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Nothing Changed but the Model: CellFill -- Bounded In-Cell Learning for Bit-Identical, Revocable Updates to Quantized LLMs

Zifeng Liu, Zhiyong Du, Yaxin Lu, Yiming Mao, Zhenhe Wang, Wenqi Shi, Zhengkun Jing

arXiv:2608.20873v1cs.LG

TL;DR

Deployed-model updates normally replace certified 4-bit checkpoints and their dependent artifacts. This paper learns within quantization cells, preserving released codes exactly while reducing cross-domain forgetting, with bounded knowledge costs and scale-dependent limitations.

  • Problem

    Updating a deployed model currently replaces the released checkpoint, forcing evaluations, caches, and certification artifacts tied to its exact integer codes and scales to be rebuilt.

  • Method

    The paper freezes 4-bit codes and scales, learns only within each weight’s quantization cell, and realizes this constraint structurally with CellFill and related paths.

  • Results

    Exact invariance nearly matches an unconstrained reference, projected updates reduce cross-domain forgetting when training converges, and bit-identical verification transfers to 27B.

  • Takeaways & Limitations

    In-cell learning preserves a fixed deployable artifact while making updates revocable and mechanically verifiable, but knowledge still incurs cross-domain perplexity cost.

  • Takeaways & Limitations

    Comparisons across unmatched rehearsal levels are not valid, pooled recall overstates transferable knowledge, and the 27B implementation is limited by dense residual storage.

Abstract

from arXiv · show

Every way of teaching a deployed language model something new -- full fine-tuning, adapter merging, model editing -- replaces the released checkpoint, and with it every evaluation and cache that referred to those exact bits. We instead learn inside the dequantization gap: with the integer codes and scales of a 4-bit release frozen, new knowledge is written only into the per-weight residual that lives strictly inside each quantization decision cell. Re-quantization then returns the released artifact bit-for-bit, a machine-checkable guarantee; updates are exactly revocable by dropping the residual; and drift is bounded. We give six propositions and three training paths, including CellFill, a bounded reparameterization that makes invariance structural rather than enforced. Exact invariance turns out to be nearly free: across three paired seeds the constrained dense path matches an unconstrained reference whose weights provably escape the artifact (58.9 vs 59.3 percent fact recall; paired difference -0.5 points, 95% CI [-5.0,+4.0]), and is better on held-out cross-domain perplexity. Against the natural null hypothesis -- serving the same update as an unmerged adapter -- projecting into the cells reduces cross-domain forgetting in every run that converged, and a diverged control shows the boundary: projection is a trust region, not a repair. What no method escapes is the cost of knowledge itself, and the apparent free lunch of in-domain perplexity improving past the anchor is an artifact of rehearsal sharing a corpus with the metric. Methods differ threefold at matched rehearsal in knowledge bought per point of cross-domain perplexity, a ranking that is not the recall ranking. The method transfers to a 27B hybrid linear-attention model (2.4e10 constrained weights, verified bit-identical), where matched recall costs about half as much cross-domain perplexity as at 1.7B.

1 Introduction

CellFill treats the released quantized checkpoint as a fixed reference, learning new knowledge inside quantization cells without changing its integer artifact. The resulting contract provides exact invariance, revocability, and bounded drift, while experiments measure the trade-off between recall and forgetting.

  • The deployment cost of continual learning is loss of certification because existing evaluations, caches, and sign-offs refer to the released integer codes and scales.
  • CellFill writes updates into per-weight residuals confined to the dequantization gap while freezing the released codes and scales.Re-quantization therefore returns the released artifact bit for bit.
  • Exact invariance is nearly free: constrained dense recall was 58.9±7.0% versus 59.3±8.7% for an unconstrained reference, with zero violations.The constrained result was measured at a matched rehearsal fraction.
  • Cross-domain perplexity rose from 28.67 at the anchor to 31.7, 33.1, 37.4, 40.7, and 52.2 as knowledge absorption increased.The earlier in-domain “free lunch” was attributed to rehearsal sharing a corpus with the metric.
  • Projecting updates into cells reduced cross-domain forgetting in all nine converged runs compared with serving the same adapter unmerged.The reduction ranged from 0.97 to 271.3 perplexity points and was largest where drift was worst.
  • The paper contributes six propositions, three constraint-realizing training paths, and a measurement methodology based on countable synthetic knowledge and disjoint forgetting metrics.

