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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Jun 12

🚨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/

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Bahareh Tolooshams @btolooshams.bsky.social · May 29

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.

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Bahareh Tolooshams @btolooshams.bsky.social · Apr 28

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/

Bahareh Tolooshams @btolooshams.bsky.social · Apr 28

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Apr 28

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Apr 28

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Apr 28

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Apr 28

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/

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Bahareh Tolooshams @btolooshams.bsky.social · Apr 28

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/

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