Cosyne 2026

My running notes from Cosyne 2026. Most were hastily written during/immediately after live presentations, so likely contain errors reflecting my misunderstandings. Apologies to the presenters.

Poster Session 1

007 Convergent motifs of early olfactory processing

• Vertebrate and invertebrate olfactory systems are similar, but not derived from a common ancestor, implies convergent evolution.
• Question: Can the structure of the olfactory system be determined normatively?
• Model
  • Sparse monomolecular concentration vectors $\cc$
  • Sensed by receptors with affinities $\WW$.
  • Expressed, not necessarily one-to-one, in ORNs according to $\bE$.
  • Hill transformed, plus isotropic additive noise, to give ORN responses.$$ \rr = \varphi(\bE \WW \cc) + \eta.$$
  • ORN responses converge, not necessarily one to one, on glomeruli
• Learned parameters of the Hill function, and mappings of ORs to ORNs, to maximize mutual information between odours and responses.
  • I think there was an energetic cost somewhere as well.
• Found the 1-1 mapping from ORs to ORNs ($\bE \approx \II$).
• Downstream: found 1-1 mapping from ORNs to glomeruli.
• Dicussion: These results depend strongly on the assumed structure of the noise.

063
Sparse glomerular representations explain odor discrimination in complex, concentration-varying mixtures

• 2AFC task with one target monomolecular odour among up to 16 distractor odours.
• Performance depended on concentration of target odour, but not number of distractor odours.
• Recapitulated in model with sparse, highly tuned receptors.
  • These only sense the target odour, unresponsive to distractors, hence affected by target SNR but not number of distractors.

140
A generative diffusion model reveals V2’s representation of natural images

• Modeled the manifold of images by training a diffusion model to produce images.
• Generated two kinds of “noise”:
  • On-manifold: Gaussian perturbations to the diffusion model input.
  • Off-manifold: Gaussian perturbations to the diffusion mode output.
• Measured responses of Macaque V2.
  • On-manifold noise produced higher variability in the responses.
    • Such “noise” produces valid, different images, so the responses will reflect the new images geneated.
    • Cosine similarity of these responses decreased with noise level.
  • Off-manifold noise produced similar responses across all noise levels.
    • This noise produces corrupted versions of the same images, so lack of variability perhaps reflects mapping of all of these to the same image.
    • Cosine similarity was similar across noise levels.
• Comment: It’s like V2 is inverting the diffusion model.
  • On-manifold noise produces variable activity as the mapping back to the image-generating latents, varies.
  • Off-manifold noise produces constant responses, as the mapping back is to the same image.

089 Interpretable time-series analysis with Gumbel dynamics

• Context was dynamics of discrete latent state generating observations.
• We track the probability of being in each state.
• We want state occupancies to be nearly one-hot, for interpretability.
  • We want the system to be mostly in one state, rather than distributed across states.
• Standard approach uses softmax, which has two problems:
  • If we work with the probabilities, then these can stay nearly uniform.
    • Downstream decoder/observation model transforming can expand the small fluctuations from uniformity as needed.
    • Hard to interpret as states occupancy will be distributed.
  • Alternatively, we can sample from the softmax.
    • Fixes the interpretability issue as exactly one state will be occupied
    • In efficient, as gradients etc. will only operate on that active state / sample.
• Solution:Gumbel Softmax: $$ z \sim \text{GS}(\pi, \tau) \iff z \sim \text{softmax}\left({\pi + \eta \over \tau}\right), \quad \eta \sim \text{Gumbel}(0,1).$$
  • Pushes the softmax probabilities so state-occupancy is nearly one-hot.
    • Helps interpretability
    • More efficient than purely one hot because states with small probabilities are also update.

065 Continuous Multinomial Logistic Regression for Neural Decoding

• Standard logistic regression: $$p(y_k|\xx) \propto \exp(-\ww_k^T \xx).$$
• Weights are fixed per class.
• Can be extended to a temporal dimension by treating each time bin independently.
  • This ignore temporal structure.
• Idea: allow $\ww_k$ to vary smoothly in time by giving it a Gaussian process prior : $$ \ww_k \sim \text{GP}(\bzero, \lambda).$$
  • I think there was also some linking of the different states as well, so that their vector evolutions were also linked.
• Take the mean $\ww_k(t)$ to compute output probabilities. $$ p(\yy_k | \xx(t)) \propto \exp(-\overline{\ww}_k(t)^T \xx).$$

