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Petar Veličković

Alumni

Publications

Softmax is not Enough (for Sharp Size Generalisation)
Petar Veličković
Christos Perivolaropoulos
Federico Barbero
Razvan Pascanu
A key property of reasoning systems is the ability to make sharp decisions on their input data. For contemporary AI systems, a key carrier o… (see more)f sharp behaviour is the softmax function, with its capability to perform differentiable query-key lookups. It is a common belief that the predictive power of networks leveraging softmax arises from "circuits" which sharply perform certain kinds of computations consistently across many diverse inputs. However, for these circuits to be robust, they would need to generalise well to arbitrary valid inputs. In this paper, we dispel this myth: even for tasks as simple as finding the maximum key, any learned circuitry must disperse as the number of items grows at test time. We attribute this to a fundamental limitation of the softmax function to robustly approximate sharp functions with increasing problem size, prove this phenomenon theoretically, and propose adaptive temperature as an ad-hoc technique for improving the sharpness of softmax at inference time.
2025-10-06
Proceedings of the 42nd International Conference on Machine Learning (published)
proceedings.mlr.press
Optimizers Qualitatively Alter Solutions And We Should Leverage This
Razvan Pascanu
Clare Lyle
Ionut-Vlad Modoranu
Naima Elosegui Borras
Dan Alistarh
Petar Veličković
Sarath Chandar
Soham De
James Martens
Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when us… (see more)ing optimizers relying only on local information, such as SGD. Indeed, this was a primary source of skepticism regarding the feasibility of DNNs in the early days of the field. The past decades of progress in deep learning have revealed this skepticism to be misplaced, and a large body of empirical evidence shows that sufficiently large DNNs following standard training protocols exhibit well-behaved optimization dynamics that converge to performant solutions. This success has biased the community to use convex optimization as a mental model for learning, leading to a focus on training efficiency, either in terms of required iteration, FLOPs or wall-clock time, when improving optimizers. We argue that, while this perspective has proven extremely fruitful, another perspective specific to DNNs has received considerably less attention: the optimizer not only influences the rate of convergence, but also the qualitative properties of the learned solutions. Restated, the optimizer can and will encode inductive biases and change the effective expressivity of a given class of models. Furthermore, we believe the optimizer can be an effective way of encoding desiderata in the learning process. We contend that the community should aim at understanding the biases of already existing methods, as well as aim to build new optimizers with the explicit intent of inducing certain properties of the solution, rather than solely judging them based on their convergence rates. We hope our arguments will inspire research to improve our understanding of how the learning process can impact the type of solution we converge to, and lead to a greater recognition of optimizers design as a critical lever that complements the roles of architecture and data in shaping model outcomes.
2025-07-16
ArXiv (preprint)
doi.org
arxiv.org
How Overconfidence in Initial Choices and Underconfidence Under Criticism Modulate Change of Mind in Large Language Models
Dharshan Kumaran
Stephen M Fleming
Larisa Markeeva
Joseph Heyward
Andrea Banino
Mrinal Mathur
Razvan Pascanu
Simon Kayode Osindero
Benedetto De Martino
Petar Veličković
Viorica Patraucean
Large language models (LLMs) exhibit strikingly conflicting behaviors: they can appear steadfastly overconfident in their initial answers wh… (see more)ilst at the same time being prone to excessive doubt when challenged. To investigate this apparent paradox, we developed a novel experimental paradigm, exploiting the unique ability to obtain confidence estimates from LLMs without creating memory of their initial judgments -- something impossible in human participants. We show that LLMs -- Gemma 3, GPT4o and o1-preview -- exhibit a pronounced choice-supportive bias that reinforces and boosts their estimate of confidence in their answer, resulting in a marked resistance to change their mind. We further demonstrate that LLMs markedly overweight inconsistent compared to consistent advice, in a fashion that deviates qualitatively from normative Bayesian updating. Finally, we demonstrate that these two mechanisms -- a drive to maintain consistency with prior commitments and hypersensitivity to contradictory feedback -- parsimoniously capture LLM behavior in a different domain. Together, these findings furnish a mechanistic account of LLM confidence that explains both their stubbornness and excessive sensitivity to criticism.
