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A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we…

The success of neural networks over the past decade has established them as effective models for many relevant data generating processes. Statistical theory on neural networks indicates graceful scaling of sample complexity. For example,…

Over the past decade, deep neural networks have proven to be adept in image classification tasks, often surpassing humans in terms of accuracy. However, standard neural networks often fail to understand the concept of hierarchical…

Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has…

An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction, which is believed to be a key factor to their superior empirical performance. To better…

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…

The realization of complex classification tasks requires training of deep learning (DL) architectures consisting of tens or even hundreds of convolutional and fully connected hidden layers, which is far from the reality of the human brain.…

Geometry-aware optimization algorithms, such as Muon, have achieved remarkable success in training deep neural networks (DNNs). These methods leverage the underlying geometry of DNNs by selecting appropriate norms for different layers and…

In theoretical ML, the teacher-student paradigm is often employed as an effective metaphor for real-life tuition. The above scheme proves particularly relevant when the student network is overparameterized as compared to the teacher…

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven…

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are latent. There are no theoretically well justified model selection criteria for HLC models in particular and…

We propose a soft gradient boosting framework for sequential regression that embeds a learnable linear feature transform within the boosting procedure. At each boosting iteration, we train a soft decision tree and learn a linear input…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Differentiable physical networks provide a simple setting in which learning can be studied through the interaction between trainable parameters and physical equilibrium constraints. We investigate sequential learning in differentiable…

The study of the distribution of volumes associated to the internal representations of learning examples allows us to derive the critical learning capacity ($\alpha_c=\frac{16}{\pi} \sqrt{\ln K}$) of large committee machines, to verify the…

Near an optimal learning point of a neural network, the learning performance of gradient descent dynamics is dictated by the Hessian matrix of the loss function with respect to the network parameters. We characterize the Hessian…

We study the complexity of training neural network models with one hidden nonlinear activation layer and an output weighted sum layer. We analyze Gradient Descent applied to learning a bounded target function on $n$ real-valued inputs. We…

Transformers have recently revolutionized many domains in modern machine learning and one salient discovery is their remarkable in-context learning capability, where models can solve an unseen task by utilizing task-specific prompts without…

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

We scrutinize the structural and operational aspects of deep learning models, particularly focusing on the nuances of learnable parameters (weight) statistics, distribution, node interaction, and visualization. By establishing correlations…