feat: Integrate MPSSynapse Component

[antonvice]

This PR introduces the MPSSynapse component, allowing for Matrix Product State (MPS) compressed synaptic transformations. This enables high-dimensional layers to scale within memory constraints of biological and robotic inference systems. Includes a utility for SVD-based matrix decomposition into MPS cores.

[ago109]

This looks great (and interesting!); thank you for contributing the MPSSynapse!

One small comment / possible minor update - is there a paper reference we could possibly attach to the main doc-string of MPSSynapse?
For example, in the MSTDPETSynapse, we refer to the source where the mathematical model that the synapse represents comes from where in the main doc-string we have:
"""

| References:
| Florian, Răzvan V. "Reinforcement learning through modulation of spike-timing-dependent synaptic plasticity."
| Neural computation 19.6 (2007): 1468-1502.
"""
That way, we pay credit to you/your team or the researchers that this synapse embodies.

If there is no reference, then possibly a link to the blog-post/tutorial/talk or source where perhaps this was proposed works as well =]

[antonvice]

Hey Alex,
To give credit where it's due, the core math for the compression comes from Stoudenmire/Schwab and Novikov. More recently, Nuijten and Chris Fields have been doing some heavy lifting to prove that Active Inference effectively is a tensor network, so I wanted to bring that logic into ngclearn.
I actually need it for my work on T-AIF (Tensor Active Inference Framework). Trying to figure out how to actually bridge these quantum-inspired contractions with local error signals so we can scale up generative world models without blowing out the RAM.

PS
| References:
| Stoudenmire, E. Miles, and David J. Schwab. "Supervised learning with
| quantum-inspired tensor networks." Advances in neural information
| processing systems 29 (2016).
|
| Novikov, Alexander, et al. "Tensorizing neural networks." Advances in
| neural information processing systems 28 (2015).
|
| Nuijten, W. W. L., et al. "A Message Passing Realization of Expected
| Free Energy Minimization." arXiv preprint arXiv:2501.03154 (2025).
|
| Wilson, P. "Performing Active Inference with Explainable Tensor
| Networks." (2024).
|
| Fields, Chris, et al. "Control flow in active inference systems."
| arXiv preprint arXiv:2303.01514 (2023).

[rxng8]

@antonvice Thank you for taking the time to contribute! We really appreciate it!
I have run pytest on your branch, here is the output specifically for the MPSSynapse:

...
>       np.testing.assert_allclose(y_mps, y_dense, atol=1e-5)
E       AssertionError: 
E       Not equal to tolerance rtol=1e-07, atol=1e-05
E       
E       Mismatched elements: 10 / 10 (100%)
E       Max absolute difference among violations: 0.00253725
E       Max relative difference among violations: 0.00251471
E        ACTUAL: array([[-0.096463,  1.658276, -2.307746,  5.297636, -0.901365,  7.161191,
E               -1.484671,  3.614738,  5.318543,  0.788785]], dtype=float32)
E        DESIRED: array([[-0.096226,  1.65959 , -2.30778 ,  5.298367, -0.899104,  7.158653,
E               -1.48596 ,  3.614866,  5.317003,  0.788097]], dtype=float32)

tests/components/synapses/test_mpsSynapse.py:42: AssertionError

You can increase the tolerance of numpy assert equal a little bit to loosen the condition (as last resort). For example, playing around with rtol and atol.

[ago109]

Hello @antonvice could you please consider @rxng8's suggestion for loosening the tolerance a tiny bit for the unit-test?

[rxng8]

The test now works for me!