2025-07-03
ArXiv (preprint)
doi.org
arxiv.org
Filter Equivariant Functions: A symmetric account of length-general extrapolation on lists
Owen Lewis
Neil Ghani
Andrew Joseph Dudzik
Christos Perivolaropoulos
Razvan Pascanu
Petar Veličković
2025-07-01
arXiv (published)
doi.org
How Overconfidence in Initial Choices and Underconfidence Under Criticism Modulate Change of Mind in Large Language Models
Dharshan Kumaran
Stephen M Fleming
Larisa Markeeva
Joseph Heyward
Andrea Banino
Mrinal Mathur
Razvan Pascanu
Simon Kayode Osindero
Benedetto De Martino
Petar Veličković
Viorica Patraucean
Large language models (LLMs) exhibit strikingly conflicting behaviors: they can appear steadfastly overconfident in their initial answers wh… (see more)ilst at the same time being prone to excessive doubt when challenged. To investigate this apparent paradox, we developed a novel experimental paradigm, exploiting the unique ability to obtain confidence estimates from LLMs without creating memory of their initial judgments -- something impossible in human participants. We show that LLMs -- Gemma 3, GPT4o and o1-preview -- exhibit a pronounced choice-supportive bias that reinforces and boosts their estimate of confidence in their answer, resulting in a marked resistance to change their mind. We further demonstrate that LLMs markedly overweight inconsistent compared to consistent advice, in a fashion that deviates qualitatively from normative Bayesian updating. Finally, we demonstrate that these two mechanisms -- a drive to maintain consistency with prior commitments and hypersensitivity to contradictory feedback -- parsimoniously capture LLM behavior in a different domain. Together, these findings furnish a mechanistic account of LLM confidence that explains both their stubbornness and excessive sensitivity to criticism.
2025-07-01
arXiv (published)
doi.org
arxiv.org
Optimizers Qualitatively Alter Solutions And We Should Leverage This
Razvan Pascanu
Clare Lyle
Ionut-Vlad Modoranu
Naima Elosegui Borras
Dan Alistarh
Petar Veličković
Sarath Chandar
Soham De
James Martens
Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when us… (see more)ing optimizers relying only on local information, such as SGD. Indeed, this was a primary source of skepticism regarding the feasibility of DNNs in the early days of the field. The past decades of progress in deep learning have revealed this skepticism to be misplaced, and a large body of empirical evidence shows that sufficiently large DNNs following standard training protocols exhibit well-behaved optimization dynamics that converge to performant solutions. This success has biased the community to use convex optimization as a mental model for learning, leading to a focus on training efficiency, either in terms of required iteration, FLOPs or wall-clock time, when improving optimizers. We argue that, while this perspective has proven extremely fruitful, another perspective specific to DNNs has received considerably less attention: the optimizer not only influences the rate of convergence, but also the qualitative properties of the learned solutions. Restated, the optimizer can and will encode inductive biases and change the effective expressivity of a given class of models. Furthermore, we believe the optimizer can be an effective way of encoding desiderata in the learning process. We contend that the community should aim at understanding the biases of already existing methods, as well as aim to build new optimizers with the explicit intent of inducing certain properties of the solution, rather than solely judging them based on their convergence rates. We hope our arguments will inspire research to improve our understanding of how the learning process can impact the type of solution we converge to, and lead to a greater recognition of optimizers design as a critical lever that complements the roles of architecture and data in shaping model outcomes.
2025-07-01
arXiv (published)
doi.org
arxiv.org
Why do LLMs attend to the first token?
Federico Barbero
'Alvaro Arroyo
Xiangming Gu
Christos Perivolaropoulos
Michael M. Bronstein
Petar Veličković
Razvan Pascanu
2025-04-01
arXiv (published)
doi.org
arxiv.org
Round and Round We Go! What makes Rotary Positional Encodings useful?
Federico Barbero
Alex Vitvitskyi
Christos Perivolaropoulos
Razvan Pascanu
Petar Veličković
Positional Encodings (PEs) are a critical component of Transformer-based Large Language Models (LLMs), providing the attention mechanism wit… (see more)h important sequence-position information. One of the most popular types of encoding used today in LLMs are Rotary Positional Encodings (RoPE), that rotate the queries and keys based on their relative distance. A common belief is that RoPE is useful because it helps to decay token dependency as relative distance increases. In this work, we argue that this is unlikely to be the core reason. We study the internals of a trained Gemma 7B model to understand how RoPE is being used at a mechanical level. We find that Gemma learns to use RoPE to construct robust "positional" attention patterns by exploiting the highest frequencies. We also find that, in general, Gemma greatly prefers to use the lowest frequencies of RoPE, which we suspect are used to carry semantic information. We mathematically prove interesting behaviours of RoPE and conduct experiments to verify our findings, proposing a modification of RoPE that fixes some highlighted issues and improves performance. We believe that this work represents an interesting step in better understanding PEs in LLMs, which we believe holds crucial value for scaling LLMs to large sizes and context lengths.
