PTQTP decomposes LLM weight matrices into two ternary (trit) planes with two free per-group scales. Tying the scales to a fixed ratio of three collapses the decomposition into a single uniform nine-level quantizer, a known balanced-ternary identity. To our knowledge, at the time of writing, this work is the first to impose that identity as a constraint inside PTQTP's solver. The two trit planes then fold losslessly into one 4-bit code plane that we make the persistent serving representation: disk bytes, expert-cache bytes, and kernel input are the same 4.0625-bits/weight blocks, consumed in one integer dot pass. For this conjunction (ratio-3 nine-level code, CPU-SIMD kernels, SSD expert streaming, identical persistent bytes) we likewise found no precedent. We apply this to the routed experts of DeepSeek-V4-Flash-0731, a 284B-A13B mixture-of-experts model, quantizing in one shot from the released MXFP4 expert weights and streaming experts from SSD on a 64 GB laptop. Against a 4.5-bit Q4_K baseline, measured one process per fixture with an expert-lossless anchor arm as reference control, the tied model matches the official serving API on 5/5 fixtures at step 0 (Q4_K: 4/5) and 12/14 captured continuation steps (11/14), scores 86 vs. 84 on a 100-item MMLU subset, decodes 6.7% faster in decode phase, and ships 9% smaller files: no detected fidelity difference at these small evaluation sizes, and every fixture-level difference between the arms traces to a single measured near-tie cell. The tied fit nevertheless shows higher weight-reconstruction error and worse perplexity, a measured dissociation between proxy metrics and reference fidelity. A cumulative trunk-ternarization ladder and bitwise-pinned aarch64/x86-64 kernels complete the report. All code, formats, and evaluation artifacts are open source in the fucina inference stack.
PTQTP decomposes LLM weight matrices into two ternary (trit) planes with two free per-group scales. Tying the scales to a fixed ratio of three collapses the decomposition into a single uniform nine-level quantizer, a known balanced-ternary identity. To our knowledge, at the time of writing, this work is the first to impose that identity as a constraint inside PTQTP's solver. The two trit planes then fold losslessly into one 4-bit code plane that we make the persistent serving representation: disk bytes, expert-cache bytes, and kernel input are the same 4.0625-bits/weight blocks, consumed in one integer dot pass. For this conjunction (ratio-3 nine-level code, CPU-SIMD kernels, SSD expert streaming, identical persistent bytes) we likewise found no precedent. We apply this to the routed experts of DeepSeek-V4-Flash-0731, a 284B-A13B mixture-of-experts model, quantizing in one shot from the released MXFP4 expert weights and streaming experts from SSD on a 64 GB laptop. Against a 4.5-bit Q4_K baseline, measured one process per fixture with an expert-lossless anchor arm as reference control, the tied model matches the official serving API on 5/5 fixtures at step 0 (Q4_K: 4/5) and 12/14 captured continuation steps (11/14), scores 86 vs. 84 on a 100-item MMLU subset, decodes 6.7% faster in decode phase, and ships 9% smaller files: no detected fidelity difference at these small evaluation sizes, and every fixture-level difference between the arms traces to a single measured near-tie cell. The tied fit nevertheless shows higher weight-reconstruction error and worse perplexity, a measured dissociation between proxy metrics and reference fidelity. A cumulative trunk-ternarization ladder and bitwise-pinned aarch64/x86-64 kernels complete the report. All code, formats, and evaluation artifacts are open source in the fucina inference stack.
We introduce ExTernD (Expanded-rank Ternary Decomposition), a post-training factorization of each LLM weight matrix A∈Rm×n into A≈Bdiag(D)C with ternary factors B∈{−1,0,+1}m×k, C∈{−1,0,+1}k×n and a real scale vector D∈Rk. The inner rank k=μmin(m,n) is deliberately expanded beyond full rank (μ>1), so that components past full rank correct the quantization error of earlier ones. We prove the residual decreases monotonically in k and can be driven below any ε>0: ExTernD approaches bf16 accuracy arbitrarily closely, which no ternary scheme with a fixed plane count can do. Memory and compute scale continuously with μ, and factor sparsity continuously with a threshold τ, so an accuracy target is hit exactly rather than rounded to the next bit-width. ExTernD matches Q4_K's per-matrix accuracy at 5.2-5.5 effective bpw (5.1-5.5 with importance weighting) on Gemma-4-E2B and Qwen3.5-4B, and a full Qwen3.5-4B conversion at μ=3 reaches 10.10 wikitext-2 perplexity against 9.78 for bf16 (+3.2%), placing it near the Q4_K/Q5_K accuracy band at ~5.7 effective bpw.
