Seemingly Redundant Modules Enhance Robust Odor Learning in Fruit Flies<\/a><\/h3>\n\n\n\n\n- Asks whether spike-frequency adaptation and lateral inhibition in the fly olfactory system are redundant or complementary<\/li>\n\n\n\n
- Tests a baseline model (no SFA or LI), against models with just one, and the full model<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2025\/12\/image-4-1024x620.png\")
<\/figure>\n\n\n\n\n- SFA and LI are better than each other depending on injected noise.<\/li>\n\n\n\n
- Full model performs best across all noise conditions:<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2025\/12\/image-5-1024x365.png\")
<\/figure>\n\n\n\nNeurons as Detectors of Coherent Sets in Sensory Dynamics<\/a><\/h3>\n\n\n\n\n- Coherent sets: subsets of state-space that move together in time.<\/li>\n\n\n\n
- Neurons, brains want to find representations that track such states.<\/li>\n\n\n\n
- Koopman operator: Linear operator in high-dimensional space that reports future state of an observable.\n
\n- Linearity means we can write it as $$K_\\tau = \\sum_{i=0} ^\\infty e^{\\lambda_i \\tau} u_i v_i^T.$$ <\/li>\n<\/ul>\n<\/li>\n\n\n\n
- 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)<\/li>\n\n\n\n
- Use the observable that <\/li>\n\n\n\n
- TBC<\/li>\n<\/ul>\n\n\n\n
BrainFlow: A Holistic Pathway of Dynamic Neural System on Manifold<\/a><\/h3>\n\n\n\n\n- The problem: linking structural connectivity and functional connectivity.<\/li>\n\n\n\n
- Both connectivities live on the manifold of symmetric, positive-definite matrices (SPD).<\/li>\n\n\n\n
- Can link them using flows along geodesics on the manifold.<\/li>\n\n\n\n
- The same structural connectivity will lead to different functional connectivities during different tasks.<\/li>\n\n\n\n
- Conversely, functional connectivity produced in different tasks should lead back to the same structural connectivity.<\/li>\n\n\n\n
- Problem: Computing flows on the SPD manifold is computationally expensive.<\/li>\n\n\n\n
- PSD manifold can be linked to the manifold of lower triangular matrices by the Cholesky decomposition.<\/li>\n\n\n\n
- Recent work shows computation on the Cholesky manifold is much easier.<\/li>\n\n\n\n
- Solution: Leveraged this recent work to compute flows linking structure and function on the cholesky manifold.<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2025\/12\/image-6-1024x482.png\")
<\/figure>\n\n\n\n\n- To get flows from different FC back to the same SC, they add a term that penalizes differences in the Cholesky manifold states.<\/li>\n<\/ul>\n\n\n\n
Dimensionality Mismatch Between Brains and Artificial Neural Networks<\/a><\/h3>\n\n\n\n\n- Measured dimensionality of representations across layers in both humans (fMRI data) and ANNs.<\/li>\n\n\n\n
- Use both linear dimensionality (participation ratio) and non-linear dimensionality, defined as below.\n
\n- As a side note, see Mackay and Gharamani’s note<\/a> on this estimator.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2025\/12\/image-7-1024x218.png\")
<\/figure>\n\n\n\n\n- The authors found that in humans both measures increase as one moves from V1 towards ventral stream. <\/li>\n\n\n\n
- In ANNs, intrinsic dimensionality seems to peak at intermediate layers. <\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2025\/12\/image-10-1024x569.png\")
<\/figure>\n\n\n\n\n- Suggests that deep-layers in ANN may be compressing their representations, losing abstraction ability.\n
\n- Though interestingly the peak still happens at a higher value than in humans.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
Modeling Neural Activity with Conditionally Linear Dynamical Systems<\/a><\/h3>\n\n\n\n\n- Model nonlinear dynamics as linear conditioned on inputs:<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2025\/12\/image-11.png\")
<\/figure>\n\n\n\n\n- Notice how inputs modify the parameters, instead of coming in as the usual additive $Bu_t$ terms.<\/li>\n\n\n\n
- GP priors on each element of $\\mathbf{A, b, C, d}$.<\/li>\n\n\n\n
- Get all the benefits of linear systems for inference, prediction etc.<\/li>\n\n\n\n
- Can learn parameters with EM: \n
\n- E-step: Use current parameter estimates to infer latent states.<\/li>\n\n\n\n
- M-step: Solve for parameters by finding coefficients in fixed GP basis.\n
\n- Closed form when assuming Gaussian noise.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n
- Can be seen as conditions specific linearizations of the dynamics.<\/li>\n\n\n\n
- Temporal correlation of GP prior can be tuned to capture interesting limits:\n
<\/figure>\n\n\n\n- \n
