Quantization

AI agents store text as embedding vectors and compress them at scale. A compression is accepted when each item's nearest neighbors survive, but agents also consolidate, delete, and compare memories, tasks that depend on which items lie far apart. We evaluate both ends with two label-free fidelities from our prior work: the local fidelity $L$ at 10 neighbors and the global fidelity $G$ at 30 to 50 percent of the memory. At 96 bytes per passage, rescored binary codes reach an $L$ of 0.97 yet move 10.1 percent of passages to another theme; PCA with 8-bit codes, at an $L$ of 0.77, moves 1.7 percent. Rescoring leaves the stored codes, and thus $G$, unchanged. We prove that across the $G$ band, $1-ν_k$ is at most 2 to 2.18 times the square root of the near-far rank-violation rate, and that this rate follows the distance noise of the compression (correlation 0.979). Our locality-aware quantization (LAQ) turns the bound into a hinge objective on the codebooks of an OPQ index, keeping its bytes, rotation, and search. To our knowledge, LAQ is the first quantizer whose objective comes from a proven bound on the far end. Reconstruction alone raises $G$ in 0 of 52 held-out runs; the far hinge raises it in all 52. LAQ raises $G$ in all 52 ($p=8.5\times 10^{-4}$ over 13 memory-encoder groups), including the external FinDER memory, has the highest $G$ of seven equal-size quantizers in all 12 Multi-Doc-2025 runs, scales to a million passages, and keeps evidence recall.

Long-context inference is bound by the KV cache, which 2-bit codes could shrink about sixfold if their error stays in check. The usual remedy rotates keys before quantizing, assuming rotation always helps. However, we observe that it does not: rotation flattens a spiky piece of a key but can give a flat one a new peak, and both coexist within one key. We therefore propose FlagRot, which stores each 32-channel piece rotated or as is, whichever has the smaller calibrated attention error, and rotates the query instead when reading. We further show that how often to decide follows the quantization axis: per-channel caches such as KIVI need one decision per head, at no write cost, while per-token caches decide per key, with the choice stored in existing sign bits. At 2.5 bits per value, FlagRot lowers the twelve-model KL divergence of KIVI from 18.7 to 12.4 x 10^-3, below RotateKV on 9 of 12 models. Served as a vLLM plugin, it raises RULER at 128k tokens by +2.9 points and the LongBench v1 mean by +0.4 to +1.9 points on the three of four models where 2-bit KIVI loses accuracy. It also lowers the error of 4-bit integer and FP4 caches.

Adam keeps two FP32 moments per parameter, twice the bytes of the FP32 weights, yet compressing them is risky: the update divides by the square root of the second moment, so small reconstruction errors can change the restored computation substantially. We study guarded moment compression, in which a coordinate's decoded moments are accepted only if they reproduce the native FP32 Adam update to within a tolerance $τ$, in units of the learning rate, for every gradient in a clipped domain; all other coordinates are stored exactly. The natural certificate, which ranges each update separately over gradient intervals, fails: on one million trained OPT-125M coordinates it escapes 98.9% of coordinates and the payload grows to 126.6% of raw FP32. Our key observation is that both updates consume the same gradient and parameter. Bounding their difference directly, with FP32 rounding-error allowances and a fixed mixed linear-logarithmic gradient partition, cuts escapes to 0.53% and the payload to 28.3% at $τ=0.01$. Across 120 complete-checkpoint restores of OPT-125M and ResNet-18, with four trained seeds and three training fractions per model, guarded 8-bit log codes shrink moment payloads by 69.5% and 71.9% relative to FP32, 40.8% and 45.4% relative to equally guarded BF16, and 29.3% and 37.6% relative to equally guarded blockwise 8-bit, and every restored first update stays within tolerance. Encoding and restoration together take 2.3-2.6$\times$ as long as guarded BF16 but less time than guarded blockwise 8-bit. Searching both moment codes jointly saves under 0.001% more bytes at 6% more codec time, so per-moment rounding suffices. The guarantee covers the first restored update under a pinned Torch operation model; we measure subsequent training empirically.

