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Feb 19

Rotary Positional Embeddings as Phase Modulation: Theoretical Bounds on the RoPE Base for Long-Context Transformers

Rotary positional embeddings (RoPE) are widely used in large language models to encode token positions through multiplicative rotations, yet their behavior at long context lengths remains poorly characterized. In this work, we reinterpret RoPE as phase modulation applied to a bank of complex oscillators, enabling analysis through classical signal processing theory. Under this formulation, we derive principled lower bounds on the RoPE base parameter that are necessary to preserve positional coherence over a target context length. These include a fundamental aliasing bound, analogous to a Nyquist limit, and a DC-component stability bound that constrains phase drift in low-frequency positional modes. We further extend this analysis to deep transformers, showing that repeated rotary modulation across layers compounds angular misalignment, tightening the base requirement as depth increases. Complementing these results, we derive a precision-dependent upper bound on the RoPE base arising from finite floating-point resolution. Beyond this limit, incremental phase updates become numerically indistinguishable, leading to positional erasure even in the absence of aliasing. Together, the lower and upper bounds define a precision- and depth-dependent feasibility region a Goldilocks zone for long-context transformers. We validate the framework through a comprehensive case study of state-of-the-art models, including LLaMA, Mistral, and DeepSeek variants, showing that observed successes, failures, and community retrofits align closely with the predicted bounds. Notably, models that violate the stability bound exhibit attention collapse and long-range degradation, while attempts to scale beyond one million tokens encounter a hard precision wall independent of architecture or training.

  • 1 authors
·
Feb 11

SwapAnything: Enabling Arbitrary Object Swapping in Personalized Visual Editing

Effective editing of personal content holds a pivotal role in enabling individuals to express their creativity, weaving captivating narratives within their visual stories, and elevate the overall quality and impact of their visual content. Therefore, in this work, we introduce SwapAnything, a novel framework that can swap any objects in an image with personalized concepts given by the reference, while keeping the context unchanged. Compared with existing methods for personalized subject swapping, SwapAnything has three unique advantages: (1) precise control of arbitrary objects and parts rather than the main subject, (2) more faithful preservation of context pixels, (3) better adaptation of the personalized concept to the image. First, we propose targeted variable swapping to apply region control over latent feature maps and swap masked variables for faithful context preservation and initial semantic concept swapping. Then, we introduce appearance adaptation, to seamlessly adapt the semantic concept into the original image in terms of target location, shape, style, and content during the image generation process. Extensive results on both human and automatic evaluation demonstrate significant improvements of our approach over baseline methods on personalized swapping. Furthermore, SwapAnything shows its precise and faithful swapping abilities across single object, multiple objects, partial object, and cross-domain swapping tasks. SwapAnything also achieves great performance on text-based swapping and tasks beyond swapping such as object insertion.

  • 10 authors
·
Apr 8, 2024

STree: Speculative Tree Decoding for Hybrid State-Space Models

Speculative decoding is a technique to leverage hardware concurrency to improve the efficiency of large-scale autoregressive (AR) Transformer models by enabling multiple steps of token generation in a single forward pass. State-space models (SSMs) are already more efficient than AR Transformers, since their state summarizes all past data with no need to cache or re-process tokens in the sliding window context. However, their state can also comprise thousands of tokens; so, speculative decoding has recently been extended to SSMs. Existing approaches, however, do not leverage the tree-based verification methods, since current SSMs lack the means to compute a token tree efficiently. We propose the first scalable algorithm to perform tree-based speculative decoding in state-space models (SSMs) and hybrid architectures of SSMs and Transformer layers. We exploit the structure of accumulated state transition matrices to facilitate tree-based speculative decoding with minimal overhead to current SSM state update implementations. With the algorithm, we describe a hardware-aware implementation that improves naive application of AR Transformer tree-based speculative decoding methods to SSMs. Furthermore, we outperform vanilla speculative decoding with SSMs even with a baseline drafting model and tree structure on three different benchmarks, opening up opportunities for further speed up with SSM and hybrid model inference. Code will be released upon paper acceptance.