2 Setting and Guarantees

The paper formalizes in-cell learning by freezing quantization codes and scales and confining updates to their decision regions. It proves bitwise invariance and bounded, revocable updates, while showing that bounded capacity decays geometrically and practical drift surrogates are not certificates.

  • A frozen artifact consists of quantization codes and frozen group scales, with each weight assigned a round-to-nearest decision cell.
  • Re-quantizing any weight vector in the interior of the invariant cells returns the original codes exactly.The guarantee requires frozen codes and scales rather than recomputed scales.
  • Coordinatewise clipping is the Euclidean projection onto the invariant cells, making clip-merge the nearest invariant model to a proposed update.
  • Nested refinement codes remain strictly interior at every truncation depth, preserving Proposition 1 while controlling reconstruction error.
  • Absorbed knowledge is bounded by the shipped update bits through the data-processing inequality.The update message contains a mask and refinement code whose length bounds its information content.
  • CellFill moves within a symmetric box of per-weight inradii, whereas projected paths can traverse the full asymmetric cell and exceed the symmetric half-width.
  • The Fisher-based drift surrogates substantially underestimate measured drift, so ρ is a calibrated dial rather than an a-priori numerical certificate.The uniform-fill mean underestimates drift by 15.9× at ρ=0.125 and 383× at ρ=1.
  • Bounded updates consume a constant fraction of remaining room, so mean inradius and task absorption decay geometrically and total no-requantization capacity is finite.Consolidating every m tasks restores room and creates a throughput trade-off controlled by m.

3 Methods

The paper compares projected and reparameterized paths for learning inside quantization cells. CellFill makes invariance structural by parameterizing bounded bin positions, producing full-rank updates despite low-rank factors.

  • Clip-merge projects a materialized LoRA update onto the quantization cells and is optimal in weight distance, though not in loss.
  • Projected dense fine-tuning constrains optimization from the first step and serves as the reference solution of the constrained problem.
  • CellFill parameterizes each weight’s bin position with a bounded tanh and per-weight half-width, so invariance holds by construction throughout training.The training-time and shipped models coincide.
  • Elementwise scaling and tanh destroy low-rank structure, allowing a rank-16 factorization to produce a rank-512 update with stable rank 110 in a 512×512 probe.
  • At rank 64, CellFill matches projected dense recall with 20× fewer trainable parameters.

4 Experimental setup

The experiments use synthetic biography facts with countable information, fresh text rehearsal, and held-out perplexity to measure knowledge absorption and forgetting. Evaluation distinguishes verbatim from paraphrase probes and uses a declared guessing floor.

  • Synthetic biography facts provide 21.7 bits of attribute entropy and three cloze probes per fact, with novelty certain by construction.
  • Fresh-per-epoch Wikitext rehearsal is used because repeating a fixed replay buffer raises test perplexity from 24.6 to 172.
  • Forgetting is measured with Wikitext-test and cross-domain LAMBADA perplexity, separate from the rehearsal corpus.
  • Capacity calculations use the 11.9 probed bits covering city, occupation, and employer rather than the full 21.7-bit fact entropy.
  • The greedy-decoding guessing floor is 6.5% for a model lacking name–attribute bindings.

5 Results

Exact invariance preserves the released artifact while retaining nearly the same fact recall as unconstrained training. However, cross-domain forgetting remains real, and methods trade knowledge efficiency, stability, and capacity differently.

