Design Study: TurboQuant-Family KV-Cache Compression for Browser-Local Rust/WASM Runtimes

1\. Executive Recommendation and Non-Goals

The integration of extreme low-bit vector quantization into browser-local transformer inference represents a critical pathway for expanding context windows without violating the stringent memory limits of WebAssembly (WASM). This design study evaluates the application of the TurboQuant family of algorithms to compress the Key-Value (KV) cache for compact transformer models ranging from 0.3B to 2B parameters within the TinyRustLM ecosystem. Based on rigorous engineering analysis of public research, the primary architectural recommendation is to adopt a multiplier-free, structured-transform approach—specifically Fast-TurboQuant utilizing a Fast Walsh-Hadamard Transform (FWHT)—for key cache quantization, coupled with an independently optimized asymmetric scalar quantizer for the value cache. The original Dense TurboQuant algorithm, which relies on dense random rotation matrices requiring quadratic computational complexity, imposes an unsustainable compute penalty during the autoregressive cache append phase on scalar and WASM SIMD128 execution targets. Furthermore, the 1-bit Quantized Johnson-Lindenstrauss (QJL) residual correction proposed by the original authors must be strictly avoided. While theoretically unbiased for isolated inner products, its high variance destructively interacts with the non-linear softmax function, resulting in severe attention degradation. Instead, the design will employ matched-norm scalar correction derived from the earlier EDEN algorithmic framework. This report establishes a clean architectural separation between three distinct engineering domains to prevent conceptual leakage. First, static model-weight quantization remains entirely out of scope; the KV cache is runtime state, and compressing it does not alter the immutable weight bytes transferred over the network nor does it render the underlying transformer a 1-bit model. Second, persistent embedding and vector-index quantization—such as the offline corpus ingestion handled by projects like TurboVec—is excluded, as autoregressive inference requires strictly online, low-latency, and append-only cache modifications rather than batch indexing. Third, the focus remains exclusively on online transformer KV-cache quantization. The paramount objective is to maintain raw conversational quality, interactive prefill latency, and deterministic output while radically compressing the runtime attention state.

2\. Source and Implementation Observation Log

The foundational algorithms, claims, and engineering architectures analyzed in this report are strictly derived from public sources and verifiable artifacts, categorized meticulously to separate empirical fact from theoretical claims. Directly observed public facts include the publication of the primary TurboQuant research by Zandieh et al. in April 2025, which introduced the two-stage process of dense random rotation followed by optimal Lloyd-Max scalar quantization and a 1-bit QJL residual correction1. We also observe the publication of PolarQuant, which proposed recursive coordinate pairing and analytical angle quantization to eliminate block normalization constants3. The Fast-TurboQuant paper, published in June 2026, is observed to replace dense Gaussian matrices with a Rademacher phase inversion and Fast Walsh-Hadamard Transform6. The DRIVE/EDEN line of work, published in 2021 and 2022, establishes the mathematical foundation for scalar quantization of rotated vectors and introduces critical scaling factors8. Finally, the public RyanCodrai/turbovec repository demonstrates a practical SIMD implementation utilizing NEON and AVX-512 for random rotations, Lloyd-Max bucketing, and length-renormalized scoring in a vector-search context10. Claims made by paper or project authors include the assertion by the TurboQuant authors that their method achieves near-optimal distortion rates and quality neutrality at 3.5 bits per channel for KV caches1. The QJL authors claim that their 1-bit sign quantization provides an unbiased inner-product estimator with zero memory overhead13. The PolarQuant authors claim superior memory efficiency by bypassing normalization parameters entirely3. Independently reproduced or externally corroborated facts drastically reshape the practical application of these algorithms. Independent validation across multiple open-source implementations confirms that the QJL stage introduces extreme variance that is catastrophically amplified by the attention softmax mechanism, degrading reasoning performance in large language models16. Multiple implementations have corroborated that omitting QJL entirely and dedicating the bit budget to standard scalar quantization improves overall perplexity16. It is also externally corroborated that the FWHT is drastically faster than dense matrix multiplication, transforming a quadratic bottleneck into a log-linear addition-only phase7. Furthermore, empirical studies such as KIVI corroborate that value caches are highly tolerant of standard uniform scalar quantization without requiring complex orthogonal transformations20. The engineering analysis and recommendations presented throughout this report synthesize these facts into a bespoke architecture for WASM environments, strictly prioritizing SIMD-friendly memory layouts and avoiding divergent branching. Facts that require local TinyRustLM verification include the specific sensitivity of the target 0.3B to 2B models to outlier channels, the browser JIT compiler's register spilling behavior during SIMD look-up table (LUT) generation, and the exact dimensional requirements for pre-RoPE head splitting within the proprietary codebase. No private TinyRustLM code, evaluation prompts, or runtime outputs were inspected or modified in the creation of this report.

