**$L_{1}$ Regularization** is a regularization technique applied to the weights of a neural network. We minimize a loss function compromising both the primary loss function and a penalty on the $L\_{1}$ Norm of the weights:

$$L\_{new}\left(w\right) = L\_{original}\left(w\right) + \lambda{||w||}\_{1}$$

where $\lambda$ is a value determining the strength of the penalty. In contrast to [weight decay](https://paperswithcode.com/method/weight-decay), $L_{1}$ regularization promotes sparsity; i.e. some parameters have an optimal value of zero.

Image Source: [Wikipedia](https://en.wikipedia.org/wiki/Regularization_(mathematics)#/media/File:Sparsityl1.png)

NICE-SLAM, a dense RGB-D SLAM system that combines neural implicit decoders with hierarchical grid-based representations, which can be applied to large-scale scenes.

Neural implicit representations have recently shown encouraging results in various domains, including promising progress in simultaneous localization and mapping (SLAM). Nevertheless, existing methods produce over-smoothed scene reconstructions and have difficulty scaling up to large scenes. These limitations are mainly due to their simple fully-connected network architecture that does not incorporate local information in the observations. In this paper, we present NICE-SLAM, a dense SLAM system that incorporates multi-level local information by introducing a hierarchical scene representation. Optimizing this representation with pre-trained geometric priors enables detailed reconstruction on large indoor scenes. Compared to recent neural implicit SLAM systems, our approach is more scalable, efficient, and robust. Experiments on five challenging datasets demonstrate competitive results of NICE-SLAM in both mapping and tracking quality.

NICE-SLAM

NICE-SLAM: Neural Implicit Scalable Encoding for SLAM

L1 Regularization

**modReLU** is an activation that is a modification of a [ReLU](https://paperswithcode.com/method/relu). It is a pointwise nonlinearity, $\sigma\_{modReLU}\left(z\right) : C \rightarrow C$, which affects only the absolute value of a complex number, defined as:

$$ \sigma\_{modReLU}\left(z\right) = \left(|z| + b\right)\frac{z}{|z|} \text{ if } |z| + b \geq 0 $$
$$ \sigma\_{modReLU}\left(z\right) = 0 \text{ if } |z| + b \leq 0 $$

where $b \in \mathbb{R}$ is a bias parameter of the nonlinearity. For a $n\_{h}$ dimensional hidden space we learn $n\_{h}$ nonlinearity bias parameters, one per dimension.

Year	1986
Data Source	CC BY-SA - https://paperswithcode.com