The Contour Proposal Network (CPN) detects possibly overlapping objects in an image while simultaneously fitting pixel-precise closed object contours. The CPN can incorporate state of the art object detection architectures as backbone networks into a fast single-stage instance segmentation model that can be trained end-to-end.

A **Projection Discriminator** is a type of discriminator for generative adversarial networks. It is motivated by a probabilistic model in which the distribution of the conditional variable $\textbf{y}$ given $\textbf{x}$ is discrete or uni-modal continuous distributions.

If we look at the original solution for the loss function $\mathcal{L}\_{D}$ in the vanilla GANs, we can decompose it into the sum of two log-likelihood ratios:

$$ f^{*}\left(\mathbf{x}, \mathbf{y}\right) = \log\frac{q\left(\mathbf{x}\mid{\mathbf{y}}\right)q\left(\mathbf{y}\right)}{p\left(\mathbf{x}\mid{\mathbf{y}}\right)p\left(\mathbf{y}\right)} = \log\frac{q\left(\mathbf{y}\mid{\mathbf{x}}\right)}{p\left(\mathbf{y}\mid{\mathbf{x}}\right)} + \log\frac{q\left(\mathbf{x}\right)}{p\left(\mathbf{x}\right)}  = r\left(\mathbf{y\mid{x}}\right) + r\left(\mathbf{x}\right) $$

We can model the log likelihood ratio $r\left(\mathbf{y\mid{x}}\right)$ and  $r\left(\mathbf{x}\right)$ by some parametric functions $f\_{1}$ and $f\_{2}$ respectively. If we make a standing assumption that $p\left(y\mid{x}\right)$ and $q\left(y\mid{x}\right)$ are simple distributions like those that are Gaussian or discrete log linear on the feature space, then the parametrization of the following form becomes natural:

$$ f\left(\mathbf{x}, \mathbf{y}; \theta\right) = f\_{1}\left(\mathbf{x}, \mathbf{y}; \theta\right) + f\_{2}\left(\mathbf{x}; \theta\right) = \mathbf{y}^{T}V\phi\left(\mathbf{x}; \theta\_{\phi}\right) + \psi\left(\phi(\mathbf{x}; \theta\_{\phi}); \theta\_{\psi}\right) $$

where $V$ is the embedding matrix of $y$, $\phi\left(·, \theta\_{\phi}\right)$ is a vector output function of $x$, and $\psi\left(·, \theta\_{\psi}\right)$ is a scalar function of the same $\phi\left(\mathbf{x}; \theta\_{\phi}\right)$ that appears in $f\_{1}$. The learned parameters $\theta = ${$V, \theta\_{\phi}, \theta\_{\psi}$} are trained to optimize the adversarial loss. This model of the discriminator is the projection.

Projection Discriminator

cGANs with Projection Discriminator

Contour Proposal Networks for Biomedical Instance Segmentation

**LLaMA** is a collection of foundation language models ranging from 7B to 65B parameters. It is based on the transformer architecture with various improvements that were subsequently proposed. The main difference with the original architecture are listed below.

- RMSNorm normalizing function is used to improve the training stability, by normalizing the input of each transformer sub-layer, instead of normalizing the output.
- The ReLU non-linearity is replaced by the SwiGLU activation function to improve performance.
- Absolute positional embeddings are removed and instead rotary positional embeddings (RoPE) are added at each layer of the network.

Source	Contour Proposal Networks for Biomedical Instance Segmentation
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com