Memory capacity and bandwidth are major bottlenecks in LLM inference, motivating weight compression beyond conventional 4-bit quantization. Vector quantization (VQ) enables approximately 2-bit weight storage but often relies on codebooks incompatible with native FP4 computation. We introduce MXCode (MX-Native Codebook Quantization), a framework bridging ultra-low-bit VQ compression with MicroXcaling (MX)-native FP4 computation. MXCode proposes three strategies: PostScale, which quantizes learned codebooks to MXFP4; PreScale, which extracts MX scales before codebook learning; and PreScale+, which further compresses these scales using VQ. These strategies explore tradeoffs among quantization quality, scale overhead, and codebook granularity. All reconstruct MX-native W4A4 operands without materializing intermediate high-precision weights. We evaluate MXCode on Qwen3 (235B), DeepSeek-R1 (671B), and GLM-5.2 (753B) using the Microsoft MX Emulation Library. MXCode achieves approximately 2 bits per weight with competitive, workload-dependent model quality. On GB300 hardware, experiments with Qwen3 (235B) show approximately 50% lower model-load memory than Native FP4 while maintaining near-Native-FP4 serving throughput. Under memory-constrained prefix reuse, P90 TTFT improves by up to 94.5%. These results demonstrate software-based reconstruction on existing FP4 hardware and inform the development of future MX-native inference systems.

Low-bit quantization enables efficient deployment of large language models by reducing memory footprint and computational cost. Achieving high accuracy at low precision requires selecting quantization ranges, linear transformations, and weight rounding decisions. Existing approaches typically optimize these components independently using local reconstruction objectives, which fail to account for the varying impact of quantization errors on downstream predictions. Direct optimization of task-level metrics would provide a more faithful objective, but is challenging due to the discontinuous nature of quantization operations and the high computational cost of evaluating their downstream effects. In this work, we derive a Hessian-guided approximation of the output change induced by joint weight and activation quantization. Based on a tractable Fisher approximation, we formulate a unified post-training quantization framework that enables the joint optimization of quantization ranges, linear transformations, and weight rounding under a common output-sensitivity objective. The resulting method remains practical for modern large language models and consistently outperforms state-of-the-art transformation and rounding methods across both channel-wise and block-wise quantization settings.

In machine learning, symbolic reasoning approaches often rely on static architectures that hinder integration into deep neural networks and gradient-based optimization. To address this, we introduce the Native Predicate Neuron, a differentiable logic-reasoning neural module that enriches standard architectures with symbolic reasoning capabilities via first-order logic quantization. The proposed neuron models relational logic by learning to alternate between operations using a single trainable parameter. It features a tailored gradient mechanism with a dual-nature formulation: executing hard logical operations during training while maintaining differentiability for backpropagation. By quantizing both its input and choice state, the Predicate Neuron approximates continuous and non-continuous functions, effectively resolving discontinuities that standard deep learning architectures struggle with. We evaluate the Predicate Neuron across Fully-Connected, Convolutional, Recurrent, and Transformer architectures on benchmarks like MNIST and Wikitext. Results show that incorporating Predicate Neurons accelerates convergence, boosts accuracy, and lowers loss in general, with particularly strong improvements in tasks requiring monotonic reasoning or handling discontinuities. Overall, the Predicate Neuron natively integrates into standard neural networks to enable fuzzy logic operations and is available in Keras and PyTorch.

Scientific rasters are often stored before the regions to be measured are known. Independent pixel-error bounds can force exact integer reconstruction when one absolute error budget covers every future rectangle. Coordinated changes allow every pixel to change while every rectangular sum remains accurate. A prefix sum accumulates values from the top-left corner. Four such sums determine any rectangular total. RangeRectQuant preserves the pixel range and designated exact samples while controlling errors in prefix sums. At each row position, we characterize exactly which errors let the remaining pixels meet these constraints. These errors form a single integer interval, even when many completions exist. A backward pass finds its endpoints; a forward pass uses them to choose quantized pixels. The resulting field meets the prescribed error budget for every axis-aligned rectangle, with linear work and workspace proportional to one row. Experiments on geographically held-out built-surface and water-occurrence maps show substantial storage savings over alternatives meeting the same requirements. Data producers encode once; later users measure arbitrary rectangles without the source, re-encoding, or query-specific correction.

Post-training quantization (PTQ) is a key technique for efficiently deploying large language models, as it compresses weights into low-bit representations without retraining. Existing PTQ solvers, including GPTQ, LDLQ, and block coordinate descent, commit each weight block to a single codeword before its neighbors are considered, leaving near-optimal alternatives unexplored. In this work, we cast row-wise PTQ as posterior inference over discrete codebooks, in which existing solvers correspond to a zero-temperature, hard-decision limit retaining only the top codeword per block. We propose Message-Passing Quantization (MPQ), which preserves soft posterior information across blocks during inference and commits to hard codewords only at the output stage. MPQ first uses vector approximate message passing to compute approximate blockwise posteriors, then refines a hard-decision initialization by exact block coordinate descent. Across 2-bit lattice and 3- and 4-bit scalar quantization on dense language models from Llama, Qwen, and Mistral families, MPQ improves perplexity and zero-shot accuracy over strong hard-decision baselines, and composes favorably with preprocessing techniques such as activation-aware scaling and incoherence processing. Our implementation is available at https://github.com/poseidonchan/MPQ.

