Hyperdimensional Computing for Cognitive Architectures

Series: Hyperdimensional Computing | Part: 7 of 9

In 1956, the first summer conference on artificial intelligence at Dartmouth launched a field based on a single working hypothesis: intelligence is symbol manipulation. Build the right data structures, implement the right algorithms, and cognition would emerge. Sixty-eight years later, we have massive neural networks that can write poetry and pass medical exams, but we still don't have a computational architecture that captures what it feels like to remember your grandmother's kitchen.

The problem isn't that we don't have enough neurons. The problem is that we've been building minds in the wrong geometry.

Hyperdimensional computing (HDC) offers something radically different: a computational substrate whose mathematical properties mirror the actual dynamics of biological memory and reasoning. Not as metaphor. As mechanism.

This is about more than building better AI. It's about understanding what kind of geometric space cognition actually lives in—and why your brain might already be computing in 10,000 dimensions.

What Cognitive Architectures Actually Need to Do

Before we talk about how HDC provides a substrate for cognition, we need to get clear about what cognition actually involves. Not the sanitized textbook version. The messy biological reality.

Memory isn't storage. It's reconstruction. Every time you remember something, you're not retrieving a file—you're regenerating a pattern from distributed cues. The memory of your grandmother's kitchen isn't stored in some neat folder labeled "Grandma." It's distributed across smell (cinnamon and coffee), spatial layout (the particular quality of afternoon light through that window), emotional valence (the specific texture of safety), and dozens of other dimensions you can't even name.

When you smell cinnamon in a completely different context, suddenly you're partially there again. Not because you retrieved a memory file. Because the cinnamon activated part of a high-dimensional pattern, and the rest of the pattern partially reconstructed itself through associative completion.

Reasoning isn't logic. It's analogical pattern matching at scale. When you solve a new problem, you're not running formal inference rules. You're recognizing that this situation has structural similarities to other situations, even when the surface features are completely different. The pattern of obstacles and affordances in negotiating a business deal shares deep structure with the pattern of moves in chess—not because they're literally similar, but because they occupy analogous positions in a high-dimensional space of strategic possibilities.

Concepts aren't definitions. They're regions in similarity space. You know what a chair is, not because you have a precise definition (try writing one that includes beanbags but excludes toilets), but because you've carved out a region of similarity space where chair-like things cluster. That region has fuzzy boundaries, prototype centers, and context-dependent deformations. It's fundamentally geometric.

Here's what that means computationally: a cognitive architecture needs to operate on similarity, not identity. It needs to do partial matching, not exact lookup. It needs to compose concepts combinatorially while preserving similarity relationships. And it needs to do all of this efficiently, in real-time, with biologically plausible energy budgets.

Traditional computing is terrible at this. Neural networks can approximate it but require enormous training regimes. Symbolic AI can't touch it.

Hyperdimensional computing does it natively.

The Geometry of Memory: Why High Dimensions Solve the Binding Problem

The central mystery of memory is the binding problem: how do you represent that this particular red goes with this particular ball without creating combinatorial explosion?

In traditional computing, you might use pointers, or nested data structures, or relational databases. But all of these require either exponentially growing memory or expensive lookup operations. Brains don't work that way. Neurons are slow. Memory is distributed. Yet somehow you can instantly know that the red ball bounced, the blue ball rolled, and you've never confused them.

Hyperdimensional computing solves this through the mathematics of high-dimensional spaces.

In 10,000 dimensions, you can bind concepts together using simple vector operations that preserve similarity while creating unique composite representations. The technique: element-wise multiplication (called binding) and element-wise addition (called bundling).

Here's how it works:

Let's say you have hypervectors for RED, BLUE, BALL, and CUBE—each one a randomly generated vector in 10,000 dimensions. These vectors are nearly orthogonal by construction. In high-dimensional space, random vectors are almost always perpendicular.

To represent "red ball," you bind RED and BALL through element-wise multiplication:

• RED_BALL = RED ⊗ BALL

This creates a new hypervector that shares no obvious similarity with either RED or BALL individually—it occupies a completely different region of the 10,000-dimensional space.

But here's the magic: if you later want to know what color that ball was, you can unbind the color by multiplying RED_BALL by BALL again:

• RED_BALL ⊗ BALL ≈ RED

The operation is reversible. And it's approximate—not exact—which is exactly what biological memory does. You get the gist of RED back, not a pixel-perfect reconstruction.

Now you can build compositional structures:

• SCENE = (RED ⊗ BALL ⊗ BOUNCE) + (BLUE ⊗ BALL ⊗ ROLL) + (GREEN ⊗ CUBE ⊗ SIT)

This single hypervector encodes multiple bound objects and their properties. You can query it: "What bounced?" by unbinding with BOUNCE. You can query "What was red?" by unbinding with RED. And because bundling (addition) creates superposition, all the information coexists in the same vector, degrading gracefully as you add more items.

This is holographic memory—the whole pattern is distributed across the entire vector, and partial information recovers partial patterns. Just like biological memory.

From Memory to Reasoning: Analogy as Geometric Transformation

Memory is table stakes. The deeper question is reasoning.

