Atlas LSH Neural Networks: Geometry as Context

 

Atlas LSH Neural Networks: Geometry as Context

Most neural networks perform essentially the same computation for every input. Every layer applies the same collection of parameters, regardless of what the input actually is. Atlas LSH neural networks explore a different idea: use the geometry of the input to determine which computation should be performed.

The first step is to take a compact geometric sample of the input using locality-sensitive hashing (LSH). Each LSH bit can be viewed as asking a simple geometric question about the input vector—for example, which side of a randomly oriented hyperplane it lies on. A few hundred such bits form a sparse fingerprint describing the input's approximate location in a high-dimensional space.

The important point is that these bits are not trying to represent the input in detail. Instead, they capture context. Similar inputs tend to produce similar bit patterns, so the LSH serves as a geometry sampler that identifies the neighborhood in which the input resides. It provides just enough information to guide the next stage of computation.

The network then uses this geometric context to select a subset of parameters or memories that are relevant to the current input. Computation is therefore conditional. Instead of every parameter participating in every inference, information is routed through the subset associated with the current geometric context. The architecture naturally separates context generation from computation.

One way to think about this is as an interaction between propositions and memory. The LSH bits represent propositions about the current state—for example, "the input is approximately in this region of state space." These propositions activate memories associated with similar situations. The resulting computation is a continual dialogue between the current context and previously learned knowledge.

This perspective also suggests why locality-sensitive hashing is attractive. It is not merely a fast indexing mechanism. It is a way of extracting stable geometric clues that allow the network to perform conditional computation while preserving similarity relationships. Nearby inputs tend to activate overlapping sets of memories, providing a smooth transition between related concepts without requiring every parameter to be active.

Whether this ultimately proves to be a useful direction is, of course, an empirical question. But the conceptual framework is straightforward:

  • Sample the geometry.

  • Infer the context.

  • Select the relevant memories.

  • Route computation through those memories.

From this viewpoint, an Atlas LSH neural network is less like a conventional dense neural network and more like a memory system guided by geometric context. Geometry determines what is relevant, and relevance determines how computation proceeds.

Further Information:

Comments

Post a Comment

Popular posts from this blog

Neon Bulb Oscillators

Image
Neon Tube Oscillators  Fig. 1 High voltage to headphones, don't do this in modern times. Very high impedance headphones are implied. A neon bulb is useful in many ways in an amateur station, but there are undoubtedly many amateurs who are not aware of the fact that the device can be made to oscillate at either audio or radio frequencies. Fig. 1 shows how a single bulb may be hooked up as an audio frequency oscillator. The L-C circuit is formed by the headphones and a condenser, and by varying the capacity the circuit can be made to oscillate at frequencies from a few cycles per second up to the highest audio frequencies.  The variable resistor in series with the bulb and battery controls the strength of oscillation, and also controls the frequency to some extent. A 1 nf variable condenser will be sufficient to cover most of the audio range.  Fig. 2 The circuit in Fig. 2 may be used when an RF oscillator is to be modulated at audio frequencies. The transformer may be an or...
Read more

A practical way to view neural networks (whiteboard view)

Image
 A whiteboard view: You can take a decision matrix view of ReLU neural networks. Instead of ReLU(Wx) you create a diagonal matrix with binary 1 or 0 entries according to the ReLU decisions (x>=0?) Then conceptually a layer is DWx. Where D is doing row selection on W. And in fact D does column selection on the weight matrix in the next layer. That is very coarse parameter selection which is linear mapping selection.
Read more

23 Circuits you can Build in an Hour - Free Book

Image
Unleash your inner electronics wizard with 23 captivating circuits you can build in a jiffy! Tired of staring at daunting circuit diagrams that seem to go on forever? Craving hands-on experience that will ignite your passion for electronics? Look no further than this electrifying collection of 23 circuits you can build in an hour or less! From the delightfully simple to the mind-bendingly clever, these circuits are guaranteed to spark your curiosity and inspire further experimentation. Whether you're a seasoned pro or a budding hobbyist, you'll find something to tantalize your taste buds in this smorgasbord of electronic delights. Get the book now, it's free. The Lost SuperFoods (sponsored) Crash GPT course (sponsored) From Zero To Off-Grid Hero (sponsored)
Read more