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<!DOCTYPE html>
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<span class="near-black" style="font-size:36px;font-weight:bold;font-family:'Avenir', sans-serif;">TopoNets: High-Performing Vision and Language models</span>
<br>
<span class="near-black" style="font-size:36px;font-weight:bold;font-family:'Avenir', sans-serif;">with Brain-Like Topography</span>
<br>
<span class="near-black" style="font-size:23px;">ICLR 2025 Spotlight</span>
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<br>
<table align="center" width="900px">
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<td align="center" width="215px">
<center>
<span style="font-size:22px"><a href="https://mayukhdeb.github.io/"><b><strong>Mayukh Deb</strong></b></a></span>
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<span style="font-size:22px"><a href="https://mainakdeb.github.io/"><b><strong>Mainak Deb</strong></b></a></span>
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<span style="font-size:22px"><a href="https://www.murtylab.com"><b><strong>N. Apurva Ratan Murty</strong></b></a></span>
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<a style="color:inherit;text-decoration:none;font-size:13px;display:flex;align-items:center;" href="https://arxiv.org/abs/2501.16396" target="_blank">
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Paper (ArXiv)
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Openreview
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Code
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Models
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<a style="color:inherit;text-decoration:none;font-size:13px;display:flex;align-items:center;" href="https://colab.research.google.com/github/toponets/toponets.github.io/blob/main/notebooks/topoloss-demo.ipynb" target="_blank">
<img style="padding-bottom:0;padding-right:1px;height:13px" src="webpage_assets/colab.png" aria-hidden="true"></img>
Colab
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Visualize
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Bibtex
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</center> -->
<!-- <br> -->
<!-- OLD INTRO -->
<!-- <p id="teaser-description">
<span id="bold">The organization of neurons in the brain is highly structured: neurons with similar functions are located near one another. But what happens when you introduce brain-like self-similarity into vision and language models?</span>
We trained a new class of models with topographic constraints on the weights, ensuring that weights closer together encode similar features. These models replicate key topographic signatures observed in the brain's visual and language cortices while achieving lower dimensionality and increased parameter efficiency, all with minimal performance trade-offs.
</p> -->
<p id="teaser-description">
The organization of neurons in the brain is highly structured: neurons performing similar functions are located near one another. This "topographic organization" is a fundamental principle of primate brains and plays an important role in shaping the brain's representations.
<br>
<br>
<span id="bold">Here we introduce TopoLoss, a simple, scalable, and effective method for inducing brain-like topography into leading AI architectures (convolutional networks and transformers) with minimal drop in model performance. The resulting models, TopoNets, are the highest-performing supervised topographic neural networks to date.</span>
</p>
<br>
<center>
<video autoplay loop controls width="640" height="360">
<source src="webpage_assets/banner_video.mp4" type="video/mp4">
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</video>
<p>GPT-Neo-125M when trained with TopoLoss show emergence of category-selective regions</p>
</center>
<center>
<video autoplay loop controls width="600" height="300">
<source src="webpage_assets/mnist-colab-demo.mp4" type="video/mp4">
<!-- Your browser does not support the video tag. -->
</video>
<!-- <video autoplay loop controls width="600" height="300">
<source src="webpage_assets/mnist_digit_interpolation_topo_7.mp4" type="video/mp4">
</video> -->
<center>
<p>Visualizing the orientation selectivity and activation of the first layer of an MLP trained with TopoLoss on MNIST.</p>
<p>Try it out <a href="https://colab.research.google.com/github/toponets/toponets.github.io/blob/main/notebooks/topoloss-demo.ipynb" target="_blank" style="color: blue;">here on colab</a></p>
</center>
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<hr>
<!-- <center>
<h1>Abstract</h1>
</center>
<table align="center" width="900px">
<tbody>
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<td>
Neurons in the brain are organized such that nearby cells tend to share similar functions. AI models lack this organization, and past efforts to introduce topography have often led to trade-offs between topography and task performance. In this work, we present TopoLoss, a new loss function that promotes spatially organized topographic representations in AI models without significantly sacrificing task performance. TopoLoss is highly adaptable and can be seamlessly integrated into the training of leading model architectures. We validate our method on both vision (ResNet-18, ResNet-50, ViT) and language models (GPT-Neo-125M, NanoGPT), collectively TopoNets. TopoNets are the highest performing supervised topographic models to date, exhibiting brain-like properties such as localized feature processing, lower dimensionality, and increased efficiency. TopoNets also predict responses in the brain and replicate the key topographic signatures observed in the brain's visual and language cortices, further bridging the gap between biological and artificial systems. This work establishes a robust and generalizable framework for integrating topography into AI, advancing the development of high performing models that more closely emulate the computational strategies of the human brain.