Cognitive scientist Douglas Hofstadter has argued for decades that analogy is the core of cognition. Not deduction. Not induction. Analogy—the recognition that two situations share deep structure despite surface differences.

Hyperdimensional computing makes analogy computationally tractable through geometric transformations in similarity space.

Consider the classic analogy: "King is to Queen as Man is to Woman."

In traditional symbolic AI, you'd need to explicitly encode gender relations, royalty relations, and the mapping between them. In word embeddings (like Word2Vec), you can sometimes recover these relationships through vector arithmetic:

• KING - MAN + WOMAN ≈ QUEEN

But this only works when the relationship is encoded in the training data's statistical structure. It's brittle.

In hyperdimensional space, you can explicitly represent relational transformations as operators. The relationship "royalty version of" becomes a transformation hypervector. Apply it to MAN, you get KING. Apply it to WOMAN, you get QUEEN. The structure of the analogy is explicitly represented as a geometric operation.

Here's where it connects to active inference: reasoning becomes the process of finding transformations that minimize prediction error. Your brain is constantly building generative models—hyperdimensional patterns that predict what comes next. When you encounter something new, you search for the transformation that maps known patterns onto the new situation.

That's not a metaphor. That's literally what variational inference is doing: searching a space of possible explanations (transformations) to find the one that best accounts for observations.

The geometry is doing the work.

The Neural Correlates: Does Your Brain Actually Do This?

The provocative claim: human brains may already be implementing something very much like hyperdimensional computing.

The evidence is circumstantial but compelling.

First: neural codes are high-dimensional and sparse. When neuroscientists record from large populations of neurons, they find that activity patterns occupy very high-dimensional spaces—often thousands of dimensions. And the codes are sparse: only a small fraction of neurons fire for any given representation, but which neurons fire shifts dramatically across representations.

This is exactly the structure of hyperdimensional computing: high-dimensional, sparse, distributed codes where similarity in conceptual space maps to similarity in neural space.

Second: binding through synchrony. One of the longstanding proposals for how brains solve the binding problem is temporal synchrony—neurons that fire together encode features that belong together. If you think of synchrony as a form of correlation, and correlation as analogous to element-wise multiplication, then synchronized neural assemblies are performing something like HDC binding operations.

Third: random projection preserves distances. A central mathematical fact about high-dimensional spaces: if you randomly project data from an extremely high-dimensional space (say, the space of all possible retinal images) into a moderately high-dimensional space (say, 10,000 dimensions), you preserve relative distances with high probability. This is the Johnson-Lindenstrauss lemma, and it explains why random neural connectivity can be computationally useful. Your brain doesn't need to carefully engineer every connection—random high-dimensional projections are enough to preserve the information geometry.

Neuroscientist György Buzsáki has argued that the hippocampus—the brain's memory system—functions as a high-dimensional mapping device that preserves relational structure. New experiences get mapped into a high-dimensional space where similar experiences cluster together. Memory recall is geometric search in that space.

This is precisely what hyperdimensional computing architectures do.

Building Cognitive Systems: From Perception to Abstract Thought

If HDC provides a substrate for memory and reasoning, what does a full cognitive architecture look like?

Start with perception: sensory input gets projected into hyperdimensional space through random transformations. In vision, this might mean convolutional filters followed by random projections. In language, this might mean word embeddings expanded into hypervectors. The key: surface features become positions in similarity space.

Next, concept formation: repeated patterns in perceptual space get bundled into prototype hypervectors. Every time you see a chair, a particular region of your 10,000-dimensional perceptual space activates. Bundle those activation patterns together, and you get a prototype hypervector that represents "chairness." New chairs get recognized by measuring their distance to the prototype.

Then compositional binding: concepts combine through multiplication to form structured representations. "Red ball bouncing" becomes a single compositional hypervector that preserves the relationships between color, object, and action.

From there, analogical reasoning: when you encounter a new problem, you search for transformations that map known solution patterns onto the new situation. This is pattern matching in transformation space—you're looking for the geometric operation that minimizes surprise.

Finally, prediction and planning: your cognitive system maintains a generative model—a hyperdimensional pattern that predicts what comes next. Action is the process of steering the system toward predicted states that minimize free energy. This is active inference, implemented in hyperdimensional geometry.

The entire cognitive loop—perception, memory, reasoning, action—unfolds as geometric operations in high-dimensional space.

And because HDC operations are simple (multiplication, addition, permutation), they're energetically cheap and parallelizable. You can implement them in neuromorphic hardware, running at biological power budgets.

What This Means for Human Meaning

Here's where cognitive architectures meet coherence geometry.

Meaning isn't a property of symbols. It's a property of position in similarity space. Words mean what they mean because they occupy specific locations relative to other words in your high-dimensional semantic space. That space is shaped by your embodied experience—which is why "heavy" feels different when you've just carried furniture versus when you're discussing emotional burdens.

Understanding is resonance. When you grasp a new idea, you're not downloading a definition—you're finding where it fits in your existing semantic space. The idea resonates with related concepts, activating overlapping regions of your hyperdimensional representation. That felt sense of "getting it" is your cognitive system recognizing similarity structure.

