Rongrong Xie

Rongrong Xie, Matteo Marsili

We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori} organisation of the feature space. We derive the internal representation by requiring that it satisfies the principles of maximal relevance and of maximal ignorance about how different features are combined. We show that, when hidden units are binary variables, these two principles identify a unique model -- the Hierarchical Feature Model (HFM) -- which is fully solvable and provides a natural interpretation in terms of features. We argue that learning machines with this architecture enjoy a number of interesting properties, like the continuity of the representation with respect to changes in parameters and data, the possibility to control the level of compression and the ability to support functions that go beyond generalisation. We explore the behaviour of the model with extensive numerical experiments and argue that models where the internal representation is fixed reproduce a learning modality which is qualitatively different from that of traditional models such as Restricted Boltzmann Machines.

Rongrong Xie, Guido Sanguinetti

Multimodal learning has increasingly become a focal point in research, primarily due to its ability to integrate complementary information from diverse modalities. Nevertheless, modality imbalance, stemming from factors such as insufficient data acquisition and disparities in data quality, has often been inadequately addressed. This issue is particularly prominent in biological data analysis, where datasets are frequently limited, costly to acquire, and inherently heterogeneous in quality. Conventional multimodal methodologies typically fall short in concurrently harnessing intermodal synergies and effectively resolving modality conflicts. In this study, we propose a novel unified framework explicitly designed to address modality imbalance by utilizing mutual information to quantify interactions between modalities. Our approach adopts a balanced multimodal learning strategy comprising two key stages: cross-modal knowledge distillation (KD) and a multitask-like training paradigm. During the cross-modal KD pretraining phase, stronger modalities are leveraged to enhance the predictive capabilities of weaker modalities. Subsequently, our primary training phase employs a multitask-like learning mechanism, dynamically calibrating gradient contributions based on modality-specific performance metrics and intermodal mutual information. This approach effectively alleviates modality imbalance, thereby significantly improving overall multimodal model performance.

Rongrong Xie, Yizhou Xu, Guido Sanguinetti

The rapid increase in multimodal data availability has sparked significant interest in cross-modal knowledge distillation (KD) techniques, where richer "teacher" modalities transfer information to weaker "student" modalities during model training to improve performance. However, despite successes across various applications, cross-modal KD does not always result in improved outcomes, primarily due to a limited theoretical understanding that could inform practice. To address this gap, we introduce the Cross-modal Complementarity Hypothesis (CCH): we propose that cross-modal KD is effective when the mutual information between teacher and student representations exceeds the mutual information between the student representation and the labels. We theoretically validate the CCH in a joint Gaussian model and further confirm it empirically across diverse multimodal datasets, including image, text, video, audio, and cancer-related omics data. Our study establishes a novel theoretical framework for understanding cross-modal KD and offers practical guidelines based on the CCH criterion to select optimal teacher modalities for improving the performance of weaker modalities.

Rongrong Xie, Matteo Marsili

We study a generic ensemble of deep belief networks which is parametrized by the distribution of energy levels of the hidden states of each layer. We show that, within a random energy approach, statistical dependence can propagate from the visible to deep layers only if each layer is tuned close to the critical point during learning. As a consequence, efficiently trained learning machines are characterised by a broad distribution of energy levels. The analysis of Deep Belief Networks and Restricted Boltzmann Machines on different datasets confirms these conclusions.

R. R. Xie, W. B. Deng, D. J. Wang et al.

We study the entropy of Chinese and English texts, based on characters in case of Chinese texts and based on words for both languages. Significant differences are found between the languages and between different personal styles of debating partners. The entropy analysis points in the direction of lower entropy, that is of higher complexity. Such a text analysis would be applied for individuals of different styles, a single individual at different age, as well as different groups of the population.