Poster Session 2

136 Statistical theory for inferring population geometry in high-dimensional neural data

• Used RMT to investigate how covariance estimation varies with the number of neurons $N$ and trials $T$.
• First result was on PCA dimension (participation ratio), showing how subsampling $N$ neurons and $T$ trials to $M$ neurons and $P$ trials affects estimation by relating the PCA dimensions at the two configuration.
• Next result was about how estimation error relative to true covariance, $\|\hat C – C\|_F^2$ varies as $D_N/T$.
  • $D_N$ is the true PCA dimensionality for $N$ neurons in the infinite trials limit.
• What if the true dimensionality is not known? Replication error, $\|\hat C_1 – \hat C_2\|_F^2$, varies as $2 \hat{D}_{N,T}/T$.
  • $\hat{D}_{N,T}$ is the dimensionality of the sample.
• Estimating eigenvectors and eigenvalues:
  • Low rank signal model: $C = U D U + \sigma^2 I$.
  • SNR for the $k$’th dimensions: $SNR_k = d_k/{N \sigma^2}$.
  • There was some critical SNR threshold above which eigenvalues and eigenvectors could be estimated.
  • Effective $R^2$ is $R^2 = {\sum_k O_k SNR_k – {K/N} \over \sum_k SNR_k -1 }.$
    • O_k is the alignment of the recovered eigenvector with the true eigenvector.
    • Recovering each mode contributes SNR, weighted by the alignment, but also brings noise (contributing $N^{-1}$ per mode).
    • Best rank to recover is the $K$ at which the numerator no longer increases, where adding one more mode brings more noise than signal.

157 Continuous partitioning of neuronal variability

• Classic models of neural responses explain them as homogeneous Poisson processes whose rates are the product of a stimulus dependent tuning $f_s$ and a trial-specific gain $g_k$: $$y \sim \text{Poisson}(f_s g_k).$$
• Innovation to capture temporal variability: the Continuous Modulated Poisson Model.
• Tunings and gains as Gaussian processes: $$ \log g(t) \sim \text{GP}(0, K_g), \quad \log f_s(t) \sim \text{GP}(0, K_f(s)).$$
• Gains modelled as $$K_g = \rho_g \exp\left(-{|t_1 – t_2|^q \over \ell_g}\right).$$
• Can then e.g. monitor how parameters like optimal temporal correlation lengths $\ell_g$ and heavy-tailed-ness $q$ vary across brain areas.

35 Gain-modulated linear networks: a tractable framework for context-dependent computations

92 Uncovering statistical structure in large-scale neural activity with restricted Boltzmann machines

• Main idea: fit RBMs to neural data.
• Marginalize out hidden states to get effective interactions between units at all orders.
  • Advantage over e.g. Schneidman’s approach by making it easier to estimate higher order interactions.
    • But surely subsampling problems must be the same? i.e. estimates of high-order interactions will be noisy due to lack of observations.
• Compute index of higher order interactions between pairs of units.
  • Can indicate either missing units in the recording, or true higher order interactions (e.g. via glia).

218 A unified theory of feature learning in RNNs and DNNs

• Compared the solutions in a regression task by RNNs and DNNs.
• RNNs can be viewed as DNNs using temporal unrolling.
• Key difference is that in the unrolled RNN, the layer weights are shared.
• Weight sharing imposes an inductive bias which can make RNNs more sample efficient e.g. when learning temporal sequences.

152 Dynamical archetype analysis: Autonomous computation

208 Plastic Circuits for Context-Dependent Decisions

• Investigated the effect of Short-Term Synaptic Plasticity (STSP) in an RNN performing the Mante 2013 task (output based on colour or motion signal, depending on context).
• STSP: Strengths are determined as the product of utilization and activity, $w_{\text{eff}, ij}(t) =w_{ij} u_j(t) x_j(t).$
  • This is mean to model e.g. vesicle pool depletion etc.
• A network using STSP could perform the task, one with Hebbian plasticity could not (?).
• Found that in STSP, context information is stored in neural activity, not the synapses.
• A network with fixed weights wanting to implement the same thing has to do so through nonlinear activations: $A(t) x(t) \to W \phi(x(t)),$, which presumably could get complicated, intractable.

173 Spatiotemporal Dynamics in Recurrent Neural Networks as Flow Invariance

045 A nonlocal variational framework for optimal neural representations