  • Efficiency: 918±183 to 1000 bits/pt for low-rank paths versus 312±10 for projected dense establishes three efficiency tiers at matched rehearsal.The efficiency ranking differs from recall ranking: projected dense has the highest recall but the worst exchange rate.
  • Efficiency: CellFill rank 64 absorbs 1.5× rank 16’s knowledge at roughly 56% of its efficiency, while projected dense absorbs 8% more than rank 64 for 2.0× the cross-domain damage.The reported cross-domain costs are 12.0 points for CellFill rank 64 versus 23.5 for projected dense.
  • Exact invariance: 58.9±7.0% versus 59.3±8.7% fact recall shows constrained dense training matches its unconstrained reference across paired seeds.The paired difference is −0.47 points with a 95% interval of [−5.0,+4.0].
  • Forgetting: Projection improves held-out cross-domain perplexity in every converged comparison with an otherwise identical unmerged adapter.The diverged controls instead show projection can worsen an already incoherent update, so it constrains converging optimization rather than repairing failed optimization.
  • Capacity: At 104 facts, absorbed knowledge grows with exponent approximately 0.78–0.83 while utilization remains 0.74–1.03%, indicating an optimization-limited regime.A reproducibility gap of 41.3% versus 34.9% recall makes the capacity exponents uncertain on the reported stack.

6 Shipping the update: nested checkpoints

The update can be distributed as nested residual refinements while preserving the released artifact bit-for-bit at every truncation depth. Two bits recover nearly all full-residual knowledge at one eighth the payload, while finer depths trade payload for recall and forgetting.

  • Encoding procedure: Proposition 3 encodes each in-cell position with k bits per weight, allowing truncation to recover the released artifact exactly.The experiment re-encodes the healed weights of a 104-fact dense run at four refinement depths.
  • Bit-identical nesting: Every refinement depth re-quantizes bit-identically across 1.409 × 10^9 constrained weights, so truncated streams remain certified older checkpoints.The integer-domain check reports zero violations for all k ∈ {1, 2, 3, 4}.
  • Quality–payload trade-off: Two bits per weight recover 99.4% of full fp16-residual knowledge, achieving 34.7% versus 34.9% at one eighth the payload.Three bits exceed the full-residual result at 35.5%.
  • Quality–payload trade-off: At k=1, LAMBADA is 87.0 versus 129.2 for fp16, while k ∈ {1, 2} reach 523 bits per point versus 413 for fp16.The residual depth acts as an operating knob that trades knowledge, payload, and forgetting.
  • Scope: The study is a single-configuration run and does not provide a fair comparison with BitDelta’s one-bit unconstrained delta compression.The paper states that constrained and unconstrained deltas require both pipelines on the same task for comparison.

7 Related work

CellFill occupies a distinct position among quantized adaptation and continual-learning methods: it keeps the quantized artifact fixed while writing bounded dense residuals inside quantization cells. Its design draws on evidence that sub-cell choices carry usable signal and on prior work in nested precision and constrained learning.

  • Frozen quantized bases: QLoRA and LoftQ train residual adapters around frozen quantized bases, whereas CellFill constrains merged dense residuals to remain inside quantization cells.QA-LoRA and low-rank QAT instead alter the int4 weights, so their merged artifacts change.
  • Sub-cell structure: AdaRound and BRECQ show that rounding directions within quantization cells affect loss, supporting the use of the dequantization gap as learning capacity.CellFill applies this signal to continual learning rather than calibration.
  • Nested and progressive precision: Prior nested-precision methods serve multiple precisions, while CellFill uses similar nesting mechanics across model versions with low bits writable and high bits immutable.The paper distinguishes this version/time axis from conventional bit-sliced deployment.
  • Continual learning and editing: Unlike soft Fisher anchoring and rehearsal, CellFill provides a hard per-weight trust region whose radii come from the quantization grid.The related-work discussion says bounded magnitude must be combined with fresh rehearsal for direction shaping.
  • Quantization stacks: The cell arithmetic applies unchanged to uniform asymmetric GPTQ and AWQ grids, but those quantization stacks were not evaluated.The paper therefore makes no results claim for those stacks.