3\. KV-Cache Equations and Capacity Model

To accurately engineer a compression format, we must rigorously define the baseline shape, lifecycle, and capacity model of the uncompressed KV cache. The KV cache exists solely to prevent the redundant recomputation of past token representations during the autoregressive generation loop. For a transformer model parameterized by batch size ![][image1], total layer count ![][image2], query heads ![][image3], key-value heads ![][image4], head dimension ![][image5], and sequence context length ![][image6], the runtime state consists of a Key tensor ![][image7] and a Value tensor ![][image8]. The lifecycle of these tensors begins at the prefill phase, where a prompt of length ![][image9] is processed simultaneously. The resulting keys and values are projected, shaped into ![][image10], and appended to the cache. During the decode phase, each new token generates a single vector of shape ![][image11], which is concatenated to the sequence dimension, incrementing ![][image6] monotonically until generation halts. Assuming a standard element type of 16-bit floating point (FP16 or BF16), the element size ![][image12] is 2 bytes. The memory requirement per token, across the entire depth of the network, is defined as the sum of the key and value storage requirements. The formulation is ![][image13]. The total cache capacity required to serve a sequence of length ![][image6] is derived by integrating the per-token cost over the sequence length and batch size, resulting in the equation ![][image14]. The architectural attention topology fundamentally alters the scaling of ![][image4] and, consequently, the baseline memory footprint. In Multi-Head Attention (MHA), the number of key-value heads equals the number of query heads (![][image15]). In Grouped-Query Attention (GQA), the query heads are divided into groups, and each group shares a single key-value head (![][image16]). In Multi-Query Attention (MQA), a single key-value head is shared across all query heads (![][image17]). To illustrate the memory pressure on browser-local WASM runtimes, consider the total cache size for a representative 1.5B parameter GQA model operating at FP16, with parameters ![][image18], ![][image19], ![][image20], and ![][image21].

The constraints of the WASM environment are severe. Standard linear memory limits typically cap contiguous allocation at 2GB to 4GB, depending on the JavaScript engine's configuration and the execution hardware. As demonstrated, supporting a 32,768-token context with a GQA topology instantly consumes approximately 786 MB. When factoring in the static model weights, dynamic heap allocations, and the potential for multi-turn chat architectures holding multiple contexts in memory, the application rapidly encroaches upon hard limits. Reducing the element size ![][image12] through extreme low-bit quantization is not merely an optimization; it is a strict functional prerequisite for long-context execution in the browser.

4\. Key-Versus-Value Error Model

A fundamental principle of effective KV-cache compression is acknowledging the profound mathematical asymmetry between the Key and Value matrices. They execute entirely different algebraic roles within the self-attention mechanism, leading to disparate error propagation profiles and mandating distinct quantization strategies. The self-attention output ![][image22] for a single query vector ![][image23] is computed by first calculating the scaled dot-product attention scores against the transposed key matrix ![][image24], applying the softmax function to generate a probability distribution ![][image25], and finally computing a weighted sum of the value matrix ![][image8]. The formulation is ![][image26]. Let ![][image27]. Thus, the final operation is linearly reduced to ![][image28]. Error propagation through the Key matrix is highly volatile. The keys undergo an inner product operation followed immediately by the exponential softmax function. If a quantization algorithm introduces an error vector ![][image29] into a reconstructed key ![][image30], the pre-softmax logit is shifted by the inner product ![][image31]. The softmax function transforms this additive error into a multiplicative distortion. According to Jensen's inequality and the properties of the moment-generating function for the normal distribution, if the inner-product error is modeled as a zero-mean Gaussian ![][image32], the expected value of the exponentiated logit is heavily biased upwards. The mathematical relationship is expressed as ![][image33]. This equation exposes the critical flaw in the QJL algorithm. QJL is explicitly designed to be an unbiased inner-product estimator, meaning ![][image34]17. However, achieving this unbiasedness by crushing the residual down to a 1-bit sign vector introduces extreme variance (![][image35]) into the estimate. When this high-variance estimate is passed through the softmax function, the ![][image36] term artificially inflates the attention scores of irrelevant keys. This inflation effectively flattens the attention distribution, destroying the model's capacity for sharp, precise retrieval and causing catastrophic failure on reasoning tasks16. Therefore, an unbiased key estimator is insufficient if it suffers from high variance. The engineering imperative is to minimize variance by optimizing for Mean-Squared Error (MSE) in the keys, accepting a predictable, uniform bias that can be partially mitigated by scalar adjustments, rather than utilizing a high-variance unbiased estimator. Conversely, error propagation through the Value matrix is purely linear. If a quantized value vector is defined as ![][image37], the error injected into the final output is exactly the sum of the value errors weighted by the attention probabilities, defined as ![][image38]. There is no exponential amplification. The reconstruction error scales predictably and linearly. As a result, the value cache is remarkably tolerant of straightforward, independent scalar quantization schemas—such as uniform per-channel or per-token mapping—without necessitating complex orthogonal transformations or optimal Lloyd-Max codebooks16. An unbiased inner-product estimator applied to keys does absolutely nothing to preserve the fidelity of value aggregation, further reinforcing the necessity of designing decoupled compression pipelines for ![][image7] and ![][image8].

