Petar Veličković

Deep Shah

2026-02-04

ArXiv (prépublication)

Perplexity Cannot Always Tell Right from Wrong

Federico Barbero

Christos Perivolaropoulos

Simon Kayode Osindero

Perplexity -- a function measuring a model's overall level of"surprise"when encountering a particular output -- has gained significant tract… (voir plus)ion in recent years, both as a loss function and as a simple-to-compute metric of model quality. Prior studies have pointed out several limitations of perplexity, often from an empirical manner. Here we leverage recent results on Transformer continuity to show in a rigorous manner how perplexity may be an unsuitable metric for model selection. Specifically, we prove that, if there is any sequence that a compact decoder-only Transformer model predicts accurately and confidently -- a necessary pre-requisite for strong generalisation -- it must imply existence of another sequence with very low perplexity, but not predicted correctly by that same model. Further, by analytically studying iso-perplexity plots, we find that perplexity will not always select for the more accurate model -- rather, any increase in model confidence must be accompanied by a commensurate rise in accuracy for the new model to be selected.

2026-01-29

ArXiv (prépublication)

Softmax is not Enough (for Sharp Size Generalisation)

Christos Perivolaropoulos

Federico Barbero

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… (voir plus)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 (publié)

proceedings.mlr.press

Softmax is not Enough (for Sharp Size Generalisation)

Christos Perivolaropoulos

Federico Barbero

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… (voir plus)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 (publié)

proceedings.mlr.press

Optimizers Qualitatively Alter Solutions And We Should Leverage This

Clare Lyle

Ionut-Vlad Modoranu

Naima Elosegui Borras

Dan Alistarh

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… (voir plus)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 (prépublication)

Optimizers Qualitatively Alter Solutions And We Should Leverage This

Clare Lyle

Ionut-Vlad Modoranu

Naima Elosegui Borras

Dan Alistarh

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… (voir plus)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 (prépublication)

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

Simon Kayode Osindero

Benedetto De Martino

Viorica Patraucean

Large language models (LLMs) exhibit strikingly conflicting behaviors: they can appear steadfastly overconfident in their initial answers wh… (voir plus)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 (prépublication)

Filter Equivariant Functions: A symmetric account of length-general extrapolation on lists

Owen Lewis

Neil Ghani

Andrew Joseph Dudzik

Christos Perivolaropoulos

2025-07-01

arXiv (publié)

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

Simon Kayode Osindero

Benedetto De Martino

Viorica Patraucean

Large language models (LLMs) exhibit strikingly conflicting behaviors: they can appear steadfastly overconfident in their initial answers wh… (voir plus)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 (publié)

Optimizers Qualitatively Alter Solutions And We Should Leverage This

Clare Lyle

Ionut-Vlad Modoranu

Naima Elosegui Borras

Dan Alistarh

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… (voir plus)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 (publié)

Why do LLMs attend to the first token?

Federico Barbero

'Alvaro Arroyo

Xiangming Gu

Christos Perivolaropoulos

Michael M. Bronstein

2025-04-01

arXiv (publié)

Round and Round We Go! What makes Rotary Positional Encodings useful?

Federico Barbero

Alex Vitvitskyi

Christos Perivolaropoulos

Positional Encodings (PEs) are a critical component of Transformer-based Large Language Models (LLMs), providing the attention mechanism wit… (voir plus)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 (publié)