In linear algebra, functional analysis, and related areas of mathematics, a **norm (l-norms)** is a function that assigns a strictly positive *length* or *size* to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A **seminorm**, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

**L1-Norm loss function is known as least absolute deviations (LAD).**

It is basically minimizing the sum of the absolute differences between the target value and the estimated values .

**L2-Norm loss function is known as least squares error (LSE).**

It is basically minimizing the sum of the square of the differences between the target value and the estimated values

**Differences between L1-L2 norm**

The differences of L1-norm and L2-norm as a loss function are the following.

L1-norm |
L2-norm |

Robust | Not robust |

Unstable solution | Stable solution |

Possible multiple solutions | Only one solution |