Cosine Similarity: The Misleading Metric in ML Models

Cosine similarity, a favored tool among machine learning practitioners for gauging vector similarity, comes under scrutiny when applied to softmax classifiers. While it's often assumed that this measure can reflect model behavior, recent findings suggest otherwise.

The Case Against Cosine

The common practice of using cosine similarity to interpret neural network model behaviors doesn't hold water softmax classifiers. Researchers have proven that, despite the cosine similarity between label representations, or "unembeddings," predictions remain unaffected. In essence, you could craft two models with identical output probabilities, yet vastly different cosine similarity scores. One might wonder, if cosine similarity isn't reliable, what's the alternative?

Consider this: even when two label representations of a softmax model exhibit a similarity of 1 or -1, their predictive capabilities can mirror each other. Translation ambiguity, as termed by researchers, is at the heart of the issue. While centering label representations can mitigate this to some extent, it doesn't ensure accuracy. This raises an important question: why do we persist with a measure that can't guarantee reliable insights into model behavior?

What They're Not Telling You

Here's what often goes unsaid: the appeal of cosine similarity lies in its simplicity, not its accuracy. It's tempting to rely on straightforward metrics, especially when they seemingly offer a direct insight into complex models. But color me skeptical. In practice, these metrics often lead us astray more than they guide us.

Even when efforts are made to fix representation lengths, the results remain unreliable. High or low cosine similarity fails to consistently predict label probability for given inputs. The claim that cosine similarity can be a dependable indicator doesn't survive scrutiny when faced with the empirical evidence provided by this research.

The Path Forward

So, where do we go from here? Well, it's time to rethink our reliance on cosine similarity as a measure of model performance. Machine learning practitioners must employ more rigorous evaluation methods that truly reflect the intricacies of model behavior. It's about time we stop chasing shadows and start demanding metrics that provide real, actionable insights.

Given the evidence, one can't help but wonder: if such a popular metric can be misleading, how many other accepted truths in machine learning require re-examination? For those committed to advancing model accuracy and understanding, this revelation serves as a stark reminder to question the status quo.