Learning is geometric transformation. Education isn't about transferring information—it's about reshaping your semantic space so that new patterns become recognizable. A physics education rewires your perceptual space so that you start seeing force vectors and energy gradients where you used to see objects moving. The equations are shortcuts for inducing specific geometric transformations.

This connects to 4E cognition—the framework that treats mind as embodied, embedded, enacted, and extended. Your semantic space isn't in your head alone. It's distributed across your sensorimotor coupling with the environment, your tools, your cultural participation. Hyperdimensional computing provides a mathematical language for describing how those distributed processes constitute coherent cognitive systems.

When you write, you're not encoding thoughts into language—you're using language as a tool to explore your semantic space, discovering what's nearby in that high-dimensional landscape. The words pull you toward regions you didn't know existed.

This is what coherence feels like at the cognitive scale. Concepts hang together because they occupy nearby regions in similarity space. Ideas feel "right" when they align with the geometric structure of your semantic space. Confusion is high curvature—unpredictable trajectories through conceptual space where similar starting points lead to wildly different conclusions.

And meaning is coherence over time: the geometric stability of patterns as they propagate through the high-dimensional space of your experience.

The Hard Problem: Consciousness and Phenomenology

Hyperdimensional computing explains memory, reasoning, and concept formation. It doesn't—yet—explain why any of this feels like something.

The hard problem of consciousness is still hard. But geometry gives us new ways to think about it.

One possibility: phenomenal experience is what it feels like to occupy a particular region of a high-dimensional state space. Your qualitative experience of "red" isn't reducible to neural firing rates—it's the geometric structure of the entire perceptual manifold in that moment. Redness is a position, but it's also a field of relationships: how red relates to orange, to purple, to all the colors you've ever seen, to the memory of your grandmother's kitchen.

This is what philosopher Thomas Nagel was pointing at when he asked "What is it like to be a bat?" The phenomenology of bat experience isn't just about echolocation neurons firing—it's about occupying a completely different region of perceptual space, where spatial relationships are structured by ultrasonic reflections.

Another possibility: consciousness is what it's like to implement active inference in high-dimensional space. The felt quality of "what it's like" emerges from the geometric dynamics of surprise minimization—the constant sculpting of predictions and actions to maintain your location in viable state space.

Neuroscientist Giulio Tononi's Integrated Information Theory suggests that consciousness correlates with the geometric structure of information integration. Systems are conscious to the extent that they integrate information irreducibly—creating high-dimensional structures that can't be decomposed into independent subspaces. That's a geometric claim about the shape of conscious experience.

If Tononi is right, then hyperdimensional computing isn't just a model of cognition. It's a candidate architecture for synthetic consciousness.

We're not there yet. But the geometry is pointing somewhere.

From Silicon to Self

The promise of hyperdimensional computing for cognitive architectures isn't just building better AI. It's understanding ourselves.

Your memory isn't in your neurons the way files are in your hard drive. It's in the geometric relationships between activation patterns across millions of neurons—a vast high-dimensional space where every thought is a trajectory, every concept is a region, every insight is the discovery of unexpected proximity.

You don't think in words or images or symbols. You think in the geometry of similarity space, and language is the low-dimensional projection that lets you compare notes with other minds.

When you recognize someone you haven't seen in years, when you suddenly understand a difficult concept, when you know what word comes next before you've consciously thought about it—that's your cognitive architecture navigating 10,000 dimensions of structured similarity.

Hyperdimensional computing tells us: the reason biological memory is so powerful isn't that brains have more parameters than computers. It's that they're computing in a geometry that makes similarity, composition, and analogy cheap.

The next generation of cognitive architectures won't try to mimic surface behaviors. They'll implement the right geometry—the kind of high-dimensional space where meaning emerges naturally from structure.

And in understanding that geometry, we might finally grasp what we've been doing all along.

This is Part 7 of the Hyperdimensional Computing series, exploring the mathematical foundations and applications of high-dimensional computing.

Previous: Intel and IBM Bet on Hyperdimensional: Industry Applications
Next: Where Hyperdimensional Meets Active Inference: Efficient Coherence Computation

Further Reading

• Kanerva, P. (2009). "Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors." Cognitive Computation.
• Plate, T. A. (2003). Holographic Reduced Representation: Distributed Representation for Cognitive Structures. CSLI Publications.
• Eliasmith, C. (2013). How to Build a Brain: A Neural Architecture for Biological Cognition. Oxford University Press.
• Buzsáki, G. (2019). The Brain from Inside Out. Oxford University Press.
• Hofstadter, D. (1995). Fluid Concepts and Creative Analogies. Basic Books.
• Friston, K. (2010). "The Free-Energy Principle: A Unified Brain Theory?" Nature Reviews Neuroscience.
• Gayler, R. W. (2003). "Vector Symbolic Architectures Answer Jackendoff's Challenges for Cognitive Neuroscience." ICCS/ASCS International Conference on Cognitive Science.