IsoQuant: Hardware-Aligned SO(4) Isoclinic Rotations for LLM KV Cache Compression

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• IsoQuant reduces forward rotation computational cost compared to RotorQuant, specifically from about 2,408 FMAs to 1,024 FMAs for IsoQuant-Full and to 512 FMAs for IsoQuant-Fast at dimension d=128.technical 95%
  Evidencepartial

  At d=128, IsoQuant-Full reduces forward rotation cost from about 2,408 FMAs in RotorQuant to 1,024, while IsoQuant-Fast further reduces it to 512.

  Implicationpartial

  Explicit numeric comparison provided in the abstract with specific FMA counts.

  Verificationpartial

  partial

• IsoQuant achieves mean kernel-level speedups of about 4.5× to 4.7× over RotorQuant across various CUDA settings, with peak speedups above 6×.result 90%
  Evidencepartial

  IsoQuant achieves mean kernel-level speedups of about 4.5×--4.7× over RotorQuant while maintaining comparable reconstruction MSE, with peak speedups above 6×.

  Implicationpartial

  Directly stated in the abstract with specific speedup ranges and mention of peak performance.

  Verificationpartial

  partial

• IsoQuant maintains reconstruction quality (MSE) comparable to RotorQuant while achieving significant speedups.result 85%
  Evidencepartial

  IsoQuant achieves mean kernel-level speedups of about 4.5×--4.7× over RotorQuant while maintaining comparable reconstruction MSE

  Implicationpartial

  Directly stated in the abstract that speedups are achieved 'while maintaining comparable reconstruction MSE'.

  Verificationpartial

  partial

• The 4D block structure of IsoQuant is more hardware-aligned than RotorQuant's 3D partition, especially for common transformer head dimensions that are powers of two.technical 80%
  Evidencepartial

  A 4D partition therefore avoids the pathological tails induced by 3D chunking in almost every common setting. At d = 128, IsoQuant uses exactly 32 blocks with no remainder, whereas a 3D design requires 42 full blocks plus a leftover

  Implicationpartial

  Strongly supported by systems argument in analysis about alignment and avoiding pathological tails, with specific example at d=128.

  Verificationpartial

  partial

• IsoQuant represents each 4D block as a quaternion and applies a closed-form transform T(v)=q_L v q̄_R, which is more computationally efficient than previous approaches.method 90%
  Evidencepartial

  It represents each 4D block as a quaternion and applies a closed-form transform T(v)=q_L v \overline{q_R}.

  Implicationpartial

  Core method explicitly described in abstract and analysis with specific mathematical formulation.

  Verificationpartial

  partial

• Current validation of IsoQuant is limited to the stage-1 quantize-dequantize path on synthetic normalized vectors, with end-to-end KV-cache evaluation remaining as future work.limitation 95%
  Evidencepartial

  Current validation is limited to the stage-1 quantize--dequantize path on synthetic normalized vectors; end-to-end KV-cache evaluation remains future work.

  Implicationpartial

  Explicit limitation statement in the abstract about scope of current evaluation.

  Verificationpartial

  partial

• IsoQuant avoids the expansion to an 8-component multivector representation required by RotorQuant's 3D Clifford blocks, keeping per-block state smaller.technical 75%
  Evidencepartial

  Compared with RotorQuant's 3D Clifford blocks, IsoQuant avoids the expansion to an 8-component multivector representation, keeps the per-block state smaller

  Implicationpartial

  Implied in analysis comparing systems arguments, though not explicitly stating the 8-component count for RotorQuant.

  Verificationpartial

  partial

• Orthogonal feature decorrelation before scalar quantization substantially improves rate-distortion behavior for online vector quantization methods.technical 85%
  Evidencepartial

  A core insight behind online vector quantization methods such as TurboQuant [1] is that decorrelating features before scalar quantization substantially improves rate–distortion behavior.

  Implicationpartial

  Presented as established insight from prior work (TurboQuant) that forms the foundation for IsoQuant's approach.

  Verificationpartial

  partial

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