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Yifeng Liu

Publications and source records attributed to Yifeng Liu.

At least 19 recordsLinked to original sources
arXiv2026

Fast Weight Attention for Continual Learning

Recurrent fast-weight memories and selective state-space models compress an expanding context into a fixed-size recurrent state, making the state transition an online learning rule. We study this rule under read-after-write autoregressive semantics. For the prefix-prediction objective considered here, the local fast-memory example revealed at step $t$ is the prefix-aligned pair $(\mathbf{x}_t,\mathbf{y}_t)=(\phi(\mathbf{k}_{t-1}),\mathbf{v}_t)$. The common same-step association $(\phi(\mathbf{k}_t),\mathbf{v}_t)$ remains causal, but optimizes a different internal objective. We derive normalized first-order updates for squared-error regression and negative inner-product objectives. The regression family comprises Falcon-1 (a scalar NLMS update), Falcon-2 (its per-column extension), and Falcon-3 (a sliding-window mini-batch update); Falcon-1A/Falcon-2A/Falcon-3A are the corresponding inner-product variants. We provide recurrent, masked-parallel, and chunk-parallel forms, together with numerically stable positive-decay renormalization. Representative variants remain competitive in language modeling and improve length extrapolation on variable-digit addition. This framework separates temporal alignment, plasticity, forgetting, and bounded rehearsal in recurrent sequence models.

cs.LG↗
arXiv2026

Self-Distilled Policy Gradient

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

cs.LG↗
arXiv2026

Unlocking Feature Learning in Gated Delta Networks at Scale

Training and scaling Large Language Models demand enormous computational resources, motivating both efficient sub-quadratic architectures and principled hyperparameter tuning methods. While the Maximal Update Parametrization ($\mu$P) has enabled zero-shot hyperparameter transfer for standard Transformers, its extension to linear models, particularly those with structured state transitions and complicated architectures, remains largely unexplored. By rigorously propagating coordinate-size estimates through the forward pass, gating mechanisms, and recurrent state dynamics, we derive the scaling rules for Gated Delta Network. Experiments on language-model pre-training confirm that our configurations enable stable learning-rate transfer across model widths under both AdamW and SGD, whereas standard parametrization fails to transfer, validating the correctness and practical utility of our analysis.

cs.LG↗
arXiv2026

Mending the Holes: Mitigating Reward Hacking in Reinforcement Learning for Multilingual Translation

Large Language Models (LLMs) have demonstrated remarkable capability in machine translation on high-resource language pairs, yet their performance on low-resource translation still lags behind. Existing post-training methods rely heavily on high-quality parallel data, which are often scarce or unavailable for low-resource languages. In this paper, we introduce WALAR, a reinforcement training method using only monolingual text to elevate LLMs' translation capabilities on massive low-resource languages while retaining their performance on high-resource languages. Our key insight is based on the observation of failure modes (or "holes") in existing source-based multilingual quality estimation (QE) models. Reinforcement learning (RL) using these QE models tends to amplify such holes, resulting in poorer multilingual LLMs. We develop techniques including word alignment and language alignment to mitigate such holes in WALAR's reward for RL training. We continually trained an LLM supporting translation of 101 languages using WALAR. The experiments show that our new model outperforms LLaMAX, one of the strongest open-source multilingual LLMs by a large margin on 1400 language directions on Flores-101 dataset.

cs.CL↗
arXiv2026

Deep Delta Learning

Transformer residual streams evolve through additive updates. Although a sufficiently expressive residual block can represent content replacement, standard architectures do not parameterize reading, comparison, and replacement as an explicit residual operation. We introduce Deep Delta Learning (DDL), a structured residual update that preserves the identity path while enabling target-seeking edits to the residual state. Each layer reads the current state along a learned direction, compares the resulting readout with a learned target, and writes back a gated rank-1 correction along the same direction. Closing the gate recovers the identity map, while fully opening it exactly overwrites the selected residual readout. We instantiate DDL with both scalar and expanded residual states. The expanded formulation provides multiple persistent value channels while keeping attention and MLP computation at the original model width, thereby separating residual-state capacity from backbone compute width. Controlled LLM pretraining experiments show that DDL improves language-modeling quality and average one-shot downstream performance over additive residual baselines in the reported runs, while introducing explicit memory and throughput tradeoffs. These results suggest that depth-wise delta-rule updates provide a useful inductive bias for managing Transformer residual streams.

