1,720,986 research outputs found
Neural networks trained with SGD learn distributions of increasing complexity
Full text linkThe ability of deep neural networks to generalise well even when they
interpolate their training data has been explained using various "simplicity
biases". These theories postulate that neural networks avoid overfitting by
first learning simple functions, say a linear classifier, before learning more
complex, non-linear functions. Meanwhile, data structure is also recognised as
a key ingredient for good generalisation, yet its role in simplicity biases is
not yet understood. Here, we show that neural networks trained using stochastic
gradient descent initially classify their inputs using lower-order input
statistics, like mean and covariance, and exploit higher-order statistics only
later during training. We first demonstrate this distributional simplicity bias
(DSB) in a solvable model of a neural network trained on synthetic data. We
empirically demonstrate DSB in a range of deep convolutional networks and
visual transformers trained on CIFAR10, and show that it even holds in networks
pre-trained on ImageNet. We discuss the relation of DSB to other simplicity
biases and consider its implications for the principle of Gaussian universality
in learning.Comment: Source code available at https://github.com/sgoldt/dist_inc_com
Fine-tuning Neural Network Quantum States
Full text linkRecent progress in the design and optimization of neural-network quantum states (NQSs) has made them an effective method to investigate ground-state properties of quantum many-body systems. In contrast to the standard approach of training a separate NQS from scratch at every point of the phase diagram, we demonstrate that the optimization of a NQS at a highly expressive point of the phase diagram (i.e., close to a phase transition) yields features that can be reused to accurately describe a wide region across the transition. We demonstrate the feasibility of our approach on different systems in one and two dimensions by initially pretraining a NQS at a given point of the phase diagram, followed by fine-tuning only the output layer for all other points. Notably, the computational cost of the fine-tuning step is very low compared to the pretraining stage. We argue that the reduced cost of this paradigm has significant potential to advance the exploration of strongly-correlated systems using NQS, mirroring the success of fine-tuning in machine learning and natural language processing.8 pages (including Appendix), 7 figure
Analysing the dynamics of online learning in over-parameterised two-layer neural networks
No full textMapping of attention mechanisms to a generalized Potts model
Full text linkTransformers are neural networks that revolutionized natural language
processing and machine learning. They process sequences of inputs, like words,
using a mechanism called self-attention, which is trained via masked language
modeling (MLM). In MLM, a word is randomly masked in an input sequence, and the
network is trained to predict the missing word. Despite the practical success
of transformers, it remains unclear what type of data distribution
self-attention can learn efficiently. Here, we show analytically that if one
decouples the treatment of word positions and embeddings, a single layer of
self-attention learns the conditionals of a generalized Potts model with
interactions between sites and Potts colors. Moreover, we show that training
this neural network is exactly equivalent to solving the inverse Potts problem
by the so-called pseudo-likelihood method, well known in statistical physics.
Using this mapping, we compute the generalization error of self-attention in a
model scenario analytically using the replica method.Comment: 5 pages, 3 figure
Bayesian reconstruction of memories stored in neural networks from their connectivity
Full text linkThe advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in a recurrent network of neurons, given its synaptic connectivity matrix. Here, we address this question by determining when solving such an inference problem is theoretically possible in specific attractor network models and by providing a practical algorithm to do so. The algorithm builds on ideas from statistical physics to perform approximate Bayesian inference and is amenable to exact analysis. We study its performance on three different models, compare the algorithm to standard algorithms such as PCA, and explore the limitations of reconstructing stored patterns from synaptic connectivity
Quantifying lottery tickets under label noise: accuracy, calibration, and complexity
No full textPruning deep neural networks is a widely used strategy to alleviate the computational burden in machine learning. Overwhelming empirical evidence suggests that pruned models retain very high accuracy even with a tiny fraction of parameters. However, relatively little work has gone into characterising the small pruned networks obtained, beyond a measure of their accuracy. In this paper, we use the sparse double descent approach to identify univocally and characterise pruned models associated with classification tasks. We observe empirically that, for a given task, iterative magnitude pruning (IMP) tends to converge to networks of comparable sizes even when starting from full networks with sizes ranging over orders of magnitude. We analyse the best pruned models in a controlled experimental setup and show that their number of parameters reflects task difficulty and that they are much better than full networks at capturing the true conditional probability distribution of the labels. On real data, we similarly observe that pruned models are less prone to overconfident predictions. Our results suggest that pruned models obtained via IMP not only have advantageous computational properties but also provide a better representation of uncertainty in learning
Redundant representations help generalization in wide neural networks
Full text linkDeep neural networks (DNNs) defy the classical bias-variance trade-off:
adding parameters to a DNN that interpolates its training data will typically
improve its generalization performance. Explaining the mechanism behind this
``benign overfitting'' in deep networks remains an outstanding challenge. Here,
we study the last hidden layer representations of various state-of-the-art
convolutional neural networks and find that if the last hidden representation
is wide enough, its neurons tend to split into groups that carry identical
information, and differ from each other only by statistically independent
noise. The number of such groups increases linearly with the width of the
layer, but only if the width is above a critical value. We show that redundant
neurons appear only when the training process reaches interpolation and the
training error is zero
Attacks on Online Learners: a Teacher-Student Analysis
No full textMachine learning models are famously vulnerable to adversarial attacks: small adhoc perturbations of the data that can catastrophically alter the model predictions.
While a large literature has studied the case of test-time attacks on pre-trained
models, the important case of attacks in an online learning setting has received
little attention so far. In this work, we use a control-theoretical perspective to study
the scenario where an attacker may perturb data labels to manipulate the learning
dynamics of an online learner. We perform a theoretical analysis of the problem
in a teacher-student setup, considering different attack strategies, and obtaining
analytical results for the steady state of simple linear learners. These results enable
us to prove that a discontinuous transition in the learner’s accuracy occurs when
the attack strength exceeds a critical threshold. We then study empirically attacks
on learners with complex architectures using real data, confirming the insights of
our theoretical analysis. Our findings show that greedy attacks can be extremely
efficient, especially when data stream in small batche
Continual Learning in the Teacher-Student Setup: Impact of Task Similarity
Full text linkContinual learning—the ability to learn many tasks in sequence—is critical for artificial learning systems. Yet standard training methods for deep networks often suffer from catastrophic forgetting, where learning new tasks erases knowledge of the earlier tasks. While catastrophic forgetting labels the problem, the theoretical reasons for interference between tasks remain unclear. Here, we attempt to narrow this gap between theory and practice by studying continual learning in the teacher-student setup. We extend previous analytical work on two-layer networks in the teacher-student setup to multiple teachers. Using each teacher to represent a different task, we investigate how the relationship between teachers affects the amount of forgetting and transfer exhibited by the student when the task switches. In line with recent work, we find that when tasks depend on similar features, intermediate task similarity leads to greatest forgetting. However, feature similarity is only one way in which tasks may be related. The teacher-student approach allows us to disentangle task similarity at the level of \textbackslashemphreadouts (hidden-to-output weights) as well as \textbackslashemphfeatures (input-to-hidden weights). We find a complex interplay between both types of similarity, initial transfer/forgetting rates, maximum transfer/forgetting, and the long-time (post-switch) amount of transfer/forgetting. Together, these results help illuminate the diverse factors contributing to catastrophic forgetting
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