- SFA and LI are better than each other depending on injected noise.<\/li>\n\n\n\n
- Full model performs best across all noise conditions:<\/li>\n<\/ul>\n\n\n\n<\/figure>\n\n\n\n
Neurons as Detectors of Coherent Sets in Sensory Dynamics<\/a><\/h3>\n\n\n\n
- \n
- Coherent sets: subsets of state-space that move together in time.<\/li>\n\n\n\n
- Neurons, brains want to find representations that track such states.<\/li>\n\n\n\n
- Koopman operator: Linear operator in high-dimensional space that reports future state of an observable.\n
- \n
- Linearity means we can write it as $$K_\\tau = \\sum_{i=0} ^\\infty e^{\\lambda_i \\tau} u_i v_i^T.$$ <\/li>\n<\/ul>\n<\/li>\n\n\n\n
- 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)<\/li>\n\n\n\n
- Use the observable that <\/li>\n\n\n\n
- TBC<\/li>\n<\/ul>\n\n\n\n
BrainFlow: A Holistic Pathway of Dynamic Neural System on Manifold<\/a><\/h3>\n\n\n\n
- \n
- The problem: linking structural connectivity and functional connectivity.<\/li>\n\n\n\n
- Both connectivities live on the manifold of symmetric, positive-definite matrices (SPD).<\/li>\n\n\n\n
- Can link them using flows along geodesics on the manifold.<\/li>\n\n\n\n
- The same structural connectivity will lead to different functional connectivities during different tasks.<\/li>\n\n\n\n
- Conversely, functional connectivity produced in different tasks should lead back to the same structural connectivity.<\/li>\n\n\n\n
- Problem: Computing flows on the SPD manifold is computationally expensive.<\/li>\n\n\n\n
- PSD manifold can be linked to the manifold of lower triangular matrices by the Cholesky decomposition.<\/li>\n\n\n\n
- Recent work shows computation on the Cholesky manifold is much easier.<\/li>\n\n\n\n
- Solution: Leveraged this recent work to compute flows linking structure and function on the cholesky manifold.<\/li>\n<\/ul>\n\n\n\n<\/figure>\n\n\n\n
- \n
- To get flows from different FC back to the same SC, they add a term that penalizes differences in the Cholesky manifold states.<\/li>\n<\/ul>\n\n\n\n
Dimensionality Mismatch Between Brains and Artificial Neural Networks<\/a><\/h3>\n\n\n\n
- \n
- Measured dimensionality of representations across layers in both humans (fMRI data) and ANNs.<\/li>\n\n\n\n
- Use both linear dimensionality (participation ratio) and non-linear dimensionality, defined as below.\n
- \n
- As a side note, see Mackay and Gharamani’s note<\/a> on this estimator.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<\/figure>\n\n\n\n
- \n
- The authors found that in humans both measures increase as one moves from V1 towards ventral stream. <\/li>\n\n\n\n
- In ANNs, intrinsic dimensionality seems to peak at intermediate layers. <\/li>\n<\/ul>\n\n\n\n<\/figure>\n\n\n\n
- \n
- Suggests that deep-layers in ANN may be compressing their representations, losing abstraction ability.\n
- \n
- Though interestingly the peak still happens at a higher value than in humans.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
Modeling Neural Activity with Conditionally Linear Dynamical Systems<\/a><\/h3>\n\n\n\n
- \n
- Model nonlinear dynamics as linear conditioned on inputs:<\/li>\n<\/ul>\n\n\n\n<\/figure>\n\n\n\n
- \n
- Notice how inputs modify the parameters, instead of coming in as the usual additive $Bu_t$ terms.<\/li>\n\n\n\n
- GP priors on each element of $\\mathbf{A, b, C, d}$.<\/li>\n\n\n\n
- Get all the benefits of linear systems for inference, prediction etc.<\/li>\n\n\n\n
- Can learn parameters with EM: \n
- \n
- E-step: Use current parameter estimates to infer latent states.<\/li>\n\n\n\n
- M-step: Solve for parameters by finding coefficients in fixed GP basis.\n
- \n
- Closed form when assuming Gaussian noise.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n
- Can be seen as conditions specific linearizations of the dynamics.<\/li>\n\n\n\n
- Temporal correlation of GP prior can be tuned to capture interesting limits:\n
- Model nonlinear dynamics as linear conditioned on inputs:<\/li>\n<\/ul>\n\n\n\n
- Though interestingly the peak still happens at a higher value than in humans.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
- Suggests that deep-layers in ANN may be compressing their representations, losing abstraction ability.\n
- As a side note, see Mackay and Gharamani’s note<\/a> on this estimator.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
- To get flows from different FC back to the same SC, they add a term that penalizes differences in the Cholesky manifold states.<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2025\/12\/image-12-1024x418.png\")
<\/figure>\n\n\n\n