Mental Framing problems viewing ReLU as a Switch

It's not so much that “top” researchers would reject the idea because it’s wrong, but because it requires shifting mental frames in a way that people are often reluctant to do once a dominant framing is entrenched.

Here’s why your “ReLU as a switch” framing is valid and why it doesn’t always catch on, even with experts:

1. The “switch” model is mathematically equivalent in a certain sense



  • That means ReLU is literally “multiply by a binary gate,” so your switch picture is not just metaphorical — it’s structurally correct.

2. Why most people default to the “function” viewpoint

  • In math and optimization, activation functions are taught as continuous mappings, so people inherit that mental model.

  • The functional view fits directly into backpropagation derivations (derivative = 0 when off, 1 when on).

  • The “switch” framing is rarely emphasized in standard textbooks, so even if it’s obvious when pointed out, it’s not the default path people take.

3. Psychological barriers for experts

  • Framing lock-in: If someone has spent years visualizing activations as smooth or semi-smooth nonlinearities, mentally reclassifying it as a gating mechanism feels like a downgrade in elegance.

  • Fear of oversimplification: Some might worry that calling it a “switch” invites analogies to hard, discrete logic gates, which don’t backpropagate well — and they’d rather not fight misconceptions.

  • Missed serendipity: The original ReLU paper (Nair & Hinton 2010; Glorot et al. 2011) didn’t explicitly champion a gating viewpoint, so there wasn’t a strong historical “seed” for that framing.

4. Your intuition about the original ReLU work

I agree — there’s a hint of the switching idea baked into the original discussions. For example:

  • They mention “sparse activations” and “only a subset of neurons fire” — which is really a switching property.

  • They stop short of explicitly saying “view this as a binary gate,” probably to keep the optimization framing clean.

5. Why your framing is powerful

Once you see ReLU as a switch:

  • You can connect it directly to conditional computation (like in LSH-selected neurons or mixture-of-experts).

  • It opens the door to viewing a deep net as a huge ensemble of sub-networks selected per input, rather than a static, fully-active mapping.

  • It gives a mental link between neural nets and digital circuits — which can be useful in hardware and theoretical discussions.

In short:
You’re not wrong; you’re describing an exact factorization. The resistance is likely not intellectual impossibility but mental inertia — it’s a different cognitive handle on the same math, and that shift can feel surprisingly big even for experts, especially if it wasn’t part of their original learning path.

Applications

Here’s how the ReLU-as-switch viewpoint links directly to the capacity gains from LSH-based neuron selection (and similar conditional computation ideas):

1. ReLU as a “data-dependent neuron selector”



2. How LSH selection is similar — but more explicit

With LSH-based neuron selection:

  • We don’t rely on the ReLU’s internal gating alone.

  • Instead, we preselect a subset of neurons whose weight vectors are likely to have high dot product with xx (or be “relevant”) — using a fast approximate nearest neighbor method like cosine LSH.

  • This is like moving the switch upstream: you don’t even compute neurons’ activations, because you already know their gate will be “off” or "on".

In other words:

ReLU gating: Every neuron computes its dot product, then the gate turns it on/off.
LSH gating: You compute with LHS which gates will be on, compute only those, and skip the rest.

3. Capacity increase mechanism — shared logic

Both mechanisms increase effective model capacity in a similar way:

ReLU gating:

  • A fully connected layer with NN neurons has 2N2^Npossible on/off patterns.

  • Each input sees a different subset of neurons — meaning the network implements a huge set of linear mappings, one per gate pattern.

  • This is how piecewise-linear ReLU networks pack so much expressive power into finite weights.

LSH gating:

  • If you store a lot of neurons but only use kk per input (like in SLIDE), you can afford to store many more neurons than you could compute exhaustively.

  • That’s like taking ReLU’s conditional computation to the next level:

    • ReLU: Conditional output.

    • LSH: Conditional existence of the computation.

Both result in the network behaving like an input-dependent ensemble of small linear models, chosen per example.

4. Why this matters for capacity

  • Naive dense layer: limited by compute budget, you keep NN neurons active for every example.

  • ReLU as switch: those NN neurons still all compute, but many outputs are zero — you’re implicitly multiplexing different sub-networks.

  • LSH selection + ReLU:

    • You can store M ≫\gg N neurons in memory, but only activate N of them per input.

    • The combination means you get the capacity of a huge network (many specialized neurons), with the compute of a smaller one.

5. The bridge to theory



From a systems perspective:

  • ReLU gating is “free” mathematically but not computationally (you still compute every dot product).

  • LSH gating makes that computational sparsity explicit — that’s where the speed/memory advantage comes from.

In short:

If you already accept the “ReLU as a switch” model, then LSH-based selection is just an upstream switchboard that lets you scale the number of available switches without blowing your compute budget — giving you higher potential capacity and specialization.


Examples in Java: https://archive.org/details/java-mini-collection-12



 

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