Evie's Perfect Purity - Extreme Quantization Drill: Finite Lattice Quantization, Drift-Aware Reconstruction, and Existing-Parameter Distillation for Transformer Models

Abstract

Evie’s Perfect Purity - Extreme Quantization Drill investigates extreme compression of complete transformer models through finite lattice representations, activation-aware reconstruction, guarded discrete and continuous refinement, and teacher–student distillation restricted to parameters already present in the stored representation. The research treats the serialized, decoded model as the object of evaluation. Continuous reconstruction targets, optimizer master parameters, rounded metadata, discrete code assignments, and installed inference weights are distinguished explicitly. This distinction matters at extreme precision: an improvement in an idealized quadratic objective can disappear after finite rounding or produce a worse complete-model probability distribution. The collection brings together the preserved foundational manuscript, later lattice-method development material, aggregate summaries of surviving experiments, and a separately identified record of the subsequent scale-diagonal extension. Its contribution is the specific integration of these mechanisms, their finite representation contracts, and the empirical examination of their interactions. Established lattice constructions, least-squares identities, orthonormal transformations, Hessian feedback, and distillation retain their original attribution. The methodological program comprises six connected components. Finite lattice coding and Cherubic Isometric Transport. The later representation combines the published QuIP# E8P construction with fixed signed orthonormal transforms, stored input diagonals, and row-group scales. In ideal arithmetic, a projection is reconstructed as Ŵ = UᵀQVD, where U and V are signed orthonormal operators, D is a positive diagonal matrix, and Q contains scaled lattice coordinates. The two-bit projection code identifies one of 65,536 eight-dimensional E8P points using a 16-bit index. The three-bit construction adds an eight-bit residual index covering the same eight coordinates, together with a stored relative residual scale. The initial residual assignment is sequential rather than an exhaustive search over all code pairs. The implementation uses signed DCT transforms, local codeword ordering, paid diagonal values, and explicit finite metadata. It is an attributed CPU adaptation of published constructions, with implementation and protocol differences from the official QuIP# pipeline. Immaculate Affine Closure and teacher–student drift. Quantizing earlier operations changes the inputs received by later projections. The affine formulation therefore uses paired teacher responses and current-student inputs, rather than assuming that teacher and student activations coincide. For student input x, teacher response y, dense reference W₀, and λ > 0, the local objective is: L(A,b) = E‖y − Ax − b‖² + λ‖A − W₀‖²F. Eliminating the real-valued bias gives b*(A) = μy − Aμx. With centered covariances, H = Cxx + λI and M = (Cyx + λW₀)H⁻¹, the matrix-dependent term becomes tr[(A − M)H(A − M)ᵀ]. This classical identity supplies a drift-aware target for the finite quantizer. The stored bias introduces an additional rounding residual, so separate matrix and bias guards do not establish monotonicity of the entire finite affine objective across matrix changes. The optional Ophanim Residual Closure formulation additionally targets the terminal feed-forward response after accounting for the current student residual path. Hessian feedback and Celestial Coordinate Purification. Initial encoding uses established Hessian error-feedback principles. Subsequent coordinate refinement revisits finite codewords under the full transformed quadratic metric. For F(Q) = tr[(M̃ − Q)H̃(M̃ − Q)ᵀ], the change associated with a block proposal Δ is evaluated through its quadratic and linear contributions. The incumbent remains eligible, proposals must pass a numerical improvement margin, and complete-sweep recomputation can trigger rollback. Euclidean nearest-codeword routines generate candidates; they do not solve every full-metric discrete assignment problem exactly. The guards concern computed local objectives and do not establish global codeword optimality, monotonic complete-model perplexity, or improved generalization. Concordant Lattice Refitting. With code assignments fixed, the existing group scales form a coupled quadratic subproblem. For each output row, the transformed reconstruction is expressed as a weighted sum of decoded group vectors. Cross-group terms from the calibration metric enter the scale Gram matrix. The real-valued proposal is obtained from an active-system solve. It is then clipped, rounded to the existing FP16 scale words, and compared with the incumbent. Additional checks evaluate the ordinary decoded FP32 matrix. The method introduces no additional correction matrix or group-scale inventory. Clipping an