Neurosciences and sparsity

Laurent Perrinet

Séminaire à l’atelier “IA embarquée” du PEPR IA

[2026-01-29]

Sparse representations in computer vision

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Neurosciences and sparsity: a survey

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Neurosciences and sparsity: a survey

Neurosciences and sparsity: a survey

Neurosciences and sparsity: a survey

Neurosciences and sparsity: a survey

Neurosciences and sparsity: a survey

Neurosciences and sparsity

Neurosciences and sparsity

Neurosciences and sparsity

Neurosciences and sparsity

Neurosciences and sparsity

Sparse representations in a nutshell

Sparse representations in a nutshell

Sparse representations in a nutshell

Sparse representations in a nutshell

Generative model of image synthesis:

$I[x, y] = $ $\sum_{i=1}^{K} a[i] \cdot \phi[i, x, y]$ $ + \varepsilon[x, y]$ Where $\phi$ is a dictionary of $K$ atoms, $a$ is a sparse vector of coefficients, and $\varepsilon$ is a noise term.

[LP (2015)]

Sparse representations in a nutshell

Sparse representations in a nutshell

Given an observation $I$,

$$ \begin{aligned} \mathcal{L}(a) & = - \log Pr( a | I ) \\ \end{aligned} $$

Sparse representations in a nutshell

Given an observation $I$,

$$ \begin{aligned} \mathcal{L}(a) & = - \log Pr( a | I ) \\ & = - \log Pr( I | a ) - \log Pr(a) \\ \end{aligned} $$

Sparse representations in a nutshell

Given an observation $I$,

$$ \begin{aligned} \mathcal{L}(a) & = - \log Pr( a | I ) \\ & = - \log Pr( I | a ) - \log Pr(a) \\ & = \frac{1}{2\sigma_n^2} \sum_{x, y} ( I[x, y] - \sum_{i=1}^{K} a[i] \cdot \phi[i, x, y])^2 - \sum_{i=1}^{K} \log Pr( a[i] ) \end{aligned} $$

Sparse representations in a nutshell

The problem is formalized as an optimization problem $a^\ast = \arg \min_a \mathcal{L}(a)$ with:

$$ \mathcal{L} = \frac{1}{2} \sum_{x, y} ( I[x, y] - \sum_{i=1}^{K} a[i] \cdot \phi[i, x, y])^2 + \lambda \cdot \sum_i ( a[i] \neq 0) $$

[LP (2015)]

Sparse representations in a nutshell

The problem is formalized as an optimization problem $a^\ast = \arg \min_a \mathcal{L}(a)$ with:

$$ \mathcal{L}(a) = \frac{1}{2} \sum_{x, y} ( I[x, y] - \sum_{i=1}^{K} a[i] \cdot \phi[i, x, y])^2 + \lambda \cdot \sum_{i=1}^{K} | a[i] | $$

Sparse representations in a nutshell

Sparse representations and learning

Convolutional Sparse Coding

Convolutional Sparse Coding

CNN: Predictive processing

CNN: Predictive processing

CNN: Predictive processing

CNN: Predictive processing

CNN: Predictive processing

SNN in neuromorphic engineering

SNN in neuromorphic engineering

SNN in neuromorphic engineering

SNN in neuromorphic engineering