5\. Placement of Transforms in Attention

Integrating rotation-based quantization algorithms like TurboQuant into an established transformer requires surgical precision regarding the placement of the transforms relative to the Rotary Positional Embedding (RoPE). The sequence of operations determines whether the spatial relationships necessary for context comprehension are preserved or irreversibly scrambled. RoPE encodes absolute positional information by applying a 2D rotation matrix to adjacent pairs of coordinates within the query and key vectors. This operation relies on the strict, unadulterated ordering of the ![][image5]\-dimensional channels. A dense orthogonal matrix or a Fast Walsh-Hadamard Transform (FWHT), however, functions by globally mixing information across all channels to distribute outlier energy uniformly. RoPE and global orthogonal rotations absolutely do not commute. If a key vector is multiplied by a Hadamard matrix prior to RoPE, its coordinate pairs are scrambled, and the specific frequency allocations required by the positional embedding are destroyed. Consequently, the exact dataflow during the cache append phase must strictly adhere to the following sequence. First, the query ![][image23], key ![][image39], and value ![][image40] tensors are generated from the standard linear projection. Second, RoPE is applied to the key ![][image39] based on its absolute positional index within the context sequence, resulting in ![][image41]. Third, the Fast-TurboQuant projection—consisting of a Rademacher phase flip followed by the FWHT—is applied exclusively to the RoPE-adjusted key, yielding ![][image42]. Fourth, this rotated key is scalar-quantized using the Lloyd-Max codebook and appended to the compressed Key Cache. Concurrently, the value ![][image40] is quantized directly without any orthogonal rotation and appended to the compressed Value Cache. During the subsequent read and score phase for a new decoding step, the query must be transformed into the same basis as the compressed keys. The query ![][image23] is extracted and RoPE is applied for the current timestep, producing ![][image43]. Crucially, the exact same Fast-TurboQuant projection (Rademacher \+ FWHT) is then applied to ![][image43]. Because the rotation matrix is orthogonal, inner products are perfectly preserved across bases, meaning ![][image44]. The attention score is then computed directly in the compressed domain without ever dequantizing the full key history. This specific dataflow relies on the assumption that head splitting occurs prior to the orthogonal transform. Engineering analysis mandates that local TinyRustLM verification is required to audit the exact tensor shapes at the RoPE stage. If head-splitting occurs after RoPE in the proprietary implementation, the FWHT must be meticulously engineered to operate strictly within the boundaries of each isolated ![][image5]\-dimensional head, rather than bleeding across the flattened multi-head sequence, which would corrupt the attention mechanism entirely.

