Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework—zigzag persistence from topological data analysis —with practical and easily applicable algorithms. Zigzag persistence is particularly effective for characterizing data as it dynamically transforms across model layers. Within this framework, we introduce topological descriptors that measure how topological features, $p$-dimensional holes, persist and evolve throughout the layers. Unlike methods that assess each layer individually and then aggregate the results, our approach directly tracks the full evolutionary path of these features. This offers a statistical perspective on how prompts are rearranged and their relative positions changed in the representation space, providing insights into the system’s operation as an integrated whole. To demonstrate the expressivity and applicability of our framework, we highlight how sensitive these descriptors are to different models and a variety of datasets. As a showcase application to a downstream task, we use zigzag persistence to establish a criterion for layer pruning, achieving results comparable to state-of-the-art methods while preserving the system-level perspective.

Recent advances in multimodal training have significantly improved the integration of image understanding and generation within a unified model. This study investigates how vision-language models (VLMs) handle image-understanding tasks, focusing on how visual information is processed and transferred to the textual domain. We compare *native multimodal VLMs*, models trained from scratch on multimodal data to generate both text and images, and *non-native multimodal VLMs*, models adapted from pre-trained large language models or capable of generating only text, highlighting key differences in information flow. We find that in native multimodal VLMs, image and text embeddings are more separated within the residual stream. Moreover, VLMs differ in how visual information reaches text: non-native multimodal VLMs exhibit a distributed communication pattern, where information is exchanged through multiple image tokens, whereas models trained natively for joint image and text generation tend to rely on a single post-image token that acts as a *narrow gate* for visual information. We show that ablating this single token significantly deteriorates image-understanding performance, whereas targeted, token-level interventions reliably steer image semantics and downstream text with fine-grained control.

In-context learning (ICL) and supervised fine-tuning (SFT) are two common strategies for improving the performance of modern large language models (LLMs) on specific tasks. Despite their different natures, these strategies often lead to comparable performance gains. However, little is known about whether they induce similar representations inside LLMs. We approach this problem by analyzing the probability landscape of their hidden representations in the two cases. More specifically, we compare how LLMs solve the same question-answering task, finding that ICL and SFT create very different internal structures, in both cases undergoing a sharp transition in the middle of the network. In the first half of the network, ICL shapes interpretable representations hierarchically organized according to their semantic content. In contrast, the probability landscape obtained with SFT is fuzzier and semantically mixed. In the second half of the model, the fine-tuned representations develop probability modes that better encode the identity of answers, while less-defined peaks characterize the landscape of ICL representations. Our approach reveals the diverse computational strategies developed inside LLMs to solve the same task across different conditions, allowing us to make a step towards designing optimal methods to extract information from language models.

MOTIVATION: Protein language models offer a new perspective for addressing challenges in structural biology, while relying solely on sequence information. Recent studies have investigated their effectiveness in forecasting shifts in thermodynamic stability caused by single amino acid mutations, a task known for its complexity due to the sparse availability of data, constrained by experimental limitations. To tackle this problem, we introduce two key novelties: leveraging a protein language model that incorporates Multiple Sequence Alignments to capture evolutionary information, and using a recently released mega-scale dataset with rigorous data preprocessing to mitigate overfitting. RESULTS: We ensure comprehensive comparisons by fine-tuning various pretrained models, taking advantage of analyses such as ablation studies and baselines evaluation. Our methodology introduces a stringent policy to reduce the widespread issue of data leakage, rigorously removing sequences from the training set when they exhibit significant similarity with the test set. The MSA Transformer emerges as the most accurate among the models under investigation, given its capability to leverage co-evolution signals encoded in aligned homologous sequences. Moreover, the optimized MSA Transformer outperforms existing methods and exhibits enhanced generalization power, leading to a notable improvement in predicting changes in protein stability resulting from point mutations. AVAILABILITY AND IMPLEMENTATION: Code and data at https://github.com/RitAreaSciencePark/PLM4Muts.

Abstract Time Series Classification (TSC) is essential in fields like medicine, environmental science, and finance, enabling tasks such as disease diagnosis, anomaly detection, and stock price analysis. While machine learning models like Recurrent Neural Networks and InceptionTime are successful in numerous applications, they can face scalability issues due to computational requirements. Recently, ROCKET has emerged as an efficient alternative, achieving state-of-the-art performance and simplifying training by utilizing a large number of randomly generated features from the time series data. However, many of these features are redundant or non-informative, increasing computational load and compromising generalization. Here we introduce Sequential Feature Detachment (SFD) to identify and prune non-essential features in ROCKET-based models, such as ROCKET, MiniRocket, and MultiRocket. SFD estimates feature importance using model coefficients and can handle large feature sets without complex hyperparameter tuning. Testing on the UCR archive shows that SFD can produce models with better test accuracy using only 10% of the original features. We named these pruned models Detach-ROCKET. We also present an end-to-end procedure for determining an optimal balance between the number of features and model accuracy. On the largest binary UCR dataset, Detach-ROCKET improves test accuracy by 0.6% while reducing features by 98.9%. By enabling a significant reduction in model size without sacrificing accuracy, our methodology improves computational efficiency and contributes to model interpretability. We believe that Detach-ROCKET will be a valuable tool for researchers and practitioners working with time series data, who can find a user-friendly implementation of the model at https://github.com/gon-uri/detach_rocket .

