide research towards scalable attention mechanisms that improve the reasoning abilities of Transformers.
We propose the first method to show theoretical limitations for one-layer softmax transformers with arbitrarily many precision bits (even infinite). We establish those limitations for three tasks that require advanced reasoning. The first task, Match 3 (Sanford et al., 2023), requires looking at all possible token triplets in an input sequence. The second and third tasks address compositionality-based reasoning: function composition (Peng et al., 2024) and binary relations composition, respectively. We formally prove the inability of one-layer softmax Transformers to solve any of these tasks. To overcome these limitations, we introduce Strassen attention and prove that, equipped with this mechanism, a one-layer transformer can in principle solve all these tasks. Importantly, we show that it enjoys sub-cubic running-time complexity, making it more scalable than similar previously proposed mechanisms, such as higher-order attention (Sanford et al., 2023). To complement our theoretical findings, we experimentally studied Strassen attention and compared it against standard (Vaswani et al, 2017), higher-order attention (Sanford et al., 2023), and triangular attention (Bergen et al. 2021). Our results help to disentangle all these attention mechanisms, highlighting their strengths and limitations. In particular, Strassen attention outperforms standard attention significantly on all the tasks. Altogether, understanding the theoretical limitations can guide research towards scalable attention mechanisms that improve the reasoning abilities of Transformers.
Automatic Short Answer Grading (ASAG) refers to automated scoring of open-ended textual responses to specific questions, both in natural language form. In this paper, we propose a method to tackle this task in a setting where annotated data is unavailable. Crucially, our method is competitive with the state-of-theart while being lighter and interpretable. We crafted a unique dataset containing a highly diverse set of questions and a small amount of answers to these questions; making it more challenging compared to previous tasks. Our method uses weak labels generated from other methods proven to be effective in this task, which are then used to train a white-box (linear) regression based on a few interpretable features. The latter are extracted expert features and learned representations that are interpretable per se and aligned with manual labeling. We show the potential of our method by evaluating it on a small annotated portion of the dataset, and demonstrate that its ability compares with that of strong baselines and state-of-the-art methods, comprising an LLM that in contrast to our method comes with a high computational price and an opaque reasoning process. We further validate our model on a public Automatic Essay Scoring dataset in English, and obtained competitive results compared to other unsupervised baselines, outperforming the LLM. To gain further insights of our method, we conducted an interpretability analysis revealing sparse weights in our linear regression model, and alignment between our features and human ratings.
Edificio de Innovación UC, Piso 2
Vicuña Mackenna 4860
Macul, Chile
Vicuña Mackenna 4860
Macul, Chile