6\. Candidate Key and Value Algorithms

Drawing upon the mathematical requirements of the error model and the performance realities of browser-based execution, we propose a bifurcated algorithmic strategy, employing disparate methods for the Key and Value caches. For Key caching, we design a modified Fast-TurboQuant pipeline that leverages structured transforms. The process begins with normalization, where the ![][image45] norm of the key vector is extracted and stored as an FP16 scalar, leaving a unit vector. We eschew dense random rotation matrices due to their prohibitive ![][image46] complexity7. Instead, we apply a Rademacher phase inversion—multiplying each element by a pseudo-random sequence of ![][image47] and ![][image48] to break symmetries—followed immediately by the Fast Walsh-Hadamard Transform (FWHT). This structured transformation forces the coordinate distribution of the key vector to approach a Gaussian ![][image49] by exploiting sub-Gaussian concentration6. Once rotated into this predictable Gaussian distribution, the coordinates are mapped using a precomputed Lloyd-Max scalar quantization codebook. Because the distribution is analytically known, the optimal codebook boundaries and centroids are fixed offline and require no data-dependent training. Finally, to counteract the systematic underestimation of inner products caused by MSE-optimal scalar quantization, we apply a residual correction scalar. Aligning with the EDEN framework, we utilize the matched-norm scale ![][image50] to restore unbiasedness without injecting the extreme variance associated with the QJL residual9. This entirely sidesteps the need to dequantize the full key history during the attention scan, as queries can be rotated and scored directly against the codebook indices. For Value caching, we reject orthogonal transformations entirely. The empirical evidence is robust: values do not suffer from the extreme channel-wise outliers induced by RoPE, and their linear aggregation profile makes MSE-optimal rotation mathematically unnecessary16. Subjecting values to the FWHT would incur a severe, unjustifiable compute penalty during the append phase. Instead, we select an asymmetric block-wise uniform quantization strategy mirroring the KIVI approach. Each ![][image5]\-dimensional value vector is quantized directly into low-bit integers on a per-token basis. The local minimum and maximum of the vector are extracted to compute a single FP16 scale and FP16 zero-point, which are stored as metadata. This approach provides excellent empirical performance, preserves spatial locality, and requires minimal computational overhead during appending. We explicitly reject PolarQuant as a candidate algorithm for either cache. While PolarQuant theoretically eliminates the need for normalization metadata by transforming vectors into a recursive tree of polar coordinates3, it relies heavily on bit-packed angle indices that must be mapped through multiple layers of trigonometric lookup tables (sine and cosine). On a GPU, this necessitates heavy reliance on constant memory and intricate warp-level shuffles26. In a WASM SIMD128 environment, managing divergent table lookups across execution lanes is extraordinarily expensive and fundamentally hostile to the hardware architecture, whereas the FWHT relies purely on SIMD-friendly additions7. The online append cost determines the viability of these algorithms. During the decode phase, a single new token must update the cache for every layer. For the Fast-TurboQuant key algorithm on a 1.5B model with ![][image51], the Rademacher flip requires 128 sign-bit toggles (virtually zero ALU cost), and the FWHT requires ![][image52] additions19. The Lloyd-Max bucketing requires 128 comparisons, and bit-packing utilizes standard shift and bitwise OR operations. The metadata computation involves a single 128-element dot product for the norm and scale. This log-linear complexity is comfortably hidden behind the memory bandwidth limits of the system. Conversely, a dense rotation would require 16,384 MACs per head, pushing the compression compute overhead beyond the bandwidth savings and crippling the tokens-per-second metric for consumer CPUs.

7\. Dense and Structured Transform Comparison

The architectural divergence between dense random rotations (as proposed in the original TurboQuant paper) and fast structured transforms (as utilized in Fast-TurboQuant) defines the boundary between academic theory and edge-deployable software. A dense random orthogonal matrix requires multiplying the ![][image5]\-dimensional input vector by a ![][image53] matrix of floating-point values. The computational complexity is strictly ![][image46] multiply-accumulate (MAC) operations. The memory complexity demands the storage of the dense matrix, equating to ![][image54] bytes per attention head. For a standard head dimension of ![][image51], evaluating a single layer requires 16,384 MACs and 65 KB of matrix storage. Across a 32-layer, 8-KV-head model, appending a single token incurs roughly 4.19 million MACs strictly for the preconditioning projection26. In a WASM environment lacking dedicated tensor cores or AMX instructions, this latency overhead completely eclipses the time saved by loading fewer cache bytes during the attention scan. Structured transforms eradicate this hardware multiplier bottleneck. The Fast Walsh-Hadamard Transform operates via an in-place divide-and-conquer butterfly network. The arithmetic complexity is reduced to ![][image55] additions and subtractions, eliminating all floating-point multiplications7. For ![][image51], this translates to exactly 896 additions per head. The Rademacher phase inversion matrix is diagonal and consists solely of ![][image47] and ![][image48] values; its application executes via sign-bit toggles using logical XOR gates on the IEEE-754 representation, consuming virtually zero ALU cycles19. Furthermore, the structured transform requires no persistent matrix storage, as the Rademacher sequence can be dynamically generated from a globally shared PRNG seed identity, ensuring cache portability across devices. A significant engineering constraint of the FWHT is its strict requirement that the dimension size be a power of two. While 64 and 128 are standard, models frequently deploy with non-power-of-two head sizes such as 80, 96, or 160\. To resolve this, vectors must be zero-padded to the next power of two (e.g., ![][image56]) prior to applying the Rademacher flip and the FWHT. Fortunately, this padding explicitly improves the sub-Gaussian concentration mandated by the Johnson-Lindenstrauss lemma, slightly lowering the mean-squared error of the resulting quantization6. The vector is then quantized and packed at the padded dimension size. While this introduces a minor storage inefficiency, it preserves the log-linear ALU acceleration required by WASM SIMD128. The transform matrices are naturally self-inverse (![][image57]), ensuring mathematical parity and identical codepaths during any theoretical dequantization phase.

8\. Packed Format and Complete Bit Accounting

Exact capacity modeling dictates that the binary layout of the quantized cache pages be meticulously engineered down to the bit level. Fractional bit rates arise strictly from mathematical division of metadata across the channel dimension, not from complex entropy coding. Variable-length entropy coding (such as Huffman or Arithmetic coding) is explicitly rejected for KV-cache implementations, as the attention scan requires strictly deterministic random access across the context sequence. Maintaining pointer offset tables for variable layouts would fracture memory contiguousness and devastate SIMD prefetching. We define the exact packed layouts for three candidate targets: 4 bits, 3 bits, and 2 bits, assuming a baseline head dimension ![][image51] and a zero-padded operating dimension where necessary.