  • 4 authors
·
May 20, 2025

Let the Code LLM Edit Itself When You Edit the Code

In this work, we investigate a typical scenario in code generation where a developer edits existing code in real time and requests a code assistant, e.g., a large language model, to re-predict the next token or next line on the fly. Naively, the LLM needs to re-encode the entire KV cache to provide an accurate prediction. However, this process is computationally expensive, especially when the sequence length is long. Simply encoding the edited subsequence and integrating it to the original KV cache meets the temporal confusion problem, leading to significantly worse performance. We address this efficiency and accuracy trade-off by introducing \textbf{Positional \textbf{Integrity Encoding} (PIE). Building upon the rotary positional encoding, PIE first removes the rotary matrices in the Key cache that introduce temporal confusion and then reapplies the correct rotary matrices. This process ensures that positional relationships between tokens are correct and requires only a single round of matrix multiplication. We validate the effectiveness of PIE through extensive experiments on the RepoBench-C-8k dataset, utilizing DeepSeek-Coder models with 1.3B, 6.7B, and 33B parameters. Our evaluation includes three real-world coding tasks: code insertion, code deletion, and multi-place code editing. Results demonstrate that PIE reduces computational overhead by over 85% compared to the standard full recomputation approach across all model sizes and tasks while well approximating the model performance.

  • 6 authors
·
Jul 3, 2024

Batch Speculative Decoding Done Right

Speculative decoding speeds up LLM inference by using a small draft model to propose multiple tokens that a target model verifies in parallel. Extending this idea to batches is essential for production serving, but it introduces the ragged tensor problem: sequences in the same batch accept different numbers of draft tokens, breaking right-alignment and corrupting position IDs, attention masks, and KV-cache state. We show that several existing batch implementations violate output equivalence-the fundamental requirement that speculative decoding must produce identical token sequences to standard autoregressive generation. These violations occur precisely due to improper handling of the ragged tensor problem. In response, we (1) characterize the synchronization requirements that guarantee correctness, (2) present a correctness-first batch speculative decoding EQSPEC that exposes realignment as consuming 40% of overhead, and (3) introduce EXSPEC, which maintains a sliding pool of sequences and dynamically forms same-length groups, to reduce the realignment overhead while preserving per-sequence speculative speedups. On the SpecBench dataset, across Vicuna-7B/68M, Qwen3-8B/0.6B, and GLM-4-9B/0.6B target/draft pairs, our approach achieves up to 3times throughput improvement at batch size 8 compared to batch size 1, with efficient scaling through batch size 8, while maintaining 95% output equivalence. Our method requires no custom kernels and integrates cleanly with existing inference stacks. Our code is available at https://github.com/eBay/spec_dec.

SeqPE: Transformer with Sequential Position Encoding

Since self-attention layers in Transformers are permutation invariant by design, positional encodings must be explicitly incorporated to enable spatial understanding. However, fixed-size lookup tables used in traditional learnable position embeddings (PEs) limit extrapolation capabilities beyond pre-trained sequence lengths. Expert-designed methods such as ALiBi and RoPE, mitigate this limitation but demand extensive modifications for adapting to new modalities, underscoring fundamental challenges in adaptability and scalability. In this work, we present SeqPE, a unified and fully learnable position encoding framework that represents each n-dimensional position index as a symbolic sequence and employs a lightweight sequential position encoder to learn their embeddings in an end-to-end manner. To regularize SeqPE's embedding space, we introduce two complementary objectives: a contrastive objective that aligns embedding distances with a predefined position-distance function, and a knowledge distillation loss that anchors out-of-distribution position embeddings to in-distribution teacher representations, further enhancing extrapolation performance. Experiments across language modeling, long-context question answering, and 2D image classification demonstrate that SeqPE not only surpasses strong baselines in perplexity, exact match (EM), and accuracy--particularly under context length extrapolation--but also enables seamless generalization to multi-dimensional inputs without requiring manual architectural redesign. We release our code, data, and checkpoints at https://github.com/ghrua/seqpe.

  • 8 authors
·
Jun 16, 2025 2

ComRoPE: Scalable and Robust Rotary Position Embedding Parameterized by Trainable Commuting Angle Matrices

The Transformer architecture has revolutionized various regions since it was proposed, and its effectiveness largely depends on the ability to encode positional information. Traditional position encoding methods exhibit significant limitations due to lack of robustness and flexibility of position. Therefore, Rotary Positional Encoding (RoPE) was proposed to alleviate these issues, which integrates positional information by rotating the embeddings in the attention mechanism. However, RoPE requires manually defined rotation matrices with limited transformation space, constraining the model's capacity. In this work, we propose ComRoPE, which generalizes RoPE by defining it in terms of trainable commuting angle matrices. Specifically, we demonstrate that pairwise commutativity of these matrices is essential for RoPE to achieve scalability and positional robustness. We formally define the RoPE Equation, which is an essential condition that ensures consistent performance with position offsets. Based on the theoretical analysis, we present two types of trainable commuting angle matrices as sufficient solutions to the RoPE equation, which significantly improve performance, surpassing the current state-of-the-art method by 1.6% at training resolution and 2.9% at higher resolution on the ImageNet-1K dataset. Furthermore, our framework shows versatility in generalizing to existing RoPE formulations and offering new insights for future positional encoding research. To ensure reproducibility, the source code and instructions are available at https://github.com/Longin-Yu/ComRoPE

