The Modeltrix!
There’s no Determinant
In the movie The Matrix (1999), the spoon boy uses telekinesis and says “There’s no spoon”. Well, in the world of AI, there’s \[obviously\] more than one matrix (Matrices) as “a singular matrix has no spoon…err…I mean no Determinant”. With that unwarranted lame joke and comparison out of our way, what are some emerging alternatives to matrix multiplications in the world of low-power, low-latency, edge driven GenAI. Can we say “There’s no Matrix”? Maybe not; but there are some emerging alternatives for sure.
While matrix multiplication (specifically, large-scale tensor operations) is fundamental to most neural networks, including Small Language Models (SLMs), there are alternative approaches for inference that can reduce reliance on traditional matrix multiplications. Given some of Quest1’s customer/partner ecosystems deeply involved with HealthCare and Edge), we found some possible alternatives. Many of these approaches are analogous to traditional performance engineering exercises done on applications / databases.
If you find yourself in situations where the models are not blackboxes; but there is a grey (gray) territory for you to optimize and explore, then there are:
Lookup Tables (Memory-based Approaches)
Instead of computing activations, pre-computed embeddings or cached results can be used. For example: kNN-LMs (using nearest neighbors instead of full matrix multiplications).
We also have winners like Redis Semantic Caching. Both Semantic Caching (conceptual meaning) and LLM Caching (input-output pairing, with token level granularity) aim to reduce redundant matrix computation and improve efficiency, but they differ in approach and use case. This is already popular in databases, search engines, and web APIs.
Sparse Computation (Avoid Full Dense Multiplication)
Low-Rank Approximations: Instead of full-rank matrices, models use low-rank factorizations (or remember Singular Value Decomposition from Linear Algebra?). Attention Pruning: Reducing the number of attention heads or connections (Token Pruning / Structured Attention Pruning / Dynamic Pruning at Runtime). Very useful in situations such as Smart Grids, where one needs to identify power fluctuations without full signal processing.
Fourier Transforms & Alternative Basis Functions
Fast Fourier Transform (FFT) or Wavelet Transforms can replace direct matrix operations in certain cases Classic Example: FNet (uses Fourier Transform instead of self-attention). Wavelet-based compression (JPEG 2000) also helps with efficient image and video analysis on low-power hardware. For use-cases such as predictive maintenance, anomaly detection (Faster processing in security cameras and smart vision), drones/robotics etc., this is a great technique if you’re constrained by power and require low-compute options.
Analog & Neuromorphic Computing
Using specialized hardware like optical computing (which can perform vector-matrix multiplication via light interference). Neuromorphic computing is much relevant for niche Edge based requirements (e.g. Neuromorphic chips like Intel’s Loihi) use spiking neural networks (SNNs) that work differently from standard matrix operations.
Bitwise & Probabilistic Computation
XOR-based operations for hashing instead of matrix products. Probabilistic circuits and Bayesian methods as alternatives to fully deterministic matrix-based models. In the past few months, we’ve seen this being leveraged extensively in Telecom and the world of Networks — in areas like Threat and DDoS detection, HyperLogLog to determine number of unique IPs in a network with minimal memory etc.
While matrix multiplication remains dominant in current SLMs, hybrid and non-matrix-based methods are being explored to reduce power consumption, improve efficiency, and enable alternative computing architectures!
Moral of the story:
“You’ll see that it is not the spoon that bends, it is only yourself”. So bend it like… 😂🤪😜