Each layout incorporates 32 bits (4 bytes) of empty padding to ensure the final vector structure lands on a 16-byte aligned memory boundary. Strict 16-byte alignment is mathematically non-negotiable for WASM execution, as the v128.load instructions will trap or suffer massive performance penalties if subjected to unaligned memory accesses across cache lines. A combined Key and Value slot for a single token at the 4-bit target requires ![][image58] bytes. The fractional effective rate is calculated purely by dividing the final aligned byte footprint by the dimension count (![][image59] bits). No separate residual sketching budgets or outlier retention arrays are appended to the per-token struct, as they would exponentially complicate the hot-loop SIMD memory access patterns.

9\. Derived Effective Memory Formulas

To contextualize the architectural gains against the constraints of the browser, we model the memory requirements for representative context lengths using the derived combined slot sizes. We compare the memory footprint of the uncompressed FP16 baseline (512 bytes per slot) against the 4-bit (144 bytes per slot) and 3-bit (112 bytes per slot) layouts. These calculations model a highly compact 0.6B parameter model utilizing Grouped-Query Attention (![][image18], ![][image20], ![][image51]) running at a batch size of 1\.

The mathematical advantage is profound. At 32,768 tokens, the FP16 baseline consumes 1.57 GB, dangerously close to exhausting the typical 2 GB linear memory limit of WASM before model weights and runtime heaps are factored in. The 4-bit implementation suppresses this requirement to a manageable 442 MB, granting the runtime the necessary headroom to process multi-turn conversations or deploy speculative decoding parallel branches. The Mixed INT8/INT4 column models a naive residual-window cache where recent tokens remain in higher precision; while it preserves quality, its memory unpredictability makes it inferior to the uniform structural compression offered by the TurboQuant methodology. Crucially, the system architecture expressly prohibits preserving a decoded FP32 shadow cache. The attention mechanism operates entirely within the compressed domain. Runtime scratch memory is limited to a single ![][image60] buffer to hold the active query projections during decoding, ensuring that peak RSS (Resident Set Size) tracks almost perfectly with the packed payload capacity without deceptive memory spikes.

10\. CPU and WASM Kernel Architecture

The viability of online quantization hinges entirely on the ability to compute the attention dot product without decompressing the keys back to floating-point values in main memory. The kernel architecture leverages a mathematical reformulation of the dot product, exploiting the fixed nature of the Lloyd-Max codebook. For Key attention scoring, the algorithm generates a Query-to-Codebook Look-Up Table (LUT). Because the quantized keys consist of indices pointing to 16 fixed centroids (for a 4-bit layout), we can pre-multiply the current query vector by every possible centroid. Prior to scanning the cache, the kernel iterates through the ![][image5]\-dimensional query. For each coordinate ![][image61], it computes ![][image62] scalar multiplications against the centroids and stores the results in L1 cache. The operation transforms the dot product into an array of index lookups: ![][image63]. For the WASM SIMD128 target, we execute this via hardware swizzle instructions. The WASM v128 register holds 16 bytes of data. The kernel loads a 16-byte chunk of the packed key (representing 32 4-bit dimensions). Bitwise masks extract the high and low nibbles into two separate registers. The core acceleration utilizes the i8x16.swizzle instruction, which functions identically to the x86 \mm\shuffle\epi8 or ARM vqtbl1q\s8 intrinsics. It accepts the pre-generated LUT (quantized to INT8 to fit the instruction constraints) and the vector of key indices, returning 16 looked-up values in a single cycle. The i16x8.dot\i8x16\i7x16\s instruction then accumulates these values into a running 32-bit integer sum. Following the scan, the accumulator is scaled by the global FP32 scaling factors, the key's ![][image45] norm, and the EDEN ![][image50] scalar to yield the final attention logit. The portable scalar path, required for fallback execution in unoptimized browser environments, simply unrolls the array indexing loop accumulator \+= LUT\[i\]\[key\index\]. Pre-fetching cache lines using linear access patterns is implicitly managed by the JavaScript engine, provided the memory is allocated linearly. Native x86 AVX-512 implementations will widen this swizzle approach to 512-bit vectors, processing 128 elements simultaneously, though such extensions are not yet formally standardized for WASM.

