Bahareh Tolooshams

Read our paper or reach out to me and my collaborators if interested. This work wouldn't be possible without my collaborators: @aditijc.bsky.social , Rayhan Zirvi, Abbas Mammadov, @jiacheny.bsky.social , Chuwei Wang, @anima-anandkumar.bsky.social 17/

Takeaway II: Equivariance is one example of global properties that can be used to regularize diffusion models; one may realize other forms of regularization to reweight and penalize trajectories deviating from the data manifold. 16/

Takeaway I: EquiReg provides a new lens to correct diffusion-based inverse solvers, not by rewriting the models, but by guiding them with symmetry. The key is to find functions that are Manifold-Preferential Equivariant, showing low equivariance error for desired solutions. 15/

Our preliminary results show that EquiReg can also be used to improve diffusion-based text-to-image guidance and generate images that are more natural-looking and feasible (see the paper for more visualizations). 14/

Improved PDE reconstruction performance: EquiReg enhances performance on PDE solving tasks. For instance, Equi-FunDPS reduces the error of FunDPS on Helmholtz and Navier-Stokes inverse problems. 13/

EquiReg improves the perceptual quality in image restoration tasks. 12/

Improved image restoration performance: We demonstrate that EquiReg significantly improves performance on linear and nonlinear image restoration tasks. EquiReg also consistently shows improvement in performance across many noise levels. 11/

We develop flexible plug-and-play losses to be integrated into a variety of pixel- and latent-space diffusion models for inverse problems. EquiReg guides the sampling trajectory toward symmetry-preserving regions, lie close to the data manifold, improving posterior sampling. 10/

We present two strategies for finding MPE functions:
a) training induced: equivariance emerges in encoder-decoder architectures trained with symmetry-preserving augmentations,
b) data inherent: MPE arises from inherent data symmetries, commonly observed in physical systems. 9/

We introduce Manifold-Preferential Equivariant (MPE) functions, which exhibit low equivariance error on the support of the data manifold (in-distribution) and higher error off-manifold (out-of-distribution). Our proposed regularization, EquiReg, is based on this MPE property. 8/

EquiReg with distribution-dependent equivariance errors: We propose a new class of regularizers grounded in distribution-dependent equivariance error, a formalism that quantifies how symmetry violations vary depending on whether samples lie on- or off-manifold. 7/

We propose EquiReg, taking equivariance as one such global property that can enforce geometric symmetries. 6/

This addresses errors arising in the likelihood score due to poor posterior approx and prior score errors resulting from off-manifold trajectories. To realize such a regularizer, we seek an approach for manifold alignment via global properties of the data distribution. 5/

We reinterpret the reversed conditional diffusion as a Wasserstein-2 gradient flow minimizing a functional over sample trajectories. This suggests employing a regularizer that reweights and penalizes trajectories deviating from the data manifold (see Propositions 4.1-4.2). 4/

This breaks down for highly complex distributions: Conditional expectation, as in the posterior mean expectation, computes a linear combination of all possible x0; hence, from the manifold perspective, the posterior mean expectation may end up being located off-manifold. 3/

Inverse problems are ill-posed: the inversion process can have many solutions; hence, they require prior information about the desired solution. SOTA methods use diffusion models as learned priors. However, they rely on an isotropic Gaussian approximation of the posterior. 2/

🚨We propose EquiReg, a generalized regularization framework that uses symmetry in generative diffusion models to improve solutions to inverse problems. arxiv.org/abs/2505.22973

@aditijc.bsky.social, Rayhan Zirvi, Abbas Mammadov, @jiacheny.bsky.social, Chuwei Wang, @anima-anandkumar.bsky.social 1/

I am joining @ualberta.bsky.social as a faculty member and
@amiithinks.bsky.social!

My research group is recruiting MSc and PhD students at the University of Alberta in Canada. Research topics include generative modeling, representation learning, interpretability, inverse problems, and neuroAI.

Our decoding package also offers a movement-imitated augmentation framework (VARS-fUSI++). By augmenting the image for decoder training with small, randomly rotated and translated images, you can increase the decoder's robustness, hence, performance. 12/

We show that VARS-fUSI can be generalized to human participants while maintaining decodeable behavior-correlated information, generating decoding accuracies and activation maps comparable to ground truth. 11/

In a motor decoding experiment, the direction of planned saccadic eye movements can be decoded as accurately from VARS-fUSI as from ground truth. The decoding relied on the same region of posterior parietal cortex, showing that VARS-fUSI conserves behavioral information. 10/

Despite the extensive reduction of required pulses, VARS-fUSI can still be used reliably for low-latency and efficient behavioral decoding in brain-computer interfaces (BCIs). We demonstrate this in monkey and human experiments. 9/

Why does VARS-fUSI perform better than other AI models?

- It respects the complex-valued nature of the data,
- It treats the temporal aspect of the data as a continuous function using neural operators,
- It captures decomposed spatially local and temporally global features. 8/

What does VARS-fUSI offer to practitioners using fUSI in clinical or neuroscience research?

VARS-fUSI offers a training pipeline, a fine-tuning procedure, and an accelerated, low-latency online imaging system. You can use VARS-fUSI to reduce the acquisition duration or rate. 7/

VARS-fUSI is SOTA!

We applied VARS-fUSI to brain images collected from mouse, monkey, and human. Our method achieves state-of-the-art performance and shows superior generalization to unseen sessions in new animals, and even across species. 6/

What are the challenges of fUSI?

fUSI is a promising neuroimaging method, inferring neural activity by detecting cerebral blood volume changes. Current methods require hundreds of frames, leading to high computational cost and memory demands.

VARS-fUSI addresses above. 5/

Change the sampling rate or duration of your data acquisition at inference time, and VARS-fUSI will still provide high-quality images. This is not possible with current AI models. VARS-fUSI reconstructs images using 10% of the time or sampling rate typically needed per image. 4/

This is part of a multi-collaboration between three research labs at @caltech.edu. Check out our manuscript and source code for VARS-fUSI.

bioRxiv: biorxiv.org/content/10.1...
code: github.com/neuraloperat... 3/

Joint work with Lydia Lin, Thierri Callier, Peter Wang, Sanvi Pal, Aditi Chandrashekar, Claire Rabut, @zongyili.bsky.social, Chase Blagden, @sumnerln.bsky.social,
@azizzadenesheli.bsky.social, Charles Liu, @mikhailshapiro.bsky.social, Richard Andersen, @anima-anandkumar.bsky.social. 2/

We have released VARS-fUSI: Variable sampling for fast and efficient functional ultrasound imaging (fUSI) using neural operators.

The first deep learning fUSI method to allow for different sampling durations and rates during training and inference. biorxiv.org/content/10.1... 1/