Large neural networks are increasingly deployed with 1-4 bit weights and 16- or 32-bit activations, yet their dot products still use one multiplier per element. We show that a length-n dot product with k-bit weight codes can be computed with n+2^k additions and at most 2^k decodes and 2^k multiplications. Each weight code is used directly as an address offset that selects one of 2^k accumulators; each activation is added into the selected accumulator; and the accumulated sums are decoded and multiplied only once, at the end, in a fused decode-and-multiply step. The decoded weight vector is never formed. The refactoring is exact for integer arithmetic, works with integer or floating-point operands and with arbitrary, including nonlinear, decoders, and extends to group-wise scales and to matrix and tensor products. The multiplier count falls by n/2^k, while total arithmetic energy improves by a smaller, bounded factor that we quantify with a cost model. We describe a scatter-accumulate processing element (SA-PE) that replaces the MAC unit in a weight-stationary systolic array, with a load/stream/reduce/drain schedule in which a small, time-shareable multiplier runs only 2^k times per tile. Because decoded weights are not stored, local weight memory shrinks by up to w_d/k for w_d-bit decoded weights. An RTL implementation synthesized for FPGA and compared with a matched MAC array shows that an unshared SA-PE is larger than a MAC PE, and that the saving appears when the reduction multiplier is shared across PEs. Software models confirm exact integer equivalence and floating-point error no worse than the conventional pipeline. We do not claim the underlying identity is new, and we discuss related work on weight sharing and lookup-based kernels.

We study quantization for inner-product estimation when storage and reading have separate budgets. In the static bit-probe model [Yao, 1981], an encoder stores $w$ bits about $x$ before seeing a query $y$, and a reader probes at most $r<w$ bits to estimate $x^\top y$. Both vectors lie in the $d$-dimensional Euclidean unit ball. Protocols may be randomized, and computation is unrestricted. Performance is measured by $d$ times the worst-case mean-squared error over $x,y$, averaged over protocol randomness. First, we show that query-independent reading cannot benefit from extra storage. Any such reader is equivalent to fully reading an $r$-bit message, even when later reads depend on previously returned bits. At fixed positive rates $W=w/d$ and $R=r/d$, the normalized minimax error converges to $1/(4^R-1)$, independent of $W$. The upper bound was already known [Ordentlich and Polyanskiy, 2025]. We prove the matching lower bound for arbitrary scalar decoders, extending the result for unbiased compressors [Safaryan et al., 2020]. Then, we show that query-dependent reading makes extra storage useful. We construct a two-batch protocol using Gaussian projections and random thresholds, with asymptotic normalized error at most $(π+o(1))/[4R\log(W/R)]$ as $W/R\to\infty$. At fixed $R$, this error vanishes as storage grows, giving an unbounded advantage over query-independent reading. We also prove a finite-dimensional lower bound for arbitrary encoders, decoders, and fully branching readers. In the doubly sparse regime $W/R\to\infty$ and $R\log(W/R)\to0$, it gives normalized error at least $(1-o(1))/[2R\log(W/R)]$. Thus, our protocol is optimal within a factor of $π/2$ in the leading constant.

Weight quantization below four bits shrinks memory and bandwidth at a perplexity that looks acceptable, but often at the cost of factual knowledge and task accuracy. Ternary weights have mostly been obtained by training from scratch or long fine-tuning. We introduce RoleQ, a quantization framework that places scales by the functional roles of Transformer units rather than by the layout of the weight matrix, as conventional formats do. Vectors that read from the residual stream take one scale per output unit; those that write to it, one per input unit. The rule is structural, needs no search, calibration or stored state, and holds on integer and ternary grids. In a rotated basis it matches a per-layer axis search at half the solver work, and at ternary it cuts perplexity by up to half against layout-based placement in two families at every size from 0.6B to 14B, where per-row scales leave MMLU at chance. Our lightweight post-training pipeline converts an existing checkpoint to 1.59 bits per weight in a few GPU-hours, a fraction of the cost of learned ternarization, and leads every post-training ternary method at matched or lower memory-resident bits on perplexity, zero-shot accuracy and MMLU, most widely on knowledge. A sparse second ternary plane placed by a per-unit Fisher saliency keeps the matmul multiplication-free and recovers what ternary loses first: at 8B, a fraction of a bit returns about half the MMLU that conversion costs, well ahead of random or Hessian-based placement at equal bits.

