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Loss functions for classification

Résumé

In machine learning and mathematical optimization, loss functions for classification are computationally feasible loss functions representing the price paid for inaccuracy of predictions in classification problems (problems of identifying which category a particular observation belongs to). Given \mathcal{X} as the space of all possible inputs (usually \mathcal{X} \subset \mathbb{R}^d), and \mathcal{Y} = { -1,1 } as the set of labels (possible outputs), a typical goal of classification algorithms is to find a function f: \mathcal{X} \to \mathcal{Y} which best predicts a label y for a given input \vec{x}. However, because of incomplete information, noise in the measurement, or probabilistic components in the underlying process, it is possible for the same \vec{x} to generate different y. As a result, the goal of the learning problem is to minimize expected loss (also known as t

Source officielle

https://en.wikipedia.org/wiki/Loss_functions_for_classification

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Chargement

Resolution-robust Large Mask In painting with Fourier Convolutions

Anastasia Remizova

Modern image inpainting systems, despite the significant progress, often struggle with large missing areas, complex geometric structures, and high-resolution images. We find that one of the main reasons for that is the lack of an effective receptive field in both the inpainting network and the loss function. To alleviate this issue, we propose a new method called large mask inpainting (LaMa). LaMa is based on i) a new inpainting network architecture that uses fast Fourier convolutions (FFCs), which have the imagewide receptive field; ii) a high receptive field perceptual loss; iii) large training masks, which unlocks the potential of the first two components. Our inpainting network improves the state-of-the-art across a range of datasets and achieves excellent performance even in challenging scenarios, e.g. completion of periodic structures. Our model generalizes surprisingly well to resolutions that are higher than those seen at train time, and achieves this at lower parameter&time costs than the competitive baselines. The code is available at https://github.com/saic-mdal/lama.

IEEE COMPUTER SOC2022

Chargement

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Johanni Michael Brea, Wulfram Gerstner, Clément Hongler, Berfin Simsek, Francesco Spadaro

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at

r_1^*! \cdots r_{L-1}^*!

isolated points that are permutations of one another, we show that adding one extra neuron to each layer is sufficient to connect all these previously discrete minima into a single manifold. For a two-layer overparameterized network of width

r^*+ h =: m

we explicitly describe the manifold of global minima: it consists of

T(r^*, m)

affine subspaces of dimension at least

h

that are connected to one another. For a network of width

m

, we identify the number

G(r,m)

of affine subspaces containing only symmetry-induced critical points that are related to the critical points of a smaller network of width

r&lt;r^*

. Via a combinatorial analysis, we derive closed-form formulas for

T

and

G

and show that the number of symmetry-induced critical subspaces dominates the number of affine subspaces forming the global minima manifold in the mildly overparameterized regime (small

h

) and vice versa in the vastly overparameterized regime (

h \gg r^*

). Our results provide new insights into the minimization of the non-convex loss function of overparameterized neural networks.

2021

Chargement

, ,

Point cloud imaging has emerged as an efficient and popular solution to represent immersive visual information. However, the large volume of data generated in the acquisition process reveals the need of efficient compression solutions in order to store and transmit such contents. Several standardization committees are in the process of finalizing efficient compression schemes to cope with the large volume of information that point clouds require. At the same time, recent efforts on learning-based compression approaches have been shown to exhibit good performance in the coding of conventional image and video contents. It is currently an open question how learning-based coding performs when applied to point cloud data. In this study, we extend recent efforts on the matter by exploring neural network implementations for separate, or joint compression of geometric and textural information from point cloud contents. Two alternative architectures are presented and compared; that is, a unified model that learns to encode point clouds in a holistic way, allowing fine-tuning for quality preservation per attribute, and a second paradigm consisting of two cascading networks that are trained separately to encode geometry and color, individually. A baseline configuration from the best-performing option is compared to the MPEG anchor, showing better performance for geometry and competitive performance for color encoding at low bit-rates. Moreover, the impact of a series of parameters is examined on the network performance, such as the selection of input block resolution for training and testing, the color space, and the loss functions. Results provide guidelines for future efforts in learning-based point cloud compression.

2020

Chargement

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Johanni Michael Brea, Wulfram Gerstner, Clément Hongler, Berfin Simsek, Francesco Spadaro

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at

r_1^*! \cdots r_{L-1}^*!

r^*+ h =: m

we explicitly describe the manifold of global minima: it consists of

T(r^*, m)

affine subspaces of dimension at least

h

that are connected to one another. For a network of width

m

, we identify the number

G(r,m)

of affine subspaces containing only symmetry-induced critical points that are related to the critical points of a smaller network of width

r&lt;r^*

. Via a combinatorial analysis, we derive closed-form formulas for

T

and

G

and show that the number of symmetry-induced critical subspaces dominates the number of affine subspaces forming the global minima manifold in the mildly overparameterized regime (small

h

) and vice versa in the vastly overparameterized regime (

h \gg r^*

). Our results provide new insights into the minimization of the non-convex loss function of overparameterized neural networks.

2021