Meh. Well, at least, possibly “meh”.

Upshot: Gaussian sampling along the parameters of nodes rather than a fixed number. This might offer one of the following:

* Better inference time accuracy on average

* Faster convergence during training

It probably costs additional inference and training compute.

The paper demonstrates worse results on MNIST, and shows the architecture is more than capable of dealing with the Iris test (which I hadn’t heard of; categorizing types of irises, I presume the flower, but maybe the eye?)

The paper claims to keep the number of parameters and depth the same, but it doesn’t report as to

* training time/flops (probably more I’d guess?)

* inference time/flops (almost certainly more)

Intuitively if you’ve got a mean, variance and mix coefficient, then you have triple the data space per parameter — no word as to whether the networks were normalized as to total data taken by the NN or just the number of “parameters”.

Upshot - I don’t think this paper demonstrates any sort of benefit here or elucidates the tradeoffs.

Quick reminder, negative results are good, too. I’d almost rather see the paper framed that way.

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zakeria 2 days ago | parent [-]

Thanks for the comment. Just to clarify, the uGMM-NN isn't simply "Gaussian sampling along the parameters of nodes."

Each neuron is a univariate Gaussian mixture with learnable mean, variance, and mixture weights. This gives the network the ability to perform probabilistic inference natively inside its architecture, rather than approximating uncertainty after the fact.

The work isn’t framed as "replacing MLPs." The motivation is to bridge two research traditions:

- probabilistic graphical models and probabilistic circuits (relatively newer)

- deep learning architectures

That's why the Iris dataset (despite being simple) was included - not as a discriminative benchmark, but to show the model could be trained generatively in a way similar to PGMs, something a standard MLP cannot do. Hence, the other benefits of the approach mentioned in the paper.

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vessenes 2 days ago | parent [-]

Thanks for writing back! I appreciate the plan to integrate the two architectures. On that front, it might be interesting to have a future research section - like what would be uniquely good about this architecture if scaled up?

On ‘usefulness’ I think I’m still at my original question - it seems like an open theoretical q to say that the combination of a tripled-or-greater training budget, data size budget of the NN, and probably a close to triple or greater inference budget, the costs of the architecture you described, cannot be closely approximated by the “fair equivalent”-ly sized MLP.

I hear you that the architecture can do more, but can you talk about this fair size question I have? That is, if a PGM of the same size as your original network in terms of weights and depth is as effective, then we’d still have a space savings to just have the two networks (MLP and PGM) side by side.

Thanks again for publishing!

	▲	zakeria a day ago \| parent [-]
		That’s a fair question. You’re right that on paper a uGMM neuron looks like it “costs” ~3× an MLP weight. But there are levers to balance that. For example, the paper discusses parameter tying, where the Gaussian component means are tied directly to the input activations. In that setup, each neuron only learns the mixture weights and variances, which cuts parameters significantly while still preserving probabilistic inference. The tradeoff may be reduced expressiveness, but it shows the model doesn’t have to be 3x heavier. More broadly: traditional graphical models were largely intractable at deep learning scale until probabilistic circuits, which introduced tractable probabilistic semantics without exploding parameter counts. Circuits do this by constraining model structure. uGMM-NN sits differently: it brings probabilistic reasoning inside dense architectures. So while compute cost is real, the “fair comparison” isn’t just params-per-weight, it’s also about what kinds of inference the model can do at all, and the added interpretability of mixture-based neurons, which traditional MLP neurons don’t provide - it shares some spirit with recent work like KAN, but tackles the problem through probabilistic modeling rather than spline-based function fitting.