Existing 3D Gaussian Splatting (3DGS) codecs report reconstruction quality after compression, and give users little control over the distortion of individual primitives. We present PLEDGE, a training-free, progressive, error-bounded codec that translates four user-declared tolerances into per-primitive quantization bounds: screen-space position, footprint deformation due to rotation and scale, view-dependent color, and opacity. The bounds apply throughout a declared camera domain, including previously unseen viewpoints. Position and opacity are bounded directly; footprint deformation is bounded under the rasterizer's affine projection model, and color is bounded over all viewing directions. PLEDGE organizes quantized residuals into a progressive bitstream with explicit error bounds for every valid prefix. Experiments across thirteen scenes verify all declared per-mechanism bounds and demonstrate competitive rate-distortion performance. The four tolerances incur substantially different rate costs, so users can spend rate where their application needs it.

Quantization has emerged as one of the primary techniques for reducing the memory footprint of large language models during inference. A prominent example is Quantized Johnson$-$Lindenstrauss (QJL), which compresses KV caches using 1-bit asymmetric quantization while approximately preserving the inner products required by the attention mechanism. Recent theoretical and practical work aims at replacing the dense Gaussian projections used by the aforementioned transforms with more structured embeddings $-$ such as compositions of randomized Hadamard transforms $-$ while retaining the same embedding dimension. In this paper, we introduce two constructions based on a composition of randomized Hadamard transforms, albeit with a Gaussian rather than Rademacher diagonal in the second stage. The first adds Gaussian dithering to smooth the quantizer, while the second inserts a random permutation to regularize the covariance structure of the resulting Gaussian measurements. We prove embedding-dimension and running-time guarantees analogous to those of Fast JL in the non-quantized setting. The first construction achieves $m=O(\varepsilon^{-2}\log^2(d/δ))$, while the second achieves $m=O(\varepsilon^{-2}\log(d/δ))$ under a restriction on $m$. Both constructions can be applied in $O(d\log d)$ time.

Quantization-aware training (QAT) can recover much of the accuracy lost when large language models are compressed below four bits. Existing re- covery stages, however, are commonly optimized on fixed completions or teacher-generated answers, whereas the deployed quantized model condi- tions on prefixes generated by itself. Quantization errors can therefore move the model into states that are absent from offline recovery data. We introduce OnlineQAT, a two-stage framework that first obtains a usable low-bit initialization through block-wise QAT and then performs on-policy distillation (OPD) on student-generated responses. At each visited pre- fix, a frozen full-precision teacher provides a sampled reverse-KL training signal. On Qwen3-1.7B, OnlineQAT obtains the best average among the compared quantized methods: 57.28 at W3A16 and 32.52 at W2A16, im- proving over ReasoningQAT by 2.90 and 0.44 points, respectively. The results suggest that student-visited states provide a useful recovery signal beyond fixed-completion training, particularly at three bits.

Extreme low-bit LLM compression is most challenging when weights, activations, and KV caches are quantized together: their distributions differ, and quantization errors interact throughout the network. We introduce CanonQ, a unified quantization-aware training framework that addresses these challenges by separating source canonicalization from task-aware adaptation. Fixed rotations and energy normalization map heterogeneous tensor sources to canonical coordinates, enabling frozen Gaussian-reference codebooks to be reused across layers and models. Joint training then adapts the network to the coupled errors of weight, activation, and cache quantization within a common scalar/vector interface. We bound frozen-codebook transfer error and local task loss, and derive an exact normalization-aware straight-through Jacobian that links quantization distortion to gradient bias. The strongest gains arise under joint W2A4KV2 compression: across LLaMA3-1B/3B/8B, CanonQ-Omni achieves up to 14.28x lower WikiText-2 perplexity and up to 57.9% higher mean zero-shot accuracy than prior state-of-the-art and representative quantization baselines. The benefits extend to Qwen3-1.7B, code generation, and mathematical reasoning: on instruction-tuned MobileLLM-Pro-1B at W2A16KV16, CanonQ achieves relative improvements of 41.7% in HumanEval pass@1 and 39.1% in GSM8K exact match over the strongest evaluated quantization baseline.