Leech-lattice quantization gives good quality at two bits per weight, but its codebooks hold more than 10^14 points, too many for a lookup table. Our earlier kernel expanded the codes at load time and read 4.804 bits per weight from GPU memory for 2 bits of code. We present Tetra, a new codebook on the same lattice. A 24-weight block still takes 48 bits, most of which index a 64-state trellis of the Golay code and one shared 16 KiB table. The kernel decodes a block with six table loads and two small lookups inside the matrix-vector product, and reads 2.148 bits per weight. For full models, we retrain one scale per matrix row, store the matrices that lose the most as 4-bit integers, and pay for them with 4-bit embedding tables. Our Qwen3-4B, 8B and 14B files hold 2.73, 2.70 and 2.73 bits per parameter over the whole model. They score 63.37, 69.58 and 75.66 on the full MMLU test set, 4.76, 4.21 and 2.46 points below 4-bit AWQ at 5.3 to 6.0 bits per parameter. They generate 113.8, 95.0 and 57.2 tokens per second in our engine. On GSM8K, through the served kernel, they lose 9.63, 4.62 and 3.26 points to FP16. At 4B our file scores 23.6 points above llama.cpp's IQ2_XXS (2.48 bits per parameter). Every number we measured for a table or figure comes from one NVIDIA L40S GPU. We preregistered the main experiments.
Quantizing the weights of large language models (LLMs) from 16-bit to lower bitwidth is the de facto approach to deploy massive transformers onto more affordable accelerators. While GPTQ emerged as one of the standard methods for one-shot post-training quantization at LLM scale, its inner workings are described as a sequence of algebraic updates that obscure geometric meaning or worst-case guarantees. In this work, we show that, when executed back-to-front (from the last to first dimension) for a linear layer, GPTQ is mathematically identical to Babai's nearest plane algorithm for the classical closest vector problem (CVP) on a lattice defined by the Hessian matrix of the layer's inputs. This equivalence is based on a sophisticated mathematical argument, and has two analytical consequences: first, the GPTQ error propagation step gains an intuitive geometric interpretation; second, GPTQ inherits the error upper bound of Babai's algorithm under the assumption that no weights are clipped. Leveraging this bound, we design post-training quantization methods that avoid clipping, and outperform the original GPTQ. In addition, we provide efficient GPU inference kernels for the resulting representation. Taken together, these results place GPTQ on a firm theoretical footing and open the door to importing decades of progress in lattice algorithms towards the design of future quantization algorithms for billion-parameter models. Source code is available at https://github.com/IST-DASLab/GPTQ-Babai.
OSIRIS v4.7.0 Monograph & Governed Release Package This technical note and empirical dataset encapsulate the complete sovereign architecture, operational history, and automated self-correction framework of the OSIRIS and dna::}{::lang project. Developed entirely on severely constrained consumer hardware—a handheld Google Pixel Fold (Node Alpha, running Termux with ARM64 NEON SIMD kernels and a 300s thermal horizon; now retired post-campaign) and a GPU-less HP laptop powered by an Intel Core i7 CPU (Node Beta, executing local quantized mentor models and NCLM continual training within WSL2)—OSIRIS proves that sovereign, verifiable scientific agency can be achieved without enterprise server clusters. Key Empirical & Architectural Contributions: Governed Execution (SYS-021): Enforces the foundational axiom 'Cognition may be distributed; authority is not.' Unverified generative models propose; deterministic AST firewalls constrain; cryptographic receipts authorize (H_payload = SHA-256(code)); and immutable Merkle DAGs record. Automated Falsification of the τ-Phase Anomaly: Under strict budget limits on the IBM Quantum Open Plan (Job dbiobimne4hc73bf2am0 on IBM Heron r2 ibm_fez), OSIRIS autonomously audited and conclusively refuted the historical December 2025 hypothesis (τ0 = 46 μs, θ_lock = 51.843°). Using 3-basis Pauli tomography (ZZ, XX, YY), OSIRIS proved that apparent 'entanglement revivals' were classical T1 relaxation artifacts to |00> (P_Bell drops to a minimum at T1*ln(2) and rebounds as qubits decay to ground; transverse coherence C_perp measures dead zero: +0.0029 ± 0.0221; θ_lock p = 0.3537). The erratum is permanently anchored under Merkle Root 7e8f20c2e0ce.... Genuine Quantum Advantage in Multi-Qubit Crosstalk Refocusing: On 156-qubit heavy-hex architecture (ibm_kingston, Job dbb4ppk24mrc73bo8ntg), OSIRIS evolved bipartite sublattice pulse-timing staggering (xy4x2_stag and osiris_evolved_g1) that crushes standard unstaggered dynamical decoupling (retaining 0.9602 and 0.9373 vs 0.8625 ground state probability) by canceling static spectator ZZ crosstalk. Continual Living Intelligence (osiris.nclm): Operates an online, byte-level transformer core governed by a permanently held-out speaking gate (≤ 2.0 bits/byte vs unigram baseline), actively distilling mentor lessons from verified writing. The package contains the full monograph, reproducible Qiskit/QPY circuit definitions, raw decoded IBM Quantum execution spans and bitstrings, Merkle governance ledgers, and the complete OSIRIS v4.7.0 codebase.
