[Verse 1] In dimensions climbing high beyond what eyes can see Binary patterns dance in vast geometry When the space grows wide enough, magic starts to show Random vectors spread apart, orthogonal they go Kanerva proved the theorem that unlocks the door In high-dimensional realms, we can store so much more [Chorus] Nearly orthogonal, patterns stand alone XOR for binding, threshold for the home Bundle up the meanings, let the sums collide In cortical columns, knowledge multiplies Store exponential memories in finite neural space Mathematics shows us how the brain finds its place [Verse 2] Take N random locations in your n-dimensional field Even when N is tiny compared to what space could yield Two to the power n seems impossibly vast But capacity scaling breaks the limits of the past Store as many patterns as locations that you hold Linear relationship, not exponential fold [Chorus] Nearly orthogonal, patterns stand alone XOR for binding, threshold for the home Bundle up the meanings, let the sums collide In cortical columns, knowledge multiplies Store exponential memories in finite neural space Mathematics shows us how the brain finds its place [Bridge] VSA composition gives us tools to build Binding joins components, structured meaning filled Component-wise operations, multiply or XOR Create the associations that weren't there before Bundling sums them up and threshold cuts the noise Distributed representations, mathematical poise [Verse 3] High fidelity retrieval from the chaos of the store Random patterns organized like never seen before Each column acts as computational distributed node Processing information in its mathematical mode From theorem to application, cortical design Shows how neural networks cross the dimensional line [Verse 4] Memory interference fades as dimensions grow Sparse activation patterns let the signals flow Binary vectors dancing in ten thousand dimensions wide Where once confusion reigned, now patterns can reside Hyperdimensional computing breaks the storage wall Infinite combinations in finite space for all [Chorus] Nearly orthogonal, patterns stand alone XOR for binding, threshold for the home Bundle up the meanings, let the sums collide In cortical columns, knowledge multiplies Store exponential memories in finite neural space Mathematics shows us how the brain finds its place [Outro] In the mathematics of the mind's architecture High dimensions hold the key to cognitive literature
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