  • 10 authors
·
Jun 4, 2025

Quamba2: A Robust and Scalable Post-training Quantization Framework for Selective State Space Models

State Space Models (SSMs) are emerging as a compelling alternative to Transformers because of their consistent memory usage and high performance. Despite this, scaling up SSMs on cloud services or limited-resource devices is challenging due to their storage requirements and computational power. To overcome this, quantizing SSMs with low bit-width data formats can reduce model size and benefit from hardware acceleration. As SSMs are prone to quantization-induced errors, recent efforts have focused on optimizing a particular model or bit-width for efficiency without sacrificing performance. However, distinct bit-width configurations are essential for different scenarios, like W4A8 for boosting large-batch decoding speed, and W4A16 for enhancing generation speed in short prompt applications for a single user. To this end, we present Quamba2, compatible with W8A8, W4A8, and W4A16 for both Mamba1 and Mamba2 backbones, addressing the growing demand for SSM deployment on various platforms. Based on the channel order preserving and activation persistence of SSMs, we propose an offline approach to quantize inputs of a linear recurrence in 8-bit by sorting and clustering for input x, combined with a per-state-group quantization for input-dependent parameters B and C. To ensure compute-invariance in the SSM output, we rearrange weights offline according to the clustering sequence. The experiments show that Quamba2-8B outperforms several state-of-the-art SSM quantization methods and delivers 1.3times and 3times speed-ups in the pre-filling and generation stages, respectively, while offering 4times memory reduction with only a 1.6% average accuracy drop. The evaluation on MMLU shows the generalizability and robustness of our framework. The code and quantized models will be released at: https://github.com/enyac-group/Quamba.

LLMs Can Achieve High-quality Simultaneous Machine Translation as Efficiently as Offline

When the complete source sentence is provided, Large Language Models (LLMs) perform excellently in offline machine translation even with a simple prompt "Translate the following sentence from [src lang] into [tgt lang]:". However, in many real scenarios, the source tokens arrive in a streaming manner and simultaneous machine translation (SiMT) is required, then the efficiency and performance of decoder-only LLMs are significantly limited by their auto-regressive nature. To enable LLMs to achieve high-quality SiMT as efficiently as offline translation, we propose a novel paradigm that includes constructing supervised fine-tuning (SFT) data for SiMT, along with new training and inference strategies. To replicate the token input/output stream in SiMT, the source and target tokens are rearranged into an interleaved sequence, separated by special tokens according to varying latency requirements. This enables powerful LLMs to learn read and write operations adaptively, based on varying latency prompts, while still maintaining efficient auto-regressive decoding. Experimental results show that, even with limited SFT data, our approach achieves state-of-the-art performance across various SiMT benchmarks, and preserves the original abilities of offline translation. Moreover, our approach generalizes well to document-level SiMT setting without requiring specific fine-tuning, even beyond the offline translation model.

  • 7 authors
·
Apr 13, 2025

Guess & Sketch: Language Model Guided Transpilation

Maintaining legacy software requires many software and systems engineering hours. Assembly code programs, which demand low-level control over the computer machine state and have no variable names, are particularly difficult for humans to analyze. Existing conventional program translators guarantee correctness, but are hand-engineered for the source and target programming languages in question. Learned transpilation, i.e. automatic translation of code, offers an alternative to manual re-writing and engineering efforts. Automated symbolic program translation approaches guarantee correctness but struggle to scale to longer programs due to the exponentially large search space. Their rigid rule-based systems also limit their expressivity, so they can only reason about a reduced space of programs. Probabilistic neural language models (LMs) produce plausible outputs for every input, but do so at the cost of guaranteed correctness. In this work, we leverage the strengths of LMs and symbolic solvers in a neurosymbolic approach to learned transpilation for assembly code. Assembly code is an appropriate setting for a neurosymbolic approach, since assembly code can be divided into shorter non-branching basic blocks amenable to the use of symbolic methods. Guess & Sketch extracts alignment and confidence information from features of the LM then passes it to a symbolic solver to resolve semantic equivalence of the transpilation input and output. We test Guess & Sketch on three different test sets of assembly transpilation tasks, varying in difficulty, and show that it successfully transpiles 57.6% more examples than GPT-4 and 39.6% more examples than an engineered transpiler. We also share a training and evaluation dataset for this task.

  • 8 authors
·
Sep 25, 2023