The rapid advancements in transformer-based language models have revolutionized natural language processing, yet understanding the internal mechanisms of these models remains a significant challenge. This paper explores the application of sparse autoencoders (SAE) to interpret the internal representations of protein language models, specifically focusing on the ESM-2 8M parameter model. By performing a statistical analysis on each latent component's relevance to distinct protein annotations, we identify potential interpretations linked to various protein characteristics, including transmembrane regions, binding sites, and specialized motifs. We then leverage these insights to guide sequence generation, shortlisting the relevant latent components that can steer the model towards desired targets such as zinc finger domains. This work contributes to the emerging field of mechanistic interpretability in biological sequence models, offering new perspectives on model steering for sequence design.

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, specifically focusing on how visual information is processed and transferred to the textual domain. We compare VLMs that generate both images and text with those that output only text, highlighting key differences in information flow. We find that in models with multimodal outputs, image and text embeddings are more separated within the residual stream. Additionally, models vary in how information is exchanged from visual to textual tokens. VLMs that only output text exhibit a distributed communication pattern, where information is exchanged through multiple image tokens. In contrast, models trained for image and text generation rely on a single token that acts as a narrow gate for the visual information. We demonstrate that ablating this single token significantly deteriorates performance on image understanding tasks. Furthermore, modifying this token enables effective steering of the image semantics, showing that targeted, local interventions can reliably control the model's global behavior.

Understanding the decision-making processes of large language models (LLMs) is critical given their widespread applications. Towards this goal, describing the topological and geometrical properties of internal representations has recently provided valuable insights. For a more comprehensive characterization of these inherently complex spaces, we present a novel framework based on zigzag persistence, a method in topological data analysis (TDA) well-suited for describing data undergoing dynamic transformations across layers. Within this framework, we introduce persistence similarity, a new metric that quantifies the persistence and transformation of topological features such as $p$-cycles throughout the model layers. Unlike traditional similarity measures, our approach captures the entire evolutionary trajectory of these features, providing deeper insights into the internal workings of LLMs. As a practical application, we leverage persistence similarity to identify and prune redundant layers, demonstrating comparable performance to state-of-the-art methods across several benchmark datasets. Additionally, our analysis reveals consistent topological behaviors across various models and hyperparameter settings, suggesting a universal structure in LLM internal representations.

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 tasks and 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.

The Backpropagation algorithm has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, the recently introduced Forward-Forward algorithm replaces the forward and backward passes of Backpropagation with two forward passes. In this work, we show that the internal representations obtained by the Forward-Forward algorithm can organise into category-specific ensembles exhibiting high sparsity - i.e. composed of an extremely low number of active units. This situation is reminiscent of what has been observed in cortical sensory areas, where neuronal ensembles are suggested to serve as the functional building blocks for perception and action. Interestingly, while this sparse pattern does not typically arise in models trained with standard Backpropagation, it can emerge in networks trained with Backpropagation on the same objective proposed for the Forward-Forward algorithm. These results suggest that the learning procedure proposed by Forward-Forward may be superior to Backpropagation in modelling learning in the cortex, even when a backward pass is used.

Time Series Classification (TSC) is essential in many fields, such as medicine, environmental science and finance, enabling tasks like disease diagnosis, anomaly detection, and stock price analysis. Machine learning models for TSC like Recurrent Neural Networks and InceptionTime, while successful in numerous applications, can face scalability limitations due to intensive computational requirements. To address this, efficient models such as ROCKET and its derivatives have emerged, simplifying training and achieving state-of-the-art performance by utilizing a large number of randomly generated features from time series data. However, due to their random nature, most of the generated features are redundant or non-informative, adding unnecessary computational load and compromising generalization. Here, we introduce Sequential Feature Detachment (SFD) as a method to identify and prune these non-essential features. SFD uses model coefficients to estimate feature importance and, unlike previous algorithms, can handle large feature sets without the need for complex hyperparameter tuning. Testing on the UCR archive demonstrates that SFD can produce models with $10\%$ of the original features while improving the accuracy $0.2\%$ on the test set. We also present an end-to-end procedure for determining an optimal balance between the number of features and model accuracy, called Detach-ROCKET. When applied to the largest binary UCR dataset, Detach-ROCKET is able to improve test accuracy by $0.6\%$ while reducing the number of features by $98.9\%$. Thus, our proposed procedure is not only lightweight to train and effective in reducing model size and enhancing generalization, but its significant reduction in feature count also paves the way for feature interpretation.

In this work, we propose a novel adversarial defence mechanism for image classification - CARSO - blending the paradigms of adversarial training and adversarial purification in a mutually-beneficial, robustness-enhancing way. The method builds upon an adversarially-trained classifier, and learns to map its internal representation associated with a potentially perturbed input onto a distribution of tentative clean reconstructions. Multiple samples from such distribution are classified by the adversarially-trained model itself, and an aggregation of its outputs finally constitutes the robust prediction of interest. Experimental evaluation by a well-established benchmark of varied, strong adaptive attacks, across different image datasets and classifier architectures, shows that CARSO is able to defend itself against foreseen and unforeseen threats, including adaptive end-to-end attacks devised for stochastic defences. Paying a tolerable clean accuracy toll, our method improves by a significant margin the state of the art for CIFAR-10 and CIFAR-100 $\ell_\infty$ robust classification accuracy against AutoAttack. Code and pre-trained models are available at https://github.com/emaballarin/CARSO .

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.