A phase transition in diffusion models reveals the hierarchical nature of data

Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural networks capture during learning. Recent advancements show that diffusion models can generate high-quality images, hinting at their ability to capture this underlying compositional structure. We study this phenomenon in a hierarchical generative model of data. We find that the backward diffusion process acting after a time t is governed by a phase transition at some threshold time, where the probability of reconstructing high-level features, like the class of an image, suddenly drops. Instead, the reconstruction of low-level features, such as specific details of an image, evolves smoothly across the whole diffusion process. This result implies that at times beyond the transition, the class has changed, but the generated sample may still be composed of low-level elements of the initial image. We validate these theoretical insights through numerical experiments on class-unconditional ImageNet diffusion models. Our analysis characterizes the relationship between time and scale in diffusion models and puts forward generative models as powerful tools to model combinatorial data properties

What can be learnt with wide convolutional neural networks?

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such as images. Yet, we lack a quantitative understanding of how such structure affects performance, e.g. the rate of decay of the generalisation error with the number of training samples. In this paper, we study deep CNNs in the kernel regime. First, we show that the spectrum of the corresponding kernel inherits the hierarchical structure of the network, and we characterise its asymptotics. Then, we use this result together with generalisation bounds to prove that deep CNNs adapt to the spatial scale of the target function. In particular, we find that if the target function depends on low-dimensional subsets of adjacent input variables, then the rate of decay of the error is controlled by the effective dimensionality of these subsets. Conversely, if the teacher function depends on the full set of input variables, then the error rate is inversely proportional to the input dimension. We conclude by computing the rate when a deep CNN is trained on the output of another deep CNN with randomly-initialised parameters. Interestingly, we find that, despite their hierarchical structure, the functions generated by deep CNNs are too rich to be efficiently learnable in high dimension

Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models

Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space: By adding the fine-tuned weights of different tasks, the model's performance can be improved on these tasks, while negating them leads to task forgetting. Yet, our understanding of the effectiveness of task arithmetic and its underlying principles remains limited. We present a comprehensive study of task arithmetic in vision-language models and show that weight disentanglement is the crucial factor that makes it effective. This property arises during pre-training and manifests when distinct directions in weight space govern separate, localized regions in function space associated with the tasks. Notably, we show that fine-tuning models in their tangent space by linearizing them amplifies weight disentanglement. This leads to substantial performance improvements across multiple task arithmetic benchmarks and diverse models. Building on these findings, we provide theoretical and empirical analyses of the neural tangent kernel (NTK) of these models and establish a compelling link between task arithmetic and the spatial localization of the NTK eigenfunctions. Overall, our work uncovers novel insights into the fundamental mechanisms of task arithmetic and offers a more reliable and effective approach to edit pre-trained models through the NTK linearization

Relative stability toward diffeomorphisms indicates performance in deep nets

Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support that it is often not the case. We revisit this question by defining a maximum-entropy distribution on diffeomorphisms, that allows to study typical diffeomorphisms of a given norm. We confirm that stability toward diffeomorphisms does not strongly correlate to performance on benchmark data sets of images. By contrast, we find that the stability toward diffeomorphisms relative to that of generic transformations $R_f$ correlates remarkably with the test error $\epsilon_t$. It is of order unity at initialization but decreases by several decades during training for state-of-the-art architectures. For CIFAR10 and 15 known architectures, we find $\epsilon_t\approx 0.2\sqrt{R_f}$, suggesting that obtaining a small $R_f$ is important to achieve good performance. We study how $R_f$ depends on the size of the training set and compare it to a simple model of invariant learning.Comment: NeurIPS 2021 Conferenc

Microplastic in drinking water: a pilot study

In recent years, microplastic pollution has been a hot topic as these compounds have been used in various production contexts such as health, food or technology due to their chemical and physical properties and “shelf-life,” making them almost indispensable products in daily life. On the other hand, they have a negative impact on the environment and, consequently, on biota and human health. It is therefore necessary to assess the actual presence of microplastics in drinking water by analysing real samples in order to estimate the possible exposure through drinking water consumption. In this pilot study, drinking water from different aqueous matrices was examined for the presence of microplastics and characterized in terms of shape, size, abundance and polymer type by Raman microspectroscopy analysis. Not all samples analysed were found to be contaminated with microplastics, indeed, some, as in the case of water kiosk samples, were found to be free of such contaminants. The results for the various matrices showed that the microplastics content ranged from less than 2 particles/L to a maximum of 5 + 1.5 particles/L, with sizes ranging from 30 to 100 μm and consisted of the most common polymers such as polyethylene, polypropylene or polyethylene terephthalate