QECTOR Decoder Benchmark Datasets & Empirical Reports This repository hosts the evolving collection of reproducible benchmark datasets, JSON measurement artifacts, and empirical performance reports for the QECTOR Decoder v3 platform (Rust/Python quantum error-correction decoder). Each versioned deposit contains environment-stamped, content-hashed JSON artifacts together with the corresponding publication-grade report. All numerical results are fully regenerable from the published wheels and the scripts listed in the reproducibility sections. Scope across versions Code-capacity and circuit-level (Stim rotated_memory_z) evaluations Throughput (shots/s, measure-s/shot), logical error rates with 95 % Wilson intervals, syndrome faithfulness (GF(2) exact check), and CUDA-vs-CPU bit identity Decoder families: FastUnionFind, UnionFind, Blossom (exact MWPM), SparseBlossom, Batch/CPUBatch, BPOSD, HybridCascade, AmbiguityCluster, LookupTable, and CUDABatch (unweighted + DEM-weighted) Hardware provenance, licence-tier disclosure (GPU gated behind Enterprise), and SHA-256 inventories of every backing artifact Version history (selected) v0.6.6 (July 2026) – Workbench Benchmark Master Report: 1 858 decode-timing measurements from 105 runs, six code topologies (Heavy Hex, Repetition, Ring, Rotated Surface, Toric, Unrotated Surface), fixed p = 0.05, distances d = 3–19. Focus on raw latency, harmonic-mean throughput and peak memory. v0.6.8 - Empirical edge-hardware benchmarks. v0.7.0 (August 2026) – Full Empirical Decoder Benchmark Report on the published wheel: nine CPU families + CUDA batch path, circuit-level LER parity with PyMatching 2.4.0, exact syndrome faithfulness, DEM-weighted GPU scaling restoration, and complete artifact inventory (Appendix A). All figures and tables in the accompanying reports are regenerated from the JSON files listed with their SHA-256 hashes; no pre-release numbers are carried forward. Related resources PyPI: qector-decoder-v3 Repository: https://github.com/GuillaumeLessard/qector-decoder Website: https://www.qector.store
Exact Binary Projections for Array-RQMC: Joint Laws and Pathwise-Preserving Execution Aoi Kawasaki. Preprint; not peer reviewed. Contribution For a specified two-dimensional Sobol net with linear matrix scrambling and a digital shift, the complete rank-ordered binary innovation vector is uniform over exactly N outcomes at N = 2^m paths. An odd mask and a fair bit describe the law, requiring m independent fair bits per step under the stated ideal randomization model. Independent adjacent antithetic pairs have the same covariance but need not have the same higher-order law; exact nonlinear witnesses give variances 0 versus 2 and 4 versus 2. This characterization enables direct generation without generating unused coordinates or sorting the point set. A second rewrite maintains exactly the reference state order for stopped scalar binary chains with monotone branches, including absorption and floating-point ties. Measured results and limits Across eight fixed benchmark cases in two input encodings, state-order maintenance reduced warm execution time by 37.2% at N = 512 and 67.5% at N = 4,096 relative to direct binary generation with full state sorting. The encodings do not create sixteen independent model laws. The measurements are from one CPU/software stack, not a held-out hardware or dynamics study. The joint-law equivalence of the library and direct generators is an ideal-law statement, not equality under the same finite integer seed. Direct and order-maintained execution do preserve the same finite-seed trajectories and outputs under the stated arithmetic conditions. No new convergence rate or universal variance advantage is claimed. Comparisons with the measured CRN and antithetic implementations remain workload- and reuse-dependent. Avoidable mask initialization was included in the measured baselines; it is not an intrinsic CRN cost. Startup and calibration can outweigh warm-time savings. The publication retains those recorded costs. Included materials and reproducibility scope The record contains the manuscript PDF and a self-contained reproducibility capsule with manuscript/build sources, three array kernels, 19 tests, saved table/figure inputs, two figures, dependency versions, and SHA-256 inventories. The tests include exact finite enumeration, within-project separate reference implementations, absorption and floating-point tie checks, and saved-data arithmetic. They are not third-party peer review. The capsule does not include every raw calibration/validation observation, bootstrap sample, timing round, or baseline/calibration driver. Regenerating saved tables and figures is not a rerun of the full original experiment. No GPU, pretrained model, private workspace, or external dataset is required. Rights and disclosure Publication materials and saved data: CC BY 4.0. Code: MPL-2.0, with per-file scope in LICENSES.txt. Generative-AI assistance is disclosed in the manuscript. The version-specific archival identifier is doi:10.5281/zenodo.22728405.