Neurips 2025 Day 3

My notes on Day 3 of NeurIPS 2025. Wanted to wait till when they were more polished, but after three months I’m just posting as is.

Poster Session 3

Asks whether spike-frequency adaptation and lateral inhibition in the fly olfactory system are redundant or complementary
Tests a baseline model (no SFA or LI), against models with just one, and the full model

Coherent sets: subsets of state-space that move together in time.
Neurons, brains want to find representations that track such states.
Koopman operator: Linear operator in high-dimensional space that reports future state of an observable.
- Linearity means we can write it as $$K_\tau = \sum_{i=0} ^\infty e^{\lambda_i \tau} u_i v_i^T.$$
Maximize P(f(X(t+\tau)) \in B | f(X(t)) \in A) + P(f(X(t+\tau)) \in B^c | f(X(t)) \in A^c)
Use the observable that
TBC

The problem: linking structural connectivity and functional connectivity.
Both connectivities live on the manifold of symmetric, positive-definite matrices (SPD).
Can link them using flows along geodesics on the manifold.
The same structural connectivity will lead to different functional connectivities during different tasks.
Conversely, functional connectivity produced in different tasks should lead back to the same structural connectivity.
Problem: Computing flows on the SPD manifold is computationally expensive.
PSD manifold can be linked to the manifold of lower triangular matrices by the Cholesky decomposition.
Recent work shows computation on the Cholesky manifold is much easier.
Solution: Leveraged this recent work to compute flows linking structure and function on the cholesky manifold.

To get flows from different FC back to the same SC, they add a term that penalizes differences in the Cholesky manifold states.

Measured dimensionality of representations across layers in both humans (fMRI data) and ANNs.
Use both linear dimensionality (participation ratio) and non-linear dimensionality, defined as below.
- As a side note, see Mackay and Gharamani’s note on this estimator.

The authors found that in humans both measures increase as one moves from V1 towards ventral stream.
In ANNs, intrinsic dimensionality seems to peak at intermediate layers.

Suggests that deep-layers in ANN may be compressing their representations, losing abstraction ability.
- Though interestingly the peak still happens at a higher value than in humans.

Notice how inputs modify the parameters, instead of coming in as the usual additive $Bu_t$ terms.
GP priors on each element of $\mathbf{A, b, C, d}$.
Get all the benefits of linear systems for inference, prediction etc.
Can learn parameters with EM:
- E-step: Use current parameter estimates to infer latent states.
- M-step: Solve for parameters by finding coefficients in fixed GP basis.
  - Closed form when assuming Gaussian noise.
Can be seen as conditions specific linearizations of the dynamics.
Temporal correlation of GP prior can be tuned to capture interesting limits:
- When time constants are small, learns independent, per-condition dynamics.
- When time constants are infinite, fits a fixed, time-invariant linear dynamics (the classical case).

Neural networks (e.g. autoencoders) trained on different samples of the same data often learn similar internal representations.
These can often be aligned with simple linear transformations.
Suggests that the same underlying manifold is being parameterized.
One canonicalization is to not represent the latents in absolute terms, but in relative terms using distances to certain anchor points.
Previously this has been done using cosine similarity.
This work: the decoder implicitly defines a pullback metric on the latent space.
Instead of cosine distance, use geodesic distance defined by this metric.