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^§Mehran Moghadam, ^†Abu Kaisar Mohammad Masum, ^†Sercan Aygun , ^§M. Hassan Najafi

^§Case Western Reserve University, ^†University of Louisiana at Lafayette

{moghadam, najafi}@case.edu, {c00591145, sercan.aygun}@louisiana.edu

Robust Data Processing for Vector Symbolic Computing

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GLSVLSI 2025

June 30 – July 2

New Orleans, LA, USA

ID:272

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Outline

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

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Introduction – Data Encoding

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Stochastic Computing (SC)

: Bit-stream

10101010, 11110000,…

♣

BS

Use uniform representation x∈[0,1]

If x=4/8, then four 1s in the eight-bit stream over time

Bitstream length determines precision

More bits ⇒ more accurate approximation of the target value

Uniform stochastic generators (e.g., using LFSRs and comparators)

Random Bit-streams

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Introduction – Data Encoding

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Stochastic Computing (SC)

Use uniform representation x∈[0,1]

If x=4, then there are four 1s in the stream are over time

10101010, 11110000, 11001010, …

SC

(00000100)₂

Base-2

Most and least-significant bits

No bit significance

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Introduction – Data Encoding

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Stochastic Computing (SC)

Low hardware cost�(e.g., multiplication = AND gate)

Advantages

👍

01010110

01111101

01010100

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Introduction – Data Encoding

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Stochastic Computing (SC)

Low hardware cost�(e.g., multiplication = AND gate)

Low power consumption

Massive parallelism and scalability

Advantages

👍

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Introduction – Data Encoding

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Stochastic Computing (SC)

Low hardware cost�(e.g., multiplication = AND gate)

Low power consumption

Fault-robustness

Advantages

👍

10101010

SC

(100)₂

Base-2

10101110

SC

Base-2

Bit-flipped

(0)₁₀

5/8=0.625

(000)₂

4/8=0.5

👍

(4)₁₀

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Introduction – Data Encoding

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Stochastic Computing (SC)

Low hardware cost�(e.g., multiplication = AND gate)

Low power consumption

Fault-robustness

Advantages

👍

Long latency

Approximate results

Weaknesses

👍

Randomness has pivotal role affecting accuracy, performance, and hardware efficiency

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Introduction – Data Encoding

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Vector Symbolic Architecture (VSA)

Brain-inspired computing

Applicable for cognitive tasks

Single-pass learning

Lightweight, energy efficient, noise-tolerant

Randomly generated Hypervectors(HV) with -1s & +1s as atomic data for encoding structured representations

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Motivation

GLSVLSI’25

Data encoding a crucial step for hardware-efficient AI systems

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Pseudo-Randomness in SC & VSA

High-discrepancy
Suboptimal performance
Increased computational demands
reduced energy efficiency

Our Solution: Novel encoding approach based on quasi-randomness using low-discrepancy (LD) sequences for better hardware efficiency and overall performance.

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Outline

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

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Pseudo-Randomness vs. Quasi-Randomness

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Pseudo-Randomness

Quasi-Randomness

Point Distribution

High-Discrepancy

Value Spread

Low-Discrepancy

(Deterministic)

Sequence-1

Sequence-2

Sequence-1

Non-Uniform

Uniform

Probability

Population

Probability

Population

Correlation

Stream-1

Stream-2

Stream-1

Stream-2

Weak

Orthogonality

Inefficient & less accurate
Requires multiple iteration

Efficient & More accurate
Runs in a Single iteration

Strong

Orthogonality

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Background

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

General VDC number in base N (VDC-N)

Fractional Value in (0,1)

VDC

Generator

Integer Value

Van der Corput (VDC) sequences

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Outline

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

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Proposed Framework

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

Powers-of-2 Van der Corput (VDC-2ⁿ) sequences

Quasi-random sequence generator
Simple & lightweight design
Generating independent (orthogonal) sequences simultaneously using different hardwiring without additional HW

Single counter with hardwiring

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GLSVLSI’25

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Improvements:

Enhances computational accuracy by 77%
Reduces power consumption by 66%
Achieves gains with significantly shorter BS lengths and a single-source RNG

Improvements:

Enhances computational accuracy by 26×

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GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

HW cost Comparison

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Lower accuracy
Requires multiple iterations
Higher runtime
Requires 784 different HVs

VSA for Image Classification

Conventional Method

Pseudo-Random Based

P & L hypervector generation

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Quasi-Random Based

No need for P hypervector generation and associated multiplication

Only L hypervector generation

Accuracy Comparison

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Quasi-Random Based

No need for P hypervector generation and associated multiplication

Only L hypervector generation

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GLSVLSI’25

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Integrating unary encoding into VSA models using quantized LD sequences for HV generation

uHD 🡪 Unary + VSA framework

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uHD 🡪 Unary + VSA framework

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lightweight, single-source dynamic HV generator

VSA for Image Classification

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Single-source orthogonal HV generator

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Single-source orthogonal HV generator

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VSA for language Classification

Leveraging N-grams for symbolic representation

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VSA for language Classification

Significantly higher accuracy with low-dimensional HVs compared to the other RNG sources

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Outline

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

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Discussion & Limitations

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Transformative quasi-random approach for highly efficient encoding in neuro-symbolic AI systems.

Outperforms conventional PRNGs (LFSRs) and even traditional quasi-random sequences like Sobol and Halton.

Ensures superior distributional evenness, reducing discrepancy and enhancing consistency in bit-streams and hypervectors.

Minimizes energy-intensive recalculations in SC and strengthens HV orthogonality in VSAs.

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Discussion & Limitations

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Limitations

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Future Directions

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Incorporate other quasi-random sequences for a hybrid approach to enhance diversity.

Potential to enhance spike-time encoding precision in neuromorphic systems and improve sampling uniformity in Bayesian inference.

Explore FPGA-based counter implementations for streamlined deployment.

Future testing in SC NNs and VSA language processing pipelines is necessary to quantify practical gains.

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Outline

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

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Conclusion

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

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GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

THANK YOU

Questions:

Mehran Moghadam

moghadam@case.edu

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Outline

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”

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Outline

GLSVLSI’25

Abu Masum- “Robust Data Processing for Vector Symbolic Computing”