11\. Paging, Lifecycle, and Cache-Identity Design

Dynamic memory allocation within WASM (memory.grow) is an exceptionally heavy operation that can trigger engine-level garbage collection stalls or out-of-memory crashes if fragmented. Therefore, geometric allocation and arbitrary pointer invalidation are unacceptable. The cache lifecycle is managed via a strict, PagedAttention-style slab allocator initialized during model instantiation. The memory is pre-allocated as a single, contiguous WASM ArrayBuffer. This buffer is divided into fixed-size logical pages, typically containing 16 or 32 KV slots. A user's conversation sequence is represented internally as a linked list of page indices. As the context grows, new pages are popped from a pre-allocated free list. When a sequence is truncated—such as when a user regenerates a response or alters a previous chat bubble—the system simply decrements the reference count of the orphaned pages and pushes their indices back onto the free list. This deterministic cleanup requires no tracing garbage collector and prevents WASM linear memory from fragmenting. Multi-turn cache authority relies on a strict Cache Identity Digest. A cached page is only semantically valid if its inputs are mathematically identical to the current execution state. The digest is a lightweight hash comprising the Model Hash, the Tokenizer ID, the specific Fast-TurboQuant PRNG seed, the bit-allocation configuration, and the sequence of token IDs that generated the page. Prefix reuse across multiple chat branches is natively supported; if two generation sequences share the same initial token IDs and identical cryptographic digests, they seamlessly point to the same physical pages in the slab allocator.

12\. Primitive Numerical Test Matrix

Prior to integration into the autoregressive generation loop, the numerical kernels must be proven algebraically sound through a rigorous matrix of offline primitive tests. Verification at this stage requires local TinyRustLM tooling.

1. Transform Orthogonality: The FWHT kernel must be proven strictly self-inverse (![][image64]). Synthetic arrays of dimension ![][image51] must preserve their ![][image45] norm to a floating-point tolerance of ![][image65] post-transformation.
2. Encode/Decode MSE Bound: Synthetic vectors uniformly distributed on the unit hypersphere are compressed and decompressed. The measured Mean-Squared Error must align with the theoretical Shannon rate bounds, scaled by the known Lloyd-Max inefficiency factor (approximately ![][image66]). Deviations indicate failure in codebook generation or bit-packing alignment.
3. Inner-Product Bias: We generate 10,000 random query-key pairs, computing ![][image67] natively and via the compressed domain logic. The residual error must center precisely at zero, validating that the EDEN ![][image50] scaling correctly offsets the scalar quantization shrinkage28.
4. Softmax Divergence: An arbitrary ![][image68] matrix is passed through the baseline TinyRustLM attention function. The output probability distribution ![][image25] is recorded. The operation is repeated with the compressed kernels. The Kullback-Leibler (KL) divergence between the distributions is measured, establishing a preregistered threshold for logit drift prior to model-level integration.

13\. Model-Level Quality Evaluation

Mathematical proofs of low distortion are necessary but insufficient; the ultimate arbiter of quality is end-to-end token generation over untouched source prompts. The evaluation protocol requires strict isolation between the baseline f32/f16 runtime and the compressed test arms (4-bit, 3.5-bit, and 3-bit). The Model-Level Quality Evaluation covers four distinct domains. First, long retrieval is assessed using "Needle in a Haystack" configurations across 1,000, 4,000, 8,000, and 16,000 token contexts. The model must retrieve the exact inserted fact without hallucination; degradation here indicates catastrophic high-variance corruption in the key scores. Second, ordinary chat competence is measured via standard multi-turn suites (e.g., MT-Bench). Output text must be generated using identical sampler configurations and PRNG seeds to guarantee deterministic alignment. Third, context-boundary behavior is audited to ensure the compression does not disrupt token continuity at the transition edges between sliding windows or physical WASM memory pages. The evaluation strictly prohibits the use of Best-of-N retries, post-generation heuristic repair, or the injection of evaluation answers into the prompt state to mask compression errors. The raw outputs generated by the compressed attention mechanism constitute the sole evidence of quality retention.

14\. Performance Benchmark Protocol

Performance evaluation must cleanly separate the prefill phase from the decode phase, as their computational profiles are entirely inverse.

• Prefill Latency (Time to First Token \- TTFT): Measures the throughput of appending hundreds or thousands of tokens simultaneously. This isolates the computational overhead of the Rademacher flip, the FWHT projection, the Lloyd-Max bucketing, and the cache-line writes.
• Decode Latency (Time Per Output Token \- TPOT): Evaluates the steady-state generation speed. This isolates the i8x16.swizzle SIMD scan, the query LUT generation, and the allocator logic.
• Memory Utilization: Peak Resident Set Size (RSS) and WASM page count are continuously monitored to verify that the theoretical memory equations (Section 9\) manifest perfectly in practice, ensuring zero memory leaks or unexpected shadow arrays.

Stop rules define the boundaries of failure. A design must be immediately rejected if it successfully saves nominal bytes but inadvertently increases peak RSS due to temporary scratch buffers, requires model-sized uncompressed shadow copies, produces unstable browser memory growth, or results in a TPOT slower than the uncompressed baseline when memory bandwidth is otherwise unsaturated.

