💬 NLP

Compiler-Driven Approximation Tuning for Hyperdimensional Computing

This paper introduces ApproxHDC, a compiler-driven framework that extends the HPVM-HDC infrastructure to automatically identify and apply high-impact software and hardware approximations across diverse computing platforms, thereby optimizing Hyperdimensional Computing workloads for performance while maintaining accuracy.

Original authors: Xavier Routh, Abdul Rafae Noor, Akash Kothari, Zheyu Li, Mahbod Afarin, Tajana Rosing, Vikram Adve

Published 2026-06-26

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CC BY 4.0

Original authors: Xavier Routh, Abdul Rafae Noor, Akash Kothari, Zheyu Li, Mahbod Afarin, Tajana Rosing, Vikram Adve

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to solve a massive puzzle, but instead of looking at one piece at a time, you are looking at a giant, high-resolution 3D map of the entire puzzle. This is how Hyperdimensional Computing (HDC) works. Instead of using tiny, fragile numbers like traditional computers do, HDC uses huge, fuzzy "vectors" (think of them as massive, multi-colored strings of beads) to represent data.

The cool thing about these bead strings is that they are incredibly tough. If you lose a few beads or the colors get a little muddy (noise), the overall picture is still clear. This means you can cut corners, skip steps, or use cheaper, fuzzier tools to process them without ruining the final answer.

The Problem:
Because there are so many ways to "cut corners" (like skipping parts of the calculation, using fewer beads, or using cheaper memory chips), the number of possible combinations is astronomical. It's like trying to find the perfect recipe for a cake by tasting every possible combination of flour, sugar, and eggs in the universe. Doing this by hand is impossible, and existing tools are either too general (like a generic cookbook) or too limited (like a recipe book that only has one cake).

The Solution: ApproxHDC
The authors built a tool called ApproxHDC. Think of this as a super-smart, automated sous-chef that knows exactly how to tweak the recipe for HDC.

Here is how it works, using simple analogies:

The Map Reader (Compiler):
First, the tool reads the computer program (the recipe) and identifies every single step where HDC is being used. It creates a detailed map of where the "bead strings" are being processed.
The Tuning Knob (Search Space):
The tool has a giant control panel with thousands of knobs. Some knobs are software-based (like telling the computer to "only look at the first half of the bead string" or "use simpler math"). Others are hardware-based (like telling a special memory chip to "store data with less precision" or "write it faster but with a tiny bit more error").
The Taste Tester (QoS Evaluator):
The tool tries out different combinations of these knobs. After each try, it checks the result. Did the computer still get the right answer? (This is called the "Quality of Service" or QoS). If the answer is still good enough, it keeps the change. If the answer is wrong, it throws that combination away.
The Pruning Shears (Smart Cutting):
Since there are too many knobs to try them all, the tool uses "pruning." It's like a gardener who knows that certain branches of a tree will never bear fruit, so it cuts them off immediately. The tool also lets the human developer say, "Don't touch this specific part of the recipe," which helps the tool find the best settings much faster.

What They Found:
The team tested this tool on four different types of tasks (like classifying letters, grouping data, analyzing relationships, and searching DNA sequences) on different types of computers (standard CPUs, powerful GPUs, and experimental memory chips).

Speed: The tool made the programs run up to 17 times faster on standard computers and 15 times faster on graphics cards, all while keeping the answers accurate enough to be useful.
Better than the Competition: They compared it to the current best tool (called MicroHD). ApproxHDC was 3.5 times faster at finding the best settings because it could look at a much wider variety of "knobs" and "recipes."
Hardware Magic: When they tested it on special experimental memory chips (ReRAM and PCM), it found ways to make them 4.7 times faster by tweaking the hardware settings directly, something other tools couldn't do.

The Bottom Line:
ApproxHDC is an automated system that figures out exactly how much "fuzziness" or "shortcuts" a Hyperdimensional Computing program can handle without breaking. It saves time and energy by automatically finding the perfect balance between speed and accuracy, making these brain-inspired computers much more practical for real-world use.

Technical Summary: Compiler-Driven Approximation Tuning for Hyperdimensional Computing

Problem Statement

As Moore's Law reaches physical and economic limits, domain-specific approaches are increasingly necessary to accelerate machine learning workloads. Hyperdimensional Computing (HDC) has emerged as a promising paradigm, offering a brain-inspired alternative to deep learning with inherent noise tolerance and hardware efficiency. However, while HDC algorithms are resilient to noise and approximation, the design space for exploiting these properties is combinatorially large.

A single HDC application may contain dozens of primitive operations, each offering multiple approximation strategies (e.g., reduced precision, skipped iterations, algorithmic variants). When targeting heterogeneous hardware (CPUs, GPUs, and in-memory accelerators like ReRAM and PCM), the search space expands further to include hardware-specific knobs such as ADC resolution, write-verify depth, and multi-level cell configurations. Manually navigating this space is impractical because configurations rarely transfer across datasets or backends, and cross-operation interactions are difficult to predict without empirical evaluation. Existing frameworks either lack domain-specific compiler support for HDC primitives (e.g., EnerJ, ApproxHPVM) or rely on limited, non-compiler-integrated hyperparameter tuning (e.g., MicroHD), failing to jointly optimize software and hardware approximations across heterogeneous targets.