8 Discussion and outlook

The contract turns model updates from checkpoint replacements into auditable, bounded increments against a fixed baseline. Its strongest value is operational: exact verification and rollback matter when certification, caches, or deployment reversibility depend on specific bits, while the evidence remains limited in scope.

  • Shipping contract: Verification is mechanical over the integer codes, and discarding the residual returns the released checkpoint bit-for-bit.The checks cover 1.409 × 10^9 constrained weights at 1.7B and 2.435 × 10^10 at 27B.
  • Operational boundary: The contract is most useful where re-certification, caches, acceptance tests, or exact low-cost reversion are deployment bottlenecks.The paper also identifies shared verifiable bases for multi-tenant customer updates as a target setting.
  • Relationship to retrieval: Retrieval keeps facts editable and attributable at query time but incurs context and latency costs, whereas in-weight facts are paid for once and available without retrieval.The paper presents the approaches as complementary and reports no RAG comparison.
  • Open problems: The demonstrated scope is factual recall on synthetic biographies; whether procedural or stylistic skills can fit the bounded per-weight trust region remains the largest open question.The paper notes that coordinated displacement required by skills may be poorly shaped by the box constraint.
  • Evidence boundary: The evidence supports operator-issued increments over a deployed lifetime, not autonomous continual learning after release.The paper explicitly labels broader autonomous-learning implications as speculation.

9 Limitations

The paper carefully bounds its evidence: experiments center on one model family, one quantization stack, synthetic factual recall, limited seeds, and several non-comparable or contaminated measurements. These constraints limit claims about scaling, skills, continual learning, and broad deployment performance.

  • Generalization: The study uses Qwen3-1.7B with bitsandbytes NF4 for nearly all results, while only two 27B runs and a small Mistral replication broaden coverage.The paper therefore has limited evidence for architecture or model-family generality.
  • Statistical precision: Seed counts reach at most three, and some cross-domain measurements use only two seeds, limiting what reported error bars can exclude.The paper explicitly avoids treating two-point spreads as confidence intervals.
  • Comparability: Table 1 rows are not uniformly matched on rehearsal, so comparisons between the first five rows and the unconstrained-control pair are invalid.The reported 166 versus 311 bits/pt gap is mostly attributed to the rehearsal difference.
  • Metric contamination: In-domain WikiText perplexity is contaminated because rehearsal and evaluation share the WikiText domain despite disjoint splits.This affects every WikiText number reported in the paper.
  • Capacity reporting: The 4,130-fact capacity headline and its 28.70 → 129.74 LAMBADA price come from different runs, so they are not one operating point.The matched re-run absorbed 3,494 facts and showed a 6.4-point reproducibility gap.
  • Scaling claims: Capacity exponents α ≈ 0.78 and α ≈ 0.83 each use exactly two measurements, leaving no residual degrees of freedom to detect curvature or a saturation knee.The measured 104-fact occupancy remains below full capacity.
  • Evaluation scope: Recall is exact-match verbatim recall with only one paraphrase probe, so it does not establish broad semantic or behavioral learning.The paraphrase probe is reported as substantially weaker where per-kind breakdowns exist.
  • Evaluation scope: The 6.5% marginal-guess floor means recall at or below that value provides no evidence of learning.Several collapsed variants fall below this floor.

10 Reproducibility

The paper documents a reproducibility stack that separates deterministic setup and integer-domain verification from GPU training results that are reproducible only within between-seed variation.

