Breaking Bottlenecks: Reshaping Neural Network Outputs

Neural networks are like overworked assembly lines, churning low-dimensional data into vast output spaces. Linear output layers become their glass ceiling, confining what these models can do. It's a rank bottleneck, especially visible in link prediction models like knowledge graph embeddings (KGEs). Here, the output space of entities can dwarf the embedding dimension. That's like trying to fit an elephant into a shoebox.

Why Rank Bottlenecks Matter

Linear output layers are the usual suspect limiting model expressivity. The larger and more connected a graph, the stricter the confines. Prior research looked at how big the embedding dimension needs to be for specific KGEs. But here's the twist: we've uncovered the necessary bounds for all KGEs with a linear output layer. And guess what? They balloon with graph size and connectivity. Think your model's doing fine? Zoom out. No, further. See it now?

Breaking Free with Non-Linearity

Now, let's shake things up. Non-linear output layers can shatter this bottleneck without adding a ton of parameters. Imagine a layer using mixtures that improves the model's ranking performance and fits better probabilistically on large datasets. This isn't just theory. It's backed by data. And it doesn't cost you an arm and a leg parameters. Everyone has a plan until liquidation hits. But neural networks, non-linear layers might just be the plan that prevails.

The Future: Unbound Neural Networks?

So why should you care? If you're relying on neural networks for meaningful insights, this shift could mean the difference between mediocrity and breakthrough. Linear output layers are the funding rate lying to you again, keeping your models from reaching their full potential. By embracing non-linearity, we can scale to large, dense graphs without getting lost in a sea of overextended parameters. The data already knows it ends badly for traditional linear layers. Are we ready to act on what the numbers are telling us?