15\. Staged Implementation Plan and Stop Rules

Attempting a monolithic rewrite of the TinyRustLM attention backend will fail due to interacting complexities. The implementation must follow a strictly gated, staged path.

1. Mathematical Prototype: Construct the FWHT and Lloyd-Max bucketing logic in Python or a standalone Rust script. Validate against the Primitive Numerical Test Matrix.
2. One-Layer Fixture: Integrate the scalar and SIMD kernels into a tiny deterministic transformer (e.g., 2 layers, sequence length 128\) outside the browser. Validate that RoPE interactions are correct.

• Stop Rule: If the layer output cosine similarity drops below 0.99 against the f32 baseline on this micro-model, halt and investigate RoPE scaling.

1. WASM SIMD Validation: Compile the kernels to WebAssembly. Execute micro-benchmarks comparing scalar to i8x16.swizzle throughput.

• Stop Rule: If the SIMD implementation fails to exceed scalar speeds by at least ![][image69], refactor memory alignment and register usage before proceeding.

1. Native Source Model: Deploy into the native x86/ARM CLI version of TinyRustLM. Execute the full Model-Level Quality Evaluation.
2. Clean-Browser Dogfooding: Execute the final application within Chrome and Firefox. Monitor JS garbage collection behavior, memory.grow instructions, and interactive conversational latency.

16\. Expected Gains

Assuming successful execution of the 4-bit Fast-TurboQuant and Asymmetric KIVI-style design, the mathematical gains are highly predictable. The memory capacity savings ratio is defined as: ![][image70] This definitively raises the context ceiling for a browser-local 1.5B model from approximately 8,000 tokens to over 28,000 tokens within a rigid 2GB WASM heap constraint. The computational compute profile for rotation shifts from ![][image71] dense operations to ![][image72] structured operations. For ![][image51], the transformation cost drops from 16,384 multiplications to exactly 896 additions. ![][image73] This ensures the transformation latency remains entirely hidden behind the memory latency wall, maintaining or improving the baseline TPOT.

17\. Unknowns Requiring Local Verification

Certain architectural realities cannot be assessed from public literature and require inspection of the proprietary TinyRustLM environment. First, the browser JIT compiler (e.g., V8, SpiderMonkey) heavily dictates SIMD performance. It is unknown if the JIT will successfully retain the query-centroid LUTs in hardware vector registers during the unrolled attention loop, or if it will trigger register spilling to the stack, which would collapse decode latency. Local profiling via browser tracing tools is mandatory. Second, recent literature suggests that attention mechanisms heavily rely on boundary layers (e.g., the first two and last two layers) to aggregate global context, requiring them to remain at higher precision16. It is unknown if the specific 0.3B to 2B models distilled for TinyRustLM require this boundary protection policy, which would marginally alter the total cache capacity equations.

18\. Annotated Primary-Source Bibliography

• TurboQuant (ICLR 2026): Zandieh, A., et al. TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate. (arXiv:2504.19874, April 2025). Provides the foundational mathematical proof that random rotation followed by optimal Lloyd-Max scalar quantization yields near-optimal distortion rates.1
• PolarQuant (AISTATS 2026): Han, I., et al. PolarQuant: Quantizing KV Caches with Polar Transformation. (arXiv:2502.02617, February 2025). Explores the elimination of metadata via radial coordinate transformation. Acknowledged for theoretical elegance, but rejected for WASM implementation due to severe branching and trigonometric lookup complexities.3
• QJL (2024): Zandieh, A., et al. QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead. (arXiv:2406.03482, June 2024). Introduces the 1-bit sign projection technique. Rejected due to independently verified variance amplification that corrupts transformer softmax operations.13
• Fast-TurboQuant (2026): Pereira, P. M. R., et al. Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach. (arXiv:2606.21448, June 2026). Essential architectural modification substituting dense Gaussian rotation for the Rademacher flip and Fast Walsh-Hadamard Transform (FWHT), enabling multiplier-free SIMD processing.6
• EDEN / DRIVE (2021/2022): Vargaftik, S., Ben-Basat, R., et al. A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work. (arXiv:2604.18555, April 2026). Provides the mathematical justification for replacing the high-variance QJL residual with optimized scalar scaling factors (![][image74] or ![][image50]) to maintain inner-product accuracy without introducing exponential softmax errors.8
• TurboVec: Codrai, R. RyanCodrai/turbovec (GitHub, 2026). Public Rust repository demonstrating real-world SIMD implementations of TurboQuant logic, look-up tables, and length-renormalized scoring. Used purely for comparative engineering of the query LUT technique.10
• vLLM TurboQuant Evaluation: TurboQuant (vLLM Blog, May 2026). Official engineering evaluation detailing the severe reasoning degradation observed at ultra-low 3-bit TurboQuant configurations on Llama-3 and Qwen architectures, substantiating the need for conservative bit allocation and asymmetric value caching.18