  • Stack and commands: The core package runs on CPU with PyTorch, while experiments additionally require CUDA libraries and records resolved software, GPU, driver, and VRAM details.The setup script is idempotent and captures these environment details in each run log.
  • What is deterministic: Explicit seeding fixes synthetic facts, rehearsal draws, probe subsamples, and healing-phase shuffles, making the data and optimizer inputs reproducible.
  • What is deterministic: Integer-domain verification re-derives codes under frozen scales and avoids floating-point comparisons, while the theory tests reproduce on CPU.The theory layer includes 25 unit tests covering NF4 assignment, fixed anchors, and in-cell invariance.
  • What is not: GPU results are not bit-reproducible because bf16 autocasting, unfixed deterministic algorithms, and kernel reduction order introduce variation.Recall and perplexity should reproduce to roughly the reported between-seed spread rather than to the final digit.
  • Frozen-artifact convention: The artifact freezes integer codes and per-group absmax scales, derives bounds from them, and shrinks each cell by a stated margin to keep values strictly interior.The margin is 1% per side for the standard run and 2% for the 27B run.
  • Verification: Invariance checks exhaustively cover every constrained weight and reject any violated run, with the projected-healing path repeating the check after training.At 1.7B the check covers 1.409 × 10^9 weights; at 27B it covers 2.435 × 10^10.

A Why invariance must be defined against frozen scales

Invariance must be defined relative to the released artifact’s frozen codes and scales, because recomputing data-dependent scales can change codes even when an update stays within its original cell.

  • Why invariance must be defined against frozen scales: Re-running the quantizer is an invalid operational definition of invariance because absmax group scales are data-dependent.The counterexample is executed as a unit test.
  • Why invariance must be defined against frozen scales: Moving the block maximum from 1.00 to 0.87 remains within its own cell and preserves both codes under the frozen scale, but recomputed scaling changes the artifact.
  • Why invariance must be defined against frozen scales: The artifact must therefore include its scales, and verification must assign codes under those scales in the integer domain.Floating-point comparisons of dequantized values are avoided because they are not reproducible across devices.

B Proof sketches

The proof framework models frozen-scale quantization through explicit decision cells and margined compact intervals, establishing interiority and well-defined projection.

  • Notation: NF4 decision regions are determined by midpoint boundaries under a frozen block scale, with ties assigned to the lower code.The outer code regions are half-infinite before the implementation’s finite caps.
  • Cell geometry: The implementation fixes cell widths and anchor reconstructions from the frozen quantization representation, distinguishing exact available radii from the looser half-width bound.
  • Cell geometry: Each margined cell is a nonempty compact interval strictly inside its code’s decision region, separated from boundaries by at least ηW_i.
  • Cell geometry: The product set of cells is a nonempty compact convex box, so Euclidean projection exists uniquely and small storage rounding cannot change a code.The latter guarantee depends on the margin ηW_i.

B.1 Proposition 2 (projection optimality)

The appendix characterizes clipping as Euclidean projection onto the product of margined cells, explains its trust-region behavior, and proves nested residual refinement preserves frozen-code invariance.

  • Projection optimality: Clipping is the unique Euclidean projection onto the cell box because the squared distance separates into one-dimensional interval problems.Coordinatewise, the solution is z_i = median(ℓ_i, y_i, u_i) = clamp(y_i, ℓ_i, u_i).
  • Projection optimality: The projection is the proximal operator of the box indicator, so projected gradient is forward–backward splitting on f + ι_C.This is the formal meaning of the optimizer seeing the cell walls.
  • Trust-region interpretation: Projection retains an update no larger than the proposal and shrinks it only along coordinates that attempt to leave their cells.The retained and clipped-away components preserve the proposal’s coordinate signs.
  • Trust-region interpretation: Projection’s empirical effect on cross-domain perplexity is not implied by the geometry, and its cost rises with clipped-away mass rather than being a numerical certificate.The appendix relates observed behavior to 0.14% clipping, 3–5% clipping, and catastrophic 30.4% clipping.
  • Limitations: Projected descent has constrained-stationarity guarantees under smooth deterministic assumptions, but the actual stochastic projected-AdamW runs do not satisfy the theorem exactly.The paper explicitly does not claim convergence to a global constrained optimum.
  • Nested refinement: Nested refinement codes are compatible across bit depths because truncating a deeper binary code yields the shallower code, including the saturating all-ones boundary case.
  • Nested refinement: At depth k, reconstruction error is bounded by the sub-cell width 2^-k, with an additional saturation-distance term only for inputs outside the cell.Training paths eliminate that second term because shipped weights are already projected or produced by bounded tanh fill.
  • Nested refinement: Strict interiority at every refinement depth guarantees frozen-scale re-quantization returns the original codes, making the 4-bit prefix bit-identical by construction.The codec never writes the 4-bit codes.