Quantization-aware training (QAT) leverages lower-precision arithmetic to reduce the cost of LLM deployment, but aggressive quantization degrades final model performance. A common remedy is mixed-precision training, in which high precision is assigned to some of the layers to maintain performance while keeping the cost constrained. This approach then requires precision assignments for model layers during training. We provide a new approach, called Q-PACE, consisting of a second-order sensitivity model that predicts the loss increase as a sum of quantization noise MSE weighted by per-layer curvature coefficients. During training, we periodically re-compute these coefficients using perturbations across layers, and re-assign precision. Pretraining and supervised fine-tuning experiments on LLMs of up to 4B parameters show that Q-PACE consistently improves over existing mixed-precision training recipes, and achieves comparable loss at substantially lower total memory budgets. We further find that quantization sensitivity is highly predictable by depth and layer type, and its stability during training allows for infrequent, cheap recalibration.

We introduce ApexQuant, a calibration-free quantization method that recursively re-quantizes the residual error, serving as a refinement layer on top of existing quantizers. We establish that a fresh random rotation returns each residual to the uniform distribution on the hypersphere, which characterizes the rate of progressive error decay across successive passes. This result lets us determine, before any weight is read, how many passes a layer needs for a target weight-space error. Every prefix is itself a valid lower-rate model, so one artifact serves several precisions. We instantiate ApexQuant with three interchangeable stages, scalar, $E_8$ and trellis, and validate it on four open-weight LLMs and on Earth-observation and medical domains where in-distribution data is often unattainable as imagery arrives under restrictive licences or due to patient material under privacy constraints. Progressive re-isotropization comes within a few percent of full precision at four bits and gives the best two-bit arm we measure, in a completely data-free setting.

Language-model systems batch questions for throughput, but unrelated questions should not change a target's answer when its input and numerical execution are fixed. We study compression of the key and value cache, which stores attention representations reused during generation. With request-local groups, Transformers' Half-Quadratic Quantization (HQQ) backend updates compression parameters separately but uses a shared average error to decide when all updates stop. Replacing only the question batched with the target changes four-bit HQQ answers in 170/384 test comparisons across two models. Replaying the other execution's update counts reproduces its complete answer and cache fingerprints in every changed pair, in both directions. Computing the stopping mean in FP32 reduces cache differences but leaves answer changes. Native HQQ also changes confirmed numerical correctness in eight arithmetic pairs. Fixed iterations and request-local stopping remove observed companion dependence under matched controls. Request-local stopping remains sensitive to synthetic padding changes at the tensor level. Fixing the original iteration budget removes this decision path without tuning. Neither repair has an established quality advantage, and natural rebatching still changes answers. Request-independence audits must cover stopping decisions as well as quantization groups.

We introduce ShamAN-Q, a sub-1-bit post-training quantization method that extends NanoQuant by replacing each its diagonal reconstruction geometry with a tractable dense curvature metric, using a general paradigm popularized by the Shampoo optimizer. For each linear weight, ShamAN-Q fits a Kronecker product to the empirical Fisher information matrix of a small calibration set by Kullback--Leibler minimization, forming a Mahalanobis reconstruction loss from the result. The continuous ADMM updates from NanoQuant become solutions to Sylvester equations, while its discrete projection and deployment format remain unchanged. Because the curvature is local to a given set of weights, ShamAN-Q re-measures the input curvature statistic for each layer immediately before layer factorization, periodically refreshing all statistics on the partially quantized model. ShamAN-Q also redistributes the uniform rank from NanoQuant across layers at the same total number of bits. On Qwen3-Base, ShamAN-Q lowers WikiText-2 perplexity at $\approx$1 bpw from 27.56 to 22.96 (0.6B), 19.21 to 16.72 (1.7B), and 14.29 to 13.80 (4B) while matching or improving zero-shot accuracy on the Eleuther LM Evaluation Harness. On 0.6B, ShamAN-Q at $\approx$0.8 bpw matches the published perplexity of NanoQuant at $\approx$1.0 bpw.

Uniform random rotations are an effective preprocessing step for quantization: they make normalized coordinate distributions approximately Gaussian, enabling the use of codebooks optimized offline. We introduce TORQUE, a framework that improves on previous quantization works that use random rotations by jointly optimizing how many and which coordinates to preserve at high precision both before and after rotation, under a fixed overall expected bit budget. Intuitively, before rotation, preserving large input coordinates at high precision can reduce overall error by preventing the rotation from spreading their values across many coordinates. Likewise, after rotation, preserving a small fraction of the largest-magnitude coordinates at high precision allows the remaining values to be quantized more accurately using codebooks optimized offline for the resulting truncated Gaussian distribution. We derive a quantization error upper bound and prove that top-$k$ pre-rotation retention minimizes it for each $k$. This reduces the search over coordinate subsets to an optimization over $k$, enabling a fast optimizer that uses offline codebooks and parallel parameter selection for practical implementation. We demonstrate an improved tradeoff between reconstruction accuracy and storage cost through numerical evaluation under the Gaussian model and experiments on nearest-neighbor retrieval, KV-cache compression, and activation compression.