Works cited

1. \[2504.19874\] TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate, https://arxiv.org/abs/2504.19874
2. TurboQuant: A First-Principles Walkthrough \- Arkar Min Aung, https://arkaung.github.io/interactive-turboquant/
3. \[2502.02617\] PolarQuant: Quantizing KV Caches with Polar Transformation \- arXiv, https://arxiv.org/abs/2502.02617
4. PolarQuant: Quantizing KV Caches with Polar Transformation \- arXiv, https://arxiv.org/html/2502.02617v1
5. PolarQuant: Quantizing KV Caches with Polar Transformation \- arXiv, https://arxiv.org/pdf/2502.02617
6. \[2606.21448\] Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach, https://arxiv.org/abs/2606.21448
7. Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach \- arXiv, https://arxiv.org/pdf/2606.21448
8. \[2604.18555\] A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work \- arXiv, https://arxiv.org/abs/2604.18555
9. A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work \- arXiv, https://arxiv.org/pdf/2604.18555
10. GitHub \- RyanCodrai/turbovec: A vector index built on TurboQuant, written in Rust with Python bindings, https://github.com/RyanCodrai/turbovec
11. TurboVec: The Rust-Powered Vector Index That's Quietly Changing the RAG Game, https://www.alphamatch.ai/blog/turbovec-rust-vector-index-rag-2026
12. (PDF) TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate \- ResearchGate, https://www.researchgate.net/publication/391246798\TurboQuant\Online\Vector\Quantization\with\Near-optimal\Distortion\_Rate
13. \[Literature Review\] QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead \- Moonlight, https://www.themoonlight.io/en/review/qjl-1-bit-quantized-jl-transform-for-kv-cache-quantization-with-zero-overhead
14. amirzandieh/QJL: QJL: 1-Bit Quantized JL transform for KV Cache Quantization with Zero Overhead \- GitHub, https://github.com/amirzandieh/QJL
15. PolarQuant: Quantizing KV Caches with Polar Transformation \- Google Research, https://research.google/pubs/polarquant-quantizing-kv-caches-with-polar-transformation/
16. turboquant\plus/README.md at main \- GitHub, https://github.com/TheTom/turboquant\plus/blob/main/README.md
17. Statistical Inference and Quality Measures of KV Cache Quantisations Inspired by TurboQuant \- arXiv, https://arxiv.org/html/2605.08114v1
18. A First Comprehensive Study of TurboQuant: Accuracy and Performance | vLLM Blog, https://vllm.ai/blog/2026-05-11-turboquant
19. Fast-TurboQuant A Multiplier-Free Online Vector Quantization Approach \- arXiv, https://arxiv.org/html/2606.21448v1
20. KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache \- GitHub, https://raw.githubusercontent.com/mlresearch/v235/main/assets/liu24bz/liu24bz.pdf
21. Kv cache quantization: ignorance, or malice? : r/LocalLLaMA \- Reddit, https://www.reddit.com/r/LocalLLaMA/comments/1t1t4nw/kv\cache\quantization\ignorance\or\_malice/
22. QJL: 1-BIT QUANTIZED JL TRANSFORM FOR KV CACHE QUANTIZATION WITH ZERO OVERHEAD \- OpenReview, https://openreview.net/pdf/b470267d0a4e09ab770de6b004939bc7c6114304.pdf
23. How a 2021 Quantization Algorithm Quietly Outperforms Its 2026 Successor, https://towardsdatascience.com/how-a-2021-quantization-algorithm-quietly-outperforms-its-2026-successor/
24. EDEN: Communication-Efficient and Robust Distributed Mean Estimation for Federated Learning \- GitHub, https://github.com/amitport/EDEN-Distributed-Mean-Estimation
25. PolarQuant: Quantizing KV Caches with Polar Transformation \- DEV Community, https://dev.to/patelchaitany/polarquant-quantizing-kv-caches-with-polar-transformation-255
26. GitHub \- AliesTaha/polar\quant: PolarQuant: Fused KV cache decode kernel that ties cuBLAS on B200 with 4.1x compression, https://github.com/AliesTaha/polar\quant
27. Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach \- ResearchGate, https://www.researchgate.net/publication/407510838\Fast-TurboQuant\A\Multiplier-Free\Online\Vector\Quantization\_Approach
28. A Note on TurboQuant and the Earlier DRIVE/EDEN Line of Work \- arXiv, https://arxiv.org/html/2604.18555v1
29. turboquant \- vLLM Documentation, https://docs.vllm.ai/en/latest/api/vllm/model\_executor/layers/quantization/turboquant/

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[image70]: 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>

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[image73]: 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>

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