Large transformers are powerful architectures used for self-supervised data analysis across various data types, including protein sequences, images, and text. In these models, the semantic structure of the dataset emerges from a sequence of transformations between one representation and the next. We characterize the geometric and statistical properties of these representations and how they change as we move through the layers. By analyzing the intrinsic dimension (ID) and neighbor composition, we find that the representations evolve similarly in transformers trained on protein language taskand image reconstruction tasks. In the first layers, the data manifold expands, becoming high-dimensional, and then contracts significantly in the intermediate layers. In the last part of the model, the ID remains approximately constant or forms a second shallow peak. We show that the semantic information of the dataset is better expressed at the end of the first peak, and this phenomenon can be observed across many models trained on diverse datasets. Based on our findings, we point out an explicit strategy to identify, without supervision, the layers that maximize semantic content: representations at intermediate layers corresponding to a relative minimum of the ID profile are more suitable for downstream learning tasks.

In recent years, Artificial Neural Networks (ANNs) pruning has become the focal point of many researches, due to the extreme overparametrization of such models. This has urged the scientific world to investigate methods for the simplification of the structure of weights in ANNs, mainly in an effort to reduce time for both training and inference. Frankle and Carbin [1], and later Renda, Frankle, and Carbin [2] introduced and refined an iterative pruning method which is able to effectively prune the network of a great portion of its parameters with little to no loss in performance. On the downside, this method requires a large amount of time for its application, since, for each iteration, the network has to be trained for (almost) the same amount of epochs of the unpruned network. In this work, we show that, for a limited setting, if targeting high overall sparsity rates, this time can be effectively reduced for each iteration, save for the last one, by more than 50%, while yielding a final product (i.e., final pruned network) whose performance is comparable to the ANN obtained using the existing method.

During the last few decades, artificial neural networks (ANN) have achieved an enormous success in regression and classification tasks. The empirical success has not been matched with an equally strong theoretical understanding of such models, as some of their working principles (training dynamics, generalization properties, and the structure of inner representations) still remain largely unknown. It is, for example, particularly difficult to reconcile the well known fact that ANNs achieve remarkable levels of generalization also in conditions of severe over-parametrization. In our work, we explore a recent network compression technique, called Iterative Magnitude Pruning (IMP), and apply it to convolutional neural networks (CNN). The pruned and unpruned models are compared layer-wise with Canonical Correlation Analysis (CCA). Our results show a high similarity between layers of pruned and unpruned CNNs in the first convolutional layers and in the fully-connected layer, while for the intermediate convolutional layers the similarity is significantly lower. This suggests that, although in intermediate layers representation in pruned and unpruned networks is markedly different, in the last part the fully-connected layers act as pivots, producing not only similar performances but also similar representations of the data, despite the large difference in the number of parameters involved.

Deep convolutional networks (DCNs) learn meaningful representations where data that share the same abstract characteristics are positioned closer and closer. Understanding these representations and how they are generated is of unquestioned practical and theoretical interest. In this work we study the evolution of the probability density of the ImageNet dataset across the hidden layers in some state-of-the-art DCNs. We find that the initial layers generate a unimodal probability density getting rid of any structure irrelevant for classification. In subsequent layers density peaks arise in a hierarchical fashion that mirrors the semantic hierarchy of the concepts. Density peaks corresponding to single categories appear only close to the output and via a very sharp transition which resembles the nucleation process of a heterogeneous liquid. This process leaves a footprint in the probability density of the output layer where the topography of the peaks allows reconstructing the semantic relationships of the categories.

Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of data representations, i.e. the minimal number of parameters needed to describe a representation. We find that, in a trained network, the ID is orders of magnitude smaller than the number of units in each layer. Across layers, the ID first increases and then progressively decreases in the final layers. Remarkably, the ID of the last hidden layer predicts classification accuracy on the test set. These results can neither be found by linear dimensionality estimates (e.g., with principal component analysis), nor in representations that had been artificially linearized. They are neither found in untrained networks, nor in networks that are trained on randomized labels. This suggests that neural networks that can generalize are those that transform the data into low-dimensional, but not necessarily flat manifolds.