Most post-training quantization pipelines fit each weight matrix to its pretrained counterpart, one matrix at a time. Whether that proxy tracks what an attention block actually computes, or how errors in the Q, K and V projections compound inside the softmax, is rarely checked. We write the objective on the attention output instead, over all three projections at once, and reuse it throughout the pipeline. JAB defines one scalar loss over the joint Q, K, V weights of a block, evaluated against the block's real causally-masked attention output, and uses it twice: to fit the quantized weights (GPTQ warm start, then STE with learnable scales), and to score the block for a multiple-choice knapsack allocation. On attention-only quantization of Mistral-7B this works. At 3 bits JAB recovers 77-90% of the gap between uniform GPTQ and full precision, and its sensitivity estimate tracks an oracle costing 73 forward passes to within a fraction of a point. It stops working once MLP layers enter the allocation. A role-aware offset rule needing no sensitivity estimate at all beats JAB on GPT-2's MLP and on the full Mistral-7B model: with a 3-bit floor it quantizes 96.4% of the weights to 4.5 bits per parameter at 6.933 perplexity, within 4.4% of full precision (6.643) at 3.56x compression, against 7.158 for JAB at the same budget. Which matrix a weight sits in matters more than any sensitivity estimate we computed. Two things came out sideways. Block-local reconstruction is an unreliable proxy for end-to-end perplexity: one run improved a block's own objective 4.6x while perplexity rose 32x, which is why every allocation here is validated end-to-end. And on attention-only quantization, fine-tuning moved weights farther from their pretrained values while pulling attention outputs closer, with net gains. Post-training seems to recover attention behavior, not weights.

Four-bit post-training quantization can reduce the memory demands of large language models, but preserving accuracy under strict MXFP4 W4A4 requires coordinating several design choices. Coordinate transforms change block-encoding errors, which in turn affect the residuals propagated through the network. The useful algorithmic decomposition is therefore not fully known before search. LLM-driven program evolution offers a way to explore these choices, but performance scores alone do not explain which design should change next. We introduce QuantForge, a PTQ discovery system that records competing explanations, selects controls that distinguish them, and checks that successor code implements the resulting conclusions. This residual compilation guides program revisions while retaining useful programs even when their original explanations are rejected. Remeasuring the revised program reveals the next error to address. This process discovers HiRes, a fixed MXFP4 quantizer that shapes coordinates, refines legal code assignments, and recovers errors along attention and MLP paths. Each stage acts on residuals measured after the preceding stage has executed. Across seven tasks, HiRes achieves the lowest seven-model Robust Fit (0.09300) and the lowest quantized Fit-7 at 32B. In matched-budget comparisons of LLM-driven program evolution, each with 240 evaluator calls, QuantForge reaches a held-out transfer target in six of eight runs, compared with three each for textual memory and reflection memory, and one for score-only evolution, despite evaluating fewer new programs. These results show that QuantForge improves the discovery of transferable PTQ algorithms by turning controlled evidence into subsequent program changes. We have open-sourced the QuantForge search framework.

Recent generative models have become increasingly powerful, but their inference cost continues to grow. Model quantization offers a promising way to compress these models and accelerate inference. However, at 4 bits, activation quantization is substantially more challenging than weight quantization. Recent post-training quantization (PTQ) and quantization-aware training (QAT) methods have made progress in 4-bit activation quantization by introducing smoothing, SVD branches, rotations, mixed precision, or advanced formats such as NVFP4. These additional operators and data types impose demanding requirements on inference engines and hardware, limiting the broad adoption of low-precision models. Can quantization be achieved using only plain low-bit operators? To answer this question, we propose JustQuant, a simple yet effective framework that moves the complexity of low-bit quantization from deployment-time operators into the training process. We first revisit model quantization from the perspective of knowledge distillation and show that a key reason existing PTQ and QAT methods fail is that they typically exploit supervision at only a single level. We then introduce Theseus QAD, a quantization-aware distillation method that progressively applies multi-level supervision, analogous to the gradual replacement process in the Ship of Theseus. Extensive experiments on DiT and diffusion large language models show two distinct regimes. For smaller models, Theseus QAD can serve as a lightweight warm-up stage that substantially improves subsequent QAT with plain operators, while naive QAD may collapse in the same setting. For larger models, Theseus QAD provides a stronger distillation training path than ordinary QAD. Across both regimes, JustQuant improves low-bit quantization quality while avoiding the complex operators required by many existing PTQ methods.