2025-01-01
ICLR (published)
doi.org
arxiv.org
Transformers meet Neural Algorithmic Reasoners
Wilfried Bounsi
Borja Ibarz
Andrew Joseph Dudzik
Jessica B. Hamrick
Larisa Markeeva
Alex Vitvitskyi
Razvan Pascanu
Petar Veličković
Transformers have revolutionized machine learning with their simple yet effective architecture. Pre-training Transformers on massive text da… (see more)tasets from the Internet has led to unmatched generalization for natural language understanding (NLU) tasks. However, such language models remain fragile when tasked with algorithmic forms of reasoning, where computations must be precise and robust. To address this limitation, we propose a novel approach that combines the Transformer's language understanding with the robustness of graph neural network (GNN)-based neural algorithmic reasoners (NARs). Such NARs proved effective as generic solvers for algorithmic tasks, when specified in graph form. To make their embeddings accessible to a Transformer, we propose a hybrid architecture with a two-phase training procedure, allowing the tokens in the language model to cross-attend to the node embeddings from the NAR. We evaluate our resulting TransNAR model on CLRS-Text, the text-based version of the CLRS-30 benchmark, and demonstrate significant gains over Transformer-only models for algorithmic reasoning, both in and out of distribution.
2024-06-01
arXiv (published)
doi.org
arxiv.org
Transformers need glasses! Information over-squashing in language tasks
Federico Barbero
Andrea Banino
Steven Kapturowski
Dharshan Kumaran
João Guilherme Madeira Araújo
Alex Vitvitskyi
Razvan Pascanu
Petar Veličković
We study how information propagates in decoder-only Transformers, which are the architectural backbone of most existing frontier large langu… (see more)age models (LLMs). We rely on a theoretical signal propagation analysis -- specifically, we analyse the representations of the last token in the final layer of the Transformer, as this is the representation used for next-token prediction. Our analysis reveals a representational collapse phenomenon: we prove that certain distinct sequences of inputs to the Transformer can yield arbitrarily close representations in the final token. This effect is exacerbated by the low-precision floating-point formats frequently used in modern LLMs. As a result, the model is provably unable to respond to these sequences in different ways -- leading to errors in, e.g., tasks involving counting or copying. Further, we show that decoder-only Transformer language models can lose sensitivity to specific tokens in the input, which relates to the well-known phenomenon of over-squashing in graph neural networks. We provide empirical evidence supporting our claims on contemporary LLMs. Our theory also points to simple solutions towards ameliorating these issues.
2024-06-01
arXiv (published)
doi.org
arxiv.org
Asynchronous Algorithmic Alignment with Cocycles
Andrew Joseph Dudzik
Tamara von Glehn
Razvan Pascanu
Petar Veličković
State-of-the-art neural algorithmic reasoners make use of message passing in graph neural networks (GNNs). But typical GNNs blur the distinc… (see more)tion between the definition and invocation of the message function, forcing a node to send messages to its neighbours at every layer, synchronously. When applying GNNs to learn to execute dynamic programming algorithms, however, on most steps only a handful of the nodes would have meaningful updates to send. One, hence, runs the risk of inefficiencies by sending too much irrelevant data across the graph. But more importantly, many intermediate GNN steps have to learn the identity functions, which is a non-trivial learning problem. In this work, we explicitly separate the concepts of node state update and message function invocation. With this separation, we obtain a mathematical formulation that allows us to reason about asynchronous computation in both algorithms and neural networks. Our analysis yields several practical implementations of synchronous scalable GNN layers that are provably invariant under various forms of asynchrony.
2024-04-17
Proceedings of the Second Learning on Graphs Conference (published)
doi.org
arxiv.org
Latent Space Representations of Neural Algorithmic Reasoners
Vladimir V. Mirjani'c
Razvan Pascanu
Petar Velivckovi'c University of Cambridge
Petar Veličković
Google Deepmind
Neural Algorithmic Reasoning (NAR) is a research area focused on designing neural architectures that can reliably capture classical computat… (see more)ion, usually by learning to execute algorithms. A typical approach is to rely on Graph Neural Network (GNN) architectures, which encode inputs in high-dimensional latent spaces that are repeatedly transformed during the execution of the algorithm. In this work we perform a detailed analysis of the structure of the latent space induced by the GNN when executing algorithms. We identify two possible failure modes: (i) loss of resolution, making it hard to distinguish similar values; (ii) inability to deal with values outside the range observed during training. We propose to solve the first issue by relying on a softmax aggregator, and propose to decay the latent space in order to deal with out-of-range values. We show that these changes lead to improvements on the majority of algorithms in the standard CLRS-30 benchmark when using the state-of-the-art Triplet-GMPNN processor. Our code is available at https://github.com/mirjanic/nar-latent-spaces
2024-04-17
Proceedings of the Second Learning on Graphs Conference (published)
doi.org
arxiv.org