Methodology: ApproxHDC

To address these challenges, the authors present ApproxHDC, an automated framework for identifying and applying domain-specific approximations in HDC workloads. ApproxHDC extends the existing HPVM-HDC compiler infrastructure to enable retargetable compilation and automated tuning.

System Architecture

The framework operates through a closed-loop compilation and tuning process:

HDC Primitive Identification: A compiler pass performs static analysis on HDC++ source code to identify all HDC primitive invocations. It extracts contextual metadata (function, basic block, execution order) and generates a structured JSON representation of the program's operations.
Approximation Design Space Construction: The ApproxHDC Tuning System (implemented in Python using OpenTuner) constructs a search space encompassing both software and hardware approximations.
- Software Approximations: Includes Reduction Perforation (skipping loop iterations in reduction operations), Automatic Binarization (converting hypervectors to packed single-bit representations), Encoding Dimensionality tuning, Element Type Representation (e.g., FP32 to INT8), and Algorithmic Choice (e.g., Cosine Similarity vs. Hamming Distance).
- Hardware Approximations: For in-memory accelerators (ReRAM/PCM), the system models knobs such as ADC resolution, write-verify cycles, analog quantization scale, and Multi-Level Cell (MLC) bits.
Search Space Pruning: To make the search tractable, ApproxHDC employs two strategies:
- Domain-Aware Pruning: The system leverages knowledge of HDC to eliminate unpromising regions (e.g., recognizing that certain encoding stages are too sensitive to approximation).
- Developer-Guided Pruning: Developers can use lightweight source annotations (__hetero_hdc_no_approx) to exclude specific primitives or subgraphs from the search space, preventing the tuner from wasting time on critical, non-tolerant stages.
Iterative Tuning: The system empirically explores configurations, measuring Quality-of-Service (QoS) metrics (e.g., accuracy, NMI score), execution time, and energy. It inserts the selected approximation annotations back into the source code, recompiles via HPVM-HDC, and iterates until a time budget or convergence limit is reached.

Key Contributions

The paper outlines four primary contributions:

ApproxHDC Framework: An auto-tuning system that automates approximation selection to jointly optimize end-to-end performance, energy, and QoS across heterogeneous hardware (CPUs, GPUs, and simulated ReRAM/PCM accelerators).
Unified Software-Hardware Support: The first framework to integrate in-memory accelerator knobs into a compiler-driven tuning loop, treating both software transformations and hardware-level parameters as first-class dimensions of the search space.
HDC-Specific Pruning Techniques: Methods to reduce the approximation search space by up to 86 orders of magnitude (e.g., reducing a space of $10^{89}$ to $10^3$ ). This combines automatic domain-aware pruning with developer annotations, enabling the discovery of high-quality configurations within minutes.
Comprehensive Evaluation: Extensive evaluation across four benchmarks (HD-Classification, HD-Clustering, RelHD, HD-HashTable) and multiple datasets, demonstrating significant speedups while adhering to user-specified QoS constraints.

Experimental Results

The evaluation was conducted on AMD EPYC CPUs, NVIDIA RTX 2080 Ti GPUs, and a SpecPCM simulator.

Performance Speedups: ApproxHDC achieved up to 17.25× speedup on CPUs, 15.02× on GPUs, and 4.69× on SpecPCM while maintaining QoS constraints (typically within 5% accuracy loss or specific NMI thresholds).
Comparison with State-of-the-Art: When compared to the MicroHD framework (a Python-based, non-compiler approach), ApproxHDC demonstrated a 3.49× speedup advantage. In a specific classification benchmark, ApproxHDC found a configuration yielding 24.65× speedup (with 4.8% accuracy loss) compared to MicroHD's best 7.07× speedup. This gap was attributed to ApproxHDC's ability to explore per-operation reduction perforation and algorithmic choices that MicroHD could not access.
Search Efficiency: The pruning techniques were critical; without them, the search space was too large to find optimal configurations within the 3-hour tuning budget. For instance, in HD-Classification, enabling full reduction perforation without hints prevented the tuner from finding high-performance configurations, whereas the "End-only + hint" configuration successfully identified optimal settings.
Hardware Approximation: On SpecPCM, the tuner successfully balanced hardware knobs (e.g., reducing ADC resolution, adjusting quantization scales) with software parameters (e.g., reducing training iterations) to achieve significant energy and latency reductions with minimal accuracy impact.

Significance and Claims

The paper claims that ApproxHDC bridges the gap between the theoretical noise tolerance of HDC and the practical difficulty of manually tuning complex approximation spaces. By treating approximation as a compiler-driven, automated process rather than a manual engineering task, the framework enables:

Retargetability: A single HDC++ application can be optimized for diverse hardware backends without maintaining multiple target-specific versions.
Scalability: The ability to navigate an exponentially large design space through intelligent pruning, making automated tuning feasible for real-world applications.
Holistic Optimization: The unique capability to jointly optimize software and hardware approximations, leveraging the specific resilience of HDC to noise in both the algorithmic and physical layers.

The authors emphasize that no single pruning strategy uniformly achieves the highest performance across all applications, underscoring the importance of providing developers with mechanisms to productively guide the search. The work demonstrates that with the right compiler infrastructure and tuning strategies, HDC can achieve substantial performance and energy gains on heterogeneous platforms while maintaining acceptable inference quality.