Quantization-aware distillation (QAD) restores much of the short-form question-answering performance lost to sub-3-bit quantization, yet leaves mathematical and code reasoning substantially impaired. Long generations often degenerate into repetitive loops, exhausting the decoding budget without completing a solution. We trace this gap to quantization-amplified exposure bias: QAD trains on fixed corpus prefixes, while quantization-induced deviations compound along the model's own autoregressive trajectories. To address this mismatch, we introduce an on-policy distillation (OPD) stage that places teacher supervision where the quantized model actually goes. Starting from a QAD checkpoint, the student generates through the quantized forward path used at deployment and receives feedback from a frozen full-precision teacher on its own prefixes, combining dense token-level guidance with task-verifier rewards. Across four models at 2.79 and 1.88 effective bits, OPD raises average BF16 performance retention from 35% to 70% on MATH-500 and from 66% to 91% on HumanEval while preserving short-form performance, with reasoning gains substantially exceeding those of continued teacher-forced QAD in matched-budget comparisons. By coupling QAD's stable low-bit initialization with OPD's on-policy reasoning recovery, our framework provides a comprehensive sub-3-bit solution that preserves broad capabilities while restoring long-form reasoning.

We show that a quantized model that keeps its classification accuracy still changes $14$ to $46\%$ of its top-1 retrieval results, and that aggregate ranking metrics reveal only part of this damage. We tie this failure to the gap between the two highest model scores and use that gap to decide when to trust a quantized answer and where additional precision should be spent. We show that the top-1 result is guaranteed to survive quantization only when this gap exceeds twice the largest rounding error. In classification, the scores are logits, and training compares the correct class against every other class, which encourages this gap. In retrieval, the scores are query-document similarities, and training compares each positive only against sampled negatives, so nothing separates the top-1 item from the second. This gap can be measured without labels. Before deployment, it predicts which models will break under quantization, and at deployment time it tells, per input, whether the quantized answer still matches the full-precision answer. Most classification inputs have a gap wide enough to trust the quantized answer, but few retrieval queries do. That gap motivates a different fix in each task. In retrieval, spending extra bit-width on the layers whose quantization moves the gap most recovers up to three-quarters of an extra bit's benefit for half its cost. In classification, routing the few low-gap inputs to full precision recovers most of the lost accuracy at a fraction of the cost.

We revisit Kashin-decomposition-based weight quantization for large language models and propose an improved algorithm with stronger convergence properties and structured, efficient orthogonal transforms. The method retains the core factorization of each weight into two components -- one with bounded infinity norm and the other with bounded infinity norm after an orthogonal transformation -- but replaces the dense random orthogonal matrix with a sign-randomized Discrete Cosine Transform (DCT), reducing the per-iteration cost from $\mathcal{O}(N^2)$ to $\mathcal{O}(N \log N)$. The proposed greedy algorithm with alternating updates guarantees the four-peak distribution required for stable 2-bit clustering of each factor and admits closed-form initialization of cluster centers, removing the multi-restart k-means bottleneck of prior work. Composed with OPTQ-style sequential error compensation and QuIP-style incoherence preprocessing, the resulting JAX pipeline is competitive with OPTQ, QuIP, QuIP-RG and a fine-tuning- and vector-quantization-free variant of QuIP# at 4-bit per channel on OPT, Llama-2 and Pythia, with favorable wall-clock scaling. The bounded-$\ell_\infty$ factorization is also notably robust: on stress configurations where QuIP variants diverge to four-digit perplexity (Pythia-6.9B) or abort with NaNs in LDL back-substitution (Mistral-7B), Kashin-DCT remains numerically stable and stays close to FP16 baseline. At inference time, each weight decomposes into two 2-bit factor codes per channel that are structurally suited to native-2-bit hardware.

Chilli (Capsicum annuum) is one of India's most economically significant crops, yet its productivity is persistently threatened by diseases that are difficult to identify without expert intervention. While Vision Transformers (ViTs) have achieved high classification accuracy, their large computational footprint makes deployment on resource constrained devices challenging. Existing compression approaches typically address pruning, quantization, and knowledge distillation in isolation, leaving the potential benefits and interactions of their combined application insufficiently explored. We propose a unified Vision Transformer compression framework that combines Hessian-Balanced Adaptive Block Pruning (H-BAC), guided by second-order sensitivity estimation, with quantization and attention-based knowledge distillation. To systematically identify the most effective configuration within each compression family, each technique is first evaluated independently through controlled ablation studies, after which the best-performing components are integrated into a sequential deployment pipeline tailored to real-world agricultural constraints. On a chilli 3-class village-split dataset with a genuine cross-village, cross-device out-of-distribution test split, the resulting compressed models match or exceed the 95.13% FP32 baseline's accuracy, alongside 74-98% model size reduction, and the fully integrated compression pipeline achieves a 54.5x size reduction (327.42 MB to 6.01 MB) at 95.13 +/- 2.32% accuracy across four tested configurations. A direct comparison further reveals that, on this dataset, a directly-trained student of the same final size, without pruning or distillation, reaches comparable accuracy of 94.87%, at the same 6.01 MB INT8 size, indicating where H-BAC and knowledge distillation are, and are not yet shown to be, worth their computational cost.