</td>
</tr>
</tbody>
</table>
<br>
<hr> -->
<br>
<br>
<center>
<h1>TopoLoss is easy to install and use</h1>
</center>
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<div class="row">
<!-- PIP Installation and Preliminaries -->
<div class="col" id="pip-container" class="code-col" style="flex-direction: column;display:flex;">
<pre><code class="language-bash">pip install topoloss</code></pre>
<div style="flex-grow: 1;"></div>
<p>Usage:</p>
<pre><code class="language-python">import torchvision.models as models
from topoloss import TopoLoss, LaplacianPyramid
model = models.resnet18(weights = "DEFAULT")
topo_loss = TopoLoss(
losses = [
LaplacianPyramid.from_layer(
model=model,
layer = model.fc, ## layer to apply topoloss on
factor_h=8.0,
factor_w=8.0,
scale = 1.0 ## strength, equivalent to "tau" in the paper
),
],
)
loss = topo_loss.compute(model=model) ## add this to your training loss during training!
loss.backward()</code></pre>
</div>
</div>
</div>
<br>
<!-- <hr> -->
<!-- <center>
<h1>Method</h1>
<div class="col" id="method-figure">
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<td>
[EDIT THIS] In vision models, TopoLoss was applied to all convolutional layers within each residual block, while in the language model, TopoLoss was applied to the c_fc module of each Transformer block (highlighted in red).
</td>
</tr>
</tbody>
</table>
</center> -->
<br>
<!-- <hr> -->
<center>
<h1>Toponets achieve high performance with comparable spatial topography</h1>
<div class="col" id="method-figure">
<img class="round" src="./webpage_assets/FigureAccuracy-updated.png" style="max-width: 100%; height: auto; object-fit: contain;">
</div>
<br>
<!-- <table align="center" width="900px">
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<td>
A. Estimated model topography (smoothness, x-axis) versus model performance (y-axis) for vision models (Resnet-18 and Resnet-50). The black filled dots with the dashed gray crosshairs indicate prior models. The dashed black lines indicate the pareto-curves for Resnet-18 and Resnet-50 models. B. Same as A. but for Language models (GPT-Neo-125M). Connected lines indicate model performance for the same model across 2 independent datasets: Openwebtext (lower numbers) and BookCorpus (higher numbers). The y-axis here denotes the language model perplexity score. The dashed gray line indicates the reported topography from a prior study.
</td>
</tr>
</tbody>
</table> -->
</center>
<br>
<hr>
<center>
<h1>Topography, not model performance, drives dimensionality reductions</h1>
<div class="col" id="method-figure">
<img class="round" src="./webpage_assets/FigureDimensionality.jpg" style="max-width: 100%; height: auto; object-fit: contain;">
</div>
<br>
<!-- <table align="center" width="900px">
<tbody>
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<td>
[EDIT THIS]A. (Left) Model performance (Imagenet accuracy, x-axis) versus effective dimensionality for vision Resnets. (Right) Measured topography (smoothness) versus effective dimensionality for vision Resnets. B. Same as A, but for language transformers </td>
</tr>
</tbody>
</table> -->
</center>
<br>
<hr>
<center>
<h1>Toponets deliver sparse, parameter-efficient language models</h1>
<div class="col" id="method-figure">
<img class="round" src="webpage_assets/FigureEfficiencyNanoGPTAppendix.png" style="max-width: 100%; height: auto; object-fit: contain;">
</div>
<br>
<table align="center" width="900px">
<tbody>
<tr>
<td>
We trained a bunch of NanoGPTs with topoloss applied on the `c_fc` modules.
Models with only 20% of the parameters remaining on the on the `c_fc` modules showed no significant drop in performance.
<!-- greek tau --> τ=0 indicates the baseline model with no topoloss applied and τ=50.0 indicates the model trained with the strongest topoloss.
</td>
</tr>
</tbody>
</table>
</center>
<br>
<hr>
<center>
<h1>Category-Selective regions in resnet18 trained with TopoLoss</h1>
</center>
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Upon training a resnet18 on ImageNet with topoloss, we observed that face and body selectivities were yoked together, while scene selectivity was distinct. This pattern mimics the organization observed in the FFA, FBA, and PPA in the ventral visual cortex.
We also confirmed this quantitatively. Face scene selectivity showed a negative correlation (structural similarity = -0.41), whereas face and body selectivity were positively correlated (0.79).
Additionally, TopoNets captured similar organizational biases for real-world size and animacy (structural similarity = 0.46), as seen in the brain.
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<h1>Temporal Integration Windows in GPT-Neo-125M trained with TopoLoss</h1>
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Studies using fMRI and invasive recordings (for example: <a href="https://www.nature.com/articles/s41562-024-01944-2" target="_blank" style="color: blue;">Regev et al.</a>) have provided evidence for distinct temporal receptive fields. Based on these results, we wondered if neurons in TopoNets were clustered by their
temporal integration windows. We used a new word-swapping method from a <a href="https://openreview.net/forum?id=1EYKYJeZtR" target="_blank" style="color: blue;">recent study</a> to investigate this in TopoNets.
Green maps show neurons which integrate information over shorter (exponential) token-windows and red maps show neurons which integrate information over longer (power law) token-windows.
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<h1>Acknowledgements</h1>
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We would like to thank Anna Ivanova, Alish Dipani, Taha Binhuraib and everyone at <a href="https://www.murtylab.com" target="_blank" style="color: blue;">Murty lab</a> for their valuable feedback and support.
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<h1 name="bibtex" id="bibtex">Bibtex</h1>
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<code style="font-size: 14px;">
@inproceedings{
deb2025toponets,
title={TopoNets: High performing vision and language models with brain-like topography}, <br>
author={Mayukh Deb and Mainak Deb and Apurva Ratan Murty}, <br>
booktitle={The Thirteenth International Conference on Learning Representations}, <br>
year={2025}, <br>
url={https://openreview.net/forum?id=THqWPzL00e}
}<br>
}
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