On the Shape of Brainscores for Large Language Models (LLMs)

TL;DR

The paper tackles how to meaningfully interpret the Brainscore metric that aligns LLM representations with human brain activity. It introduces a topological feature framework based on Persistent Homology and $q$-Wasserstein distances to compare fMRI data and LLM embeddings, then uses cross-validated Linear Regression to identify reliable, interpretable feature combinations across ROIs and hemispheres. The results reveal distinct feature sets that aid Brainscore interpretation, while highlighting limitations in predictive power and suggesting directions to improve stability, including tuning $q$, $p$, and regression approaches. Overall, the work advances interpretable cross-domain analysis between neural data and large language models, with potential implications for developing brain-like AI representations and evaluation metrics.

Abstract

With the rise of Large Language Models (LLMs), the novel metric "Brainscore" emerged as a means to evaluate the functional similarity between LLMs and human brain/neural systems. Our efforts were dedicated to mining the meaning of the novel score by constructing topological features derived from both human fMRI data involving 190 subjects, and 39 LLMs plus their untrained counterparts. Subsequently, we trained 36 Linear Regression Models and conducted thorough statistical analyses to discern reliable and valid features from our constructed ones. Our findings reveal distinctive feature combinations conducive to interpreting existing brainscores across various brain regions of interest (ROIs) and hemispheres, thereby significantly contributing to advancing interpretable machine learning (iML) studies. The study is enriched by our further discussions and analyses concerning existing brainscores. To our knowledge, this study represents the first attempt to comprehend the novel metric brainscore within this interdisciplinary domain.

Figures (92)

• Figure 1: This figure delineates the four steps of our proposed approach: (1) Extracting data representations from human fMRI and diverse LLMs, (2) Characterising those data representations by Persistent Homology, (3) Constructing features by computing $q$-Wasserstein Distances between pairs of Persistence Diagrams, and (4) Systematically filter in reliable and valid features by learning Linear Regression Models with statistical analyses.
• Figure 2: The original images are from https://www.ndcn.ox.ac.uk/divisions/fmrib/what-is-fmri/introduction-to-fmri. The image on the left is a typical research scanner that has a field strength of 3 teslas (T), about 50,000 times greater than the Earth’s field. The right one is the result of an fMRI experiment, and the processed image is the brain's "activation map" during the experiment.
• Figure 3: The original figures are from https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-persistence-diagrams.ipynb, and also appear in chazal2021introduction and hashemi2024deep. a) For the radius $r = 0$, the union of balls is reduced to the initial finite set of point, each of them corresponding to a $0$-dimensional feature, i.e. a connected component; an interval is created for the birth for each of these features at $r = 0$. b) Some of the balls started to overlap resulting in the death of some connected components that get merged together; the persistence diagram keeps track of these deaths, putting an end point to the corresponding intervals as they disappear. c) New components have merged giving rise to a single connected component and, so, all the intervals associated to a $0$-dimensional feature have been ended, except the one corresponding to the remaining components; two new $1$-dimensional features, have appeared resulting in two new intervals (in blue) starting at their birth scale. d) One of the two $1$-dimensional cycles has been filled, resulting in its death in the filtration and the end of the corresponding blue interval. e) all the $1$-dimensional features have died, it only remains the long (and never dying) red interval. The final barcode can also be equivalently represented as a persistence diagram where every interval $(a,b)$ is represented by the the point of coordinate $(a,b)$ in $\mathbb{R}$. Intuitively the longer is an interval in the barcode or, equivalently the farther from the diagonal is the corresponding point in the diagram, the more persistent, and thus relevant, is the corresponding homological feature across the filtration.
• Figure 4: The figure on the left is originally from nakazato2021geometrical, which is a schematic of the $L^2$-Wasserstein distance. They here consider optimal transport from the probability distribution $p(\mathbf{x})$ to the probability distribution $p(\mathbf{y})$. The length of the green arrow shows the optimal transportation distance $||\mathbf{x} - \mathcal{T}_{p \to q}(\mathbf{x})||$, and the square of the $L^2$-Wasserstein distance is given by the expected value of the square of its optimal transportation distance. The plot on the right, originally from zhang2021time, shows that the Wasserstein distance is the sum of $p$-th power of the distance between all points matching two persistence diagrams. If no corresponding matching point is found, it will match to diagonal.
• Figure 5: The averaged fMRI for the whole brain mask for the task: "Pie Man"