B.3 Proposition 4 (capacity bound)

Proposition 4 bounds the information that a bounded update can communicate through its residual message while preserving a fixed quantized artifact. The bound depends on message length and requires novelty of the learned facts relative to the released model.

  • Message length: The message encodes written coordinates and k refinement bits, with declared masks reducing its length to at most kN_t + log2 N bits.When the mask is fixed and public, the receiver already knows the written coordinate set.
  • Information bound: Data processing bounds the learned information by message entropy, yielding the Proposition 4 capacity ceiling.The argument follows the Markov chain from facts to message to updated model and uses H(m) ≤ |m|.
  • Quantitative implication: 5.6 × 10^9 bits is the case-(a) ceiling for N = 1.409 × 10^9 constrained weights with k = 4.This is a one-sided information ceiling, not an achievability claim.
  • Assumption: The capacity interpretation requires post-release novelty: if the released model already depended on the facts, zero message bits could still yield large mutual information.The synthetic corpus satisfies this independence by construction, whereas real post-release facts require the assumption to be argued.
  • Quantitative implication: 4,130 facts absorbed at 104 presented correspond to approximately 49 kbit versus a 5.6 Gbit ceiling, indicating an optimization-limited rather than capacity-limited regime.The empirical gap is five orders of magnitude.

B.4 Proposition 5 (forgetting budget)

Proposition 5 gives an exact second-order Fisher-form identity and an exact quadratic scaling law for bounded in-cell perturbations, but the diagonal surrogate is not a reliable numerical forgetting certificate. The paper therefore calibrates the radius empirically rather than treating the theoretical surrogate as a bound.

  • Proposition 5: The smooth-model expansion identifies the Fisher information as the Hessian at the quantized anchor and controls drift with a quadratic Fisher form plus a third-order remainder.The remainder is uniform over the box but is not measured.
  • Proposition 5: ρ^2 scaling is exact for the Fisher quadratic form because the radius-ρ constraint set is a scaled fixed box.This homogeneity holds for diagonal and non-diagonal Fisher matrices.
  • Measurement: Uniform in-cell fills use independent zero-mean coordinate perturbations, making the second-order predictor applicable to measured evaluation NLL as well as KL.The same symmetry removes the first-order loss term in expectation.
  • Empirical test: The diagonal surrogate underestimates measured ΔNLL by 16× at ρ = 0.125 and 383× at ρ = 1, with a fitted exponent of 2.43 rather than 2.Intermediate underestimation factors are 196×, 291×, and 340× at ρ = 0.25, 0.5, and 0.75.
  • Interpretation: A 14–39% seed fluctuation is far smaller than the 196–383× gap, ruling out high-dimensional off-diagonal Fisher mass as its explanation.The off-diagonal terms cancel in the mean under independent zero-mean coordinate perturbations and contribute only to variance.
  • Limitations: The remaining explanations are truncation failure at macroscopic full-dimensional displacement and a Fisher estimator biased low by chunk-averaged gradients.The measured exponent above 2 supports the truncation concern, while the estimator gap may be of order 1024.
  • Status: Proposition 5 supplies no computable a-priori certificate, so ρ is treated as a calibrated dial and the measured curve is reported instead of a bound.The diagonal surrogate is off by 16–383×.
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