Serving large language models cheaply increasingly means shipping models that are both structurally compressed to a fraction of their parameters and quantized to 4 bits. Together these steps degrade reasoning, mathematics, coding, and long-context behavior enough to require a recovery, or healing, stage before deployment. The default recipe, quantization-aware training (QAT), re-fits the compressed, quantized model to hard labels; in our pipeline it converged slowly and collapsed past its peak. We adopted Quantization-Aware Healing (QAH) instead. Because a structurally compressed model is never independently trained at full precision, its bfloat16 checkpoint is a distillation-recovered approximation of the original; QAH distills the 4-bit student directly from the original, uncompressed model. On a GPT-OSS 120B to 60B to MXFP4 pipeline, the QAH student matches or beats its bfloat16 source on 7 of 9 benchmarks at roughly 4 times less weight memory and half the teacher's parameter count, and is released open-weight as Hypernova-60B. Against a matched QAT baseline it reaches a comparable peak about 7 times faster and stays stable under continued training, without hand-tuned early stopping. We also report deployment lessons, including a large, reproducible quality gap between distributed-training backends. Our aim is a recipe deployable without a multi-week hyper-parameter search.

Post-training quantization (PTQ) is widely used to reduce the memory and computational cost of large language models. Existing PTQ methods typically obtain an initial quantized model through heuristic rules or greedy optimization, and once quantization is completed the resulting integer assignments are usually treated as final. This observation motivates a complementary optimization stage within PTQ that keeps quantized weights improvable after an executable quantized model has been produced, while preserving the quantized format. We introduce ReQuant, a backpropagation-free fixed-grid refinement procedure for this stage. Agnostic to the PTQ initializer, ReQuant takes an existing quantized model as a feasible starting point and iteratively revisits its discrete weight assignments on the fixed quantization grid. Accepted updates strictly reduce the mean squared reconstruction error and remain on the original grid. In this way, ReQuant turns the initially fixed PTQ output into an iteratively optimizable discrete solution and serves as a plug-and-play post-processing stage for existing PTQ pipelines. Experiments across diverse model families, bit-widths, and downstream tasks show that ReQuant consistently improves quantized models from heterogeneous PTQ initializers, with especially large gains on simple initializers and lower bit-widths. Notably, ReQuant can refine a simple round-to-nearest initialization across multiple sweeps until it approaches or surpasses GPTAQ under the same quantization format. These results establish ReQuant as a practical complementary stage for further improving existing PTQ pipelines.

Quantization saves memory by storing model weights with fewer bits. It can also change model decisions, such as whether to call a tool or which option to choose from a finite set. We study these decision changes in 16 language models from 8 families at 4, 3 and 2 bits, across several post-training quantization settings. Our evaluation covers tool use, safety, general knowledge and social bias, using BFCL, XSTest, MMLU, BoolQ, BBQ and synthetic tasks. The decision margin is the score difference between two possible first tokens, measured before and after quantization. Writing the margin before quantization as $m$ and the margin after quantization as $m'$, we find an approximately linear relationship across decisions: $m' \approx c m + b$. The slope $c$ is usually below one and becomes smaller as precision falls, so quantization progressively shrinks decision margins. The offset $b$ is the same for every decision of one kind. Quantization therefore does not simply add random noise, and even a strong preference at full precision can flip. Quantization also affects different kinds of decisions to different degrees. Within tool use, whether to call a tool is often more sensitive than which tool to call: on 400 BFCL tasks, three of five models lose more completed calls than correct tool selections at 3-bit round-to-nearest. Under GPTQ and GGUF far fewer whether-to-call decisions flip than under plain rounding, so there is no single 3-bit failure point. The same relationship predicts how often decisions flip. Across 1,082 combinations of models, quantization settings, bit-widths and decision types, we fit the slope, the offset and the spread around the fitted line on half of the decisions and predict the flip rate on the other half. The predicted flip rate differs from the observed flip rate by a median of 1.0 percentage point, while reusing the flip rate of the first half misses by 1.3.