How Lossless Is Lossless Speculative Decoding? The Role of Numerical Precision in Orthrus

We introduce Orthrus, a simple and efficient dual-architecture framework that unifies the exact generation fidelity of autoregressive Large Language Models (LLMs) with the high-speed parallel token generation of diffusion models. The sequential nature of standard autoregressive decoding represents a fundamental bottleneck for high-throughput inference. While diffusion language models attempt to break this barrier via parallel generation, they suffer from significant performance degradation, high training costs, and a lack of rigorous convergence guarantees. Orthrus resolves this dichotomy natively. Designed to seamlessly integrate into existing Transformers, the framework augments a frozen LLM with a lightweight, trainable module to create a parallel diffusion view alongside the standard autoregressive view. In this unified system, both views attend to the exact same high-fidelity Key-Value (KV) cache; the autoregressive head executes context pre-filling to construct accurate KV representations, while the diffusion head executes parallel generation. By employing an exact consensus mechanism between the two views, Orthrus guarantees lossless inference, delivering up to a 7.8x speedup with only an O(1) memory cache overhead and minimal parameter additions.

Inference optimizations are routinely evaluated by throughput alone, without verifying output correctness. We conduct a forensic analysis of batch speculative decoding and find that several widely-used implementations silently produce corrupted outputs (repetitive tokens, <unk> symbols) while reporting competitive speed; failures invisible to metrics like ROUGE. We trace the root cause to the ragged tensor problem: variable token acceptance desynchronizes position IDs, attention masks, and KV-cache across a batch. We formalize the synchronization invariants (rectangular alignment and position-ID contiguity) that valid batched inference must preserve and show that maintaining them incurs superlinear alignment overhead under contiguous layouts. EQSPEC enforces the invariants without custom kernels; EXSPEC schedules same-length sequences to bypass realignment. On SpecBench across three model families, EXSPEC reaches 3 x throughput at batch size 8 with 95% exact match to standard decoding; residual divergence traces to floating-point non-determinism, not synchronization error. Code:https://github.com/eBay/spec_dec

Single-stream autoregressive decoding of large language models is bound by memory bandwidth: each generated token requires one full forward pass through the target model, and successive passes cannot be parallelized. Speculative decoding restructures this computation: a small draft model proposes $K$ tokens autoregressively, the target model scores all of them in one batched pass, and a rejection-sampling rule provably preserves the target model's output distribution. We present a from-scratch, device-agnostic (CUDA/MPS/CPU) implementation and an empirical study across five draft/target backend configurations on a consumer Apple-silicon laptop. Distribution equivalence is verified at three levels, culminating in a two-sample test over roughly 9,200 real-model tokens per method ($χ^2 = 162.5$, dof $= 200$, $p = 0.976$) and exact greedy-sequence agreement. The best configuration reaches a measured $1.61\times$ wall-clock speedup at $K=6$, on an acceptance profile declining from 69.7% at $K=1$ to 37.8% at the optimum, while three of five configurations decelerate, either because the draft fails to out-speed a small target or because the quantized Metal backend executes "parallel" verification serially, an effect we isolate and quantify. The failures are as instructive as the successes: speculative decoding pays off only when verification is genuinely batch-parallel and the draft/target latency gap is real.