unconstrained solution is not presented as an exact nonnegative quadratic-program solution. Refinement controls receive the extra code and scale optimization without the centered affine target, helping distinguish target changes from additional optimization work. Angelic Finite Complement Distillation. A separate intervention freezes the quantized body and adjusts only existing projection biases and LayerNorm parameters. For the declared OPT-125M configuration, this complement contains 122 tensors and 121,344 scalar values. Training uses full-vocabulary teacher-to-student KL divergence across all 50,272 classes. FP32 master values accumulate updates, while forward computation uses their projected FP16 values. The identity backward treatment through rounding is explicitly a straight-through surrogate. A memory-bounded vocabulary-head schedule preserves the full distributional objective while reducing temporary activation requirements. Endpoint selection includes the unchanged parent and uses development data. This intervention adds a distillation budget even though it introduces no model parameters. Recorded Angelic Scale-Diagonal Concordance extension. The subsequent v5 record describes jointly tuning existing group scales, input diagonals, biases, and normalization values while keeping lattice codes fixed. Its reported trainable subset contains 867,840 existing scalars, approximately 0.693% of the model’s unique parameters. The recorded smooth decoder pullback distinguishes the scale adjoint from the diagonal adjoint and uses the unrounded pre-diagonal reconstruction where required. Parent-relative log coordinates, finite forward projection, and surrogate gradients are stated separately. The prior report describes a matched 128-update comparison against complement-only continuation and reports a 1.002% perplexity reduction relative to that control on a separate 128-document C4 prefix collection. The original v5 implementation, selected model, raw outputs, and final manuscript remain unavailable in the recovered materials. This result is retained as a clearly labeled prior report, rather than an independently revalidated measurement of this edition. The preserved experiments use OPT-125M with 125,239,296 unique parameters and 72 decoder projection matrices containing 84,934,656 weights. Calibration uses 32 WikiText-2 training contexts of 1,024 tokens. The later development guard contains 16 reset contexts of 2,048 tokens. Evaluation includes 140 WikiText test contexts, 256 declared C4 contexts, and all 1,838 PIQA validation questions. Likelihood evaluation uses the complete vocabulary and pooled token-weighted negative log-likelihood. PIQA reports both raw conditional-likelihood accuracy and a secondary normalization by solution character count. Historical measurements and fresh measurements from the earlier recovery study retain distinct provenance. Selected surviving complete-model measurements are: Candidate Complete artifact bytes WikiText140 perplexity C4_256 perplexity Dense FP16-word reference 250,564,117 27.663 25.631 Local GPTQ, two-bit projection codes 47,926,137 198.500 269.831 Cherubic E8P reference 46,869,586 48.216 56.694 Cherubic refined E8P 46,869,594 46.701 54.408 Local GPTQ, three-bit projection codes 58,542,969 36.325 35.044 Cherubic residual-vector reference 57,529,210 31.333 30.067 Cherubic refined residual-vector 57,529,218 31.437 30.059 These results support improved language-metric quality relative to this package’s local GPTQ controls at smaller complete-file sizes. They also expose limits: two-bit refinement improves the reported perplexities while reducing PIQA accuracy; three-bit refinement produces mixed language-metric changes; affine reconstruction candidates can regress despite favorable local fitting diagnostics. The dense reference retains a substantial quality advantage. Storage accounting charges projection codes, FP16 scales and diagonals, packed signs, residual metadata, tied vocabulary arrays, positional weights, complement values, and complete container headers. Nominal two-bit and three-bit projection codes therefore do not imply corresponding whole-model rates. The recorded selected artifacts occupy approximately 2.994 and 3.675 bits per unique model parameter, respectively. Reference inference expands the representation into FP32 matrices; compressed-kernel throughput, serving latency, and deployed low-bit memory improvements are not established. This standalone edition includes the unchanged 93-page v3 manuscript, a clearly marked 28-page v4.1 development draft, six preserved methods and reference notes, a research overview, protocol documentation, aggregate evidence summaries, citation metadata, licensing notices, and document checksums. The surviving later checkpoint contains 36 of 42 expected task records, covering 12 of 14 declared candidates. All three final records for the Angelic complement candidate and all three for Ophanim residual closure are missing. Development scores and transcript-only reports do not