Fatigue in Multiple Sclerosis: a resting-state EEG microstate study

Fatigue affects approximately 80% of people with Multiple Sclerosis (PwMS) and can impact several domains of daily life. However, the neural underpinnings of fatigue in MS are still not completely clear. The aim of our study was to investigate the spontaneous large-scale networks functioning associated with fatigue in PwMS using the EEG microstate approach with a spectral decomposition. Forty-three relapsing-remitting MS patients and twenty-four healthy controls (HCs) were recruited. All participants underwent an administration of Modified Fatigue Impact scale (MFIS) and a 15-min resting-state high-density EEG recording. We compared the microstates of healthy subjects, fatigued (F-MS) and non-fatigued (nF-MS) patients with MS; correlations with clinical and behavioral fatigue scores were also analyzed. Microstates analysis showed six templates across groups and frequencies. We found that in the F-MS emerged a significant decrease of microstate F, associated to the salience network, in the broadband and in the beta band. Moreover, the microstate B, associated to the visual network, showed a significant increase in fatigued patients than healthy subjects in broadband and beta bands. The multiple linear regression showed that the high cognitive fatigue was predicted by both an increase and decrease, respectively, in delta band microstate B and beta band microstate F. On the other hand, higher physical fatigue was predicted with lower occurrence microstate F in beta band. The current findings suggest that in MS the higher level of fatigue might be related to a maladaptive functioning of the salience and visual network

Inflammation-based scores in patients with pheochromocytoma

Background: Pheochromocytoma is associated with systemic inflammation, but the underlying mechanisms are unclear. Therefore, we investigated the relationship between plasma metanephrine levels and haematological parameters – as a surrogate of inflammation – in patients with pheochromocytoma and the influence of preoperative α-blockade treatment.Design and Methods: We retrospectively studied 68 patients with pheochromocytoma who underwent adrenalectomy (median age 53 years, 64.7% females) and two control groups matched for age, sex, and body mass index (BMI): 68 patients with non-functioning adrenocortical tumors (NFAT) and 53 with essential hypertension (EAH). The complete blood count (CBC) and several inflammation-based scores [Neutrophil-to-Lymphocyte Ratio (NLR), Platelet-to-Lymphocyte Ratio (PLR), Lymphocyte-to-Monocyte Ratio (LMR), Systemic-Immune-Inflammation Index (SII), Prognostic-Nutrition Index (PNI)] were assessed in all patients and, in a subset of pheochromocytomas, after adrenalectomy (n=26) and before and after preoperative α-blockade treatment (n=29).Results: A higher inflammatory state, as indicated by both CBC and inflammation-based scores, was observed in patients with pheochromocytoma compared to NFAT and EAH. Plasma metanephrine levels showed a positive correlation with NLR (r=0.4631), PLR (r=0.3174), SII (r=0.3709), and a negative correlation with LMR (r=0.4368) and PNI (r=0.3741), even after adjustment for age, sex, ethnicity, BMI and tumor size (except for PLR). After adrenalectomy, we observed a reduction in NLR (p=0.001), PLR (p=0.003), SII (p=0.004) and a concomitant increase in LMR (p=0.0002). Similarly, α-blockade treatment led to a reduction in NLR (p=0.007) and SII (p=0.03).Conclusions: Inflammation-based scores in patients with pheochromocytoma showed pro-inflammatory changes that correlated with plasma metanephrine levels and are ameliorated by adrenalectomy and α-blockade

Inside the history of Italian coloring industries. An investigation of ACNA dyes through a novel analytical protocol for synthetic dye extraction and characterization

The introduction of synthetic dyes completely changed the industrial production and use of colorants for art materials. From the synthesis of the first synthetic dye, mauveine, in 1856 until today, artists have enjoyed a wider range of colors and selection of chemical properties than was ever available before. However, the introduction of synthetic dyes introduced a wider variety and increased the complexity of the chemical structures of marketed dyes. This work looks towards the analysis of synthetically dyed objects in heritage collections, applying an extraction protocol based on the use of ammonia, which is considered favorable for natural anthraquinone dyes but has never before been applied to acid synthetic dyes. This work also presents an innovative cleanup step based on the use of an ion pair dispersive liquid–liquid microextraction for the purification and preconcentration of historical synthetic dyes before analysis. This approach was adapted from food science analysis and is applied to synthetic dyes in heritage science for the first time in this paper. The results showed adequate recovery of analytes and allowed for the ammonia-based extraction method to be applied successfully to 15 samples of suspected azo dyes from the Azienda Coloranti Nazionali e Affini (ACNA) synthetic dye collection, identified through untargeted HPLC-HRMS analyses

New advances in dye analyses. In situ gel-supported liquid extraction from paint layers and textiles for SERS and HPLC-MS/MS Identification

To date, it is still not possible to obtain exhaustive information about organic materials in cultural heritage without sampling. Nonetheless, when studying unique objects with invaluable artistic or historical significance, preserving their integrity is a priority. In particular, organic dye identification is of significant interest for history and conservation research, but it is still hindered by analytes’ low concentration and poor fastness. In this work, a minimally invasive approach for dye identification is presented. The procedure is designed to accompany noninvasive analyses of inorganic substances for comprehensive studies of complex cultural heritage matrices, in compliance with their soundness. Liquid extraction of madder, turmeric, and indigo dyes was performed directly from paint layers and textiles. The extraction was supported by hydrogels, which themselves can undergo multitechnique analyses in the place of samples. After extraction, Ag colloid pastes were applied on the gels for SERS analyses, allowing for the identification of the three dyes. For the HPLC-MS/MS analyses, re-extraction of the dyes was followed by a clean-up step that was successfully applied on madder and turmeric. The colour change perceptivity after extraction was measured with colorimetry. The results showed ΔE values mostly below the upper limit of rigorous colour change, confirming the gentleness of the procedure