相关论文: Associative Memory in Iterated Overparameterized S…

Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing and controlling the network Jacobian. We first provide a…

The Neural Tangent Kernel (NTK) framework explains optimization in over-parameterized neural networks via approximately linearized dynamics, yielding exponential convergence guarantees. However, existing results are often overly pessimistic…

Understanding how the brain encodes stimuli has been a fundamental problem in computational neuroscience. Insights into this problem have led to the design and development of artificial neural networks that learn representations by…

Despite their prevalence in deep-learning communities, over-parameterized models convey high demands of computational costs for proper training. This work studies the fine-grained, modular-level learning dynamics of over-parameterized…

Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In…

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…

Neural networks are known for their ability to approximate smooth functions, yet they fail to generalize perfectly to unseen inputs when trained on discrete operations. Such operations lie at the heart of algorithmic tasks such as…

Larger and deeper networks generalise well despite their increased capacity to overfit. Understanding why this happens is theoretically and practically important. One recent approach looks at the infinitely wide limits of such networks and…

A recent line of work has shown that an overparametrized neural network can perfectly fit the training data, an otherwise often intractable nonconvex optimization problem. For (fully-connected) shallow networks, in the best case scenario,…

Deep linear networks trained with gradient descent yield low rank solutions, as is typically studied in matrix factorization. In this paper, we take a step further and analyze implicit rank regularization in autoencoders. We show greedy…

This work focuses on the training dynamics of one associative memory module storing outer products of token embeddings. We reduce this problem to the study of a system of particles, which interact according to properties of the data…

Humans learn and form memories in stochastic environments. Auto-associative memory systems model these processes by storing patterns and later recovering them from corrupted versions. Here, memories are learned by associating each pattern…

This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel methods tied to the neural tangent kernel theory, the diagonal…

Matching animal-like flexibility in recognition and the ability to quickly incorporate new information remains difficult. Limits are yet to be adequately addressed in neural models and recognition algorithms. This work proposes a…

The NTK is a widely used tool in the theoretical analysis of deep learning, allowing us to look at supervised deep neural networks through the lenses of kernel regression. Recently, several works have investigated kernel models for…

We provide new theoretical insights on why over-parametrization is effective in learning neural networks. For a $k$ hidden node shallow network with quadratic activation and $n$ training data points, we show as long as $ k \ge \sqrt{2n}$,…

Self-supervised pre-training methods have brought remarkable breakthroughs in the understanding of text, image, and speech. Recent developments in genomics has also adopted these pre-training methods for genome understanding. However, they…

Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for…

Small generalization errors of over-parameterized neural networks (NNs) can be partially explained by the frequency biasing phenomenon, where gradient-based algorithms minimize the low-frequency misfit before reducing the high-frequency…

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…