cs.LG↗
arXiv2025

Group Representational Position Encoding

We present GRAPE (Group Representational Position Encoding), a unified framework for positional encoding based on group actions. GRAPE unifies two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in $\operatorname{SO}(d)$ and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group $\mathrm{GL}$. In Multiplicative GRAPE, a position $n \in \mathbb{Z}$ (or $t \in \mathbb{R}$) acts as $\mathbf{G}(n) = \exp(n \, \omega \, \mathbf{L})$ with a rank-2 skew-symmetric generator $\mathbf{L} \in \mathbb{R}^{d \times d}$, yielding a relative, compositional, norm-preserving map with a closed-form matrix exponential. RoPE is recovered exactly when the $d/2$ planes correspond to canonical coordinate pairs with a log-uniform spectrum. Learned commuting subspaces and compact non-commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at $O(d)$ and $O(r d)$ cost per head, respectively. In Additive GRAPE, additive logits arise from rank-1 (or low-rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Overall, GRAPE provides a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases. Project page: https://github.com/model-architectures/GRAPE.

cs.LG↗
arXiv2025

MARS-M: When Variance Reduction Meets Matrices

Matrix-based preconditioned optimizers, such as Muon, have recently been shown to be more efficient than scalar-based optimizers for training large-scale neural networks, including large language models (LLMs). Recent benchmark studies of LLM pretraining optimizers have demonstrated that variance-reduction techniques such as MARS can substantially speed up training compared with standard optimizers that do not employ variance reduction. In this paper, we introduce MARS-M, a new optimizer that integrates MARS-style variance reduction with Muon. Under standard regularity conditions, we prove that MARS-M converges to a first-order stationary point at a rate of $\tilde{\mathcal{O}}(T^{-1/3})$, improving upon the $\tilde{\mathcal{O}}(T^{-1/4})$ rate attained by Muon. Empirical results on language modeling and computer vision tasks demonstrate that MARS-M consistently yields lower losses and improved performance across various downstream benchmarks. The implementation of MARS-M is available at https://github.com/AGI-Arena/MARS/tree/main/MARS_M.

cs.LG↗
arXiv2025

Robust Layerwise Scaling Rules by Proper Weight Decay Tuning

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization ($\mu$P) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading $\mu$P transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as $\sqrt{\eta/\lambda}$ with an approximately invariant shape; under width scaling $d$, we observe that the top singular value scales approximately as $\sqrt{\eta/\lambda}\cdot d^{0.75}$. Combining this observation with the $\mu$P learning-rate rule $\eta_2\propto d^{-1}$ for matrix-like parameters implies an empirical weight-decay scaling rule $\lambda_2\propto \sqrt{d}$ that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at $\eta_1=\Theta_d(1)$ and $\lambda_1=0$, this yields \emph{zero-shot} transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend $\mu$P beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

cs.LG↗
arXiv2025

Developing a ChatGPT-Based Tool for Physics Experiment Teaching

This paper examines how advanced AI assistants can help physics educators create practical teaching tools without specialized programming skills. Using the square-wave synthesis experiment as a case, we target common obstacles in laboratory instruction-complex setup, unstable signals, and limited class time-and show how AI-assisted development can shift attention from wiring and calibration to core physical ideas. To address this need, we guided an AI assistant through iterative prompts to generate a clean, runnable program that visualizes square-wave synthesis from its component sine waves. The tool supports step-by-step construction of the waveform, adjustable parameters (amplitude, frequency, and phase), and immediate comparison with an ideal reference using simple error measures. We packaged the result as a standalone application so it runs reliably on standard classroom computers, enabling pre-lab demonstrations and interactive exploration that reduce procedural friction and highlight underlying concepts. Building on this proof of concept, we argue the same workflow extends to other topics-such as simple harmonic motion and optical interference-where adjustable parameters and real-time visualization deepen understanding. We conclude that AI-assisted co-design can improve teaching efficiency, enhance student engagement with foundational principles, and provide a scalable path for developing customizable physics education tools.

physics.ed-ph↗
arXiv2025

A Novel Approach to Differential Privacy with Alpha Divergence

As data-driven technologies advance swiftly, maintaining strong privacy measures becomes progressively difficult. Conventional $(\epsilon, \delta)$-differential privacy, while prevalent, exhibits limited adaptability for many applications. To mitigate these constraints, we present alpha differential privacy (ADP), an innovative privacy framework grounded in alpha divergence, which provides a more flexible assessment of privacy consumption. This study delineates the theoretical underpinnings of ADP and contrasts its performance with competing privacy frameworks across many scenarios. Empirical assessments demonstrate that ADP offers enhanced privacy guarantees in small to moderate iteration contexts, particularly where severe privacy requirements are necessary. The suggested method markedly improves privacy-preserving methods, providing a flexible solution for contemporary data analysis issues in a data-centric environment.

cs.CR↗
arXiv2025

On the Design of KL-Regularized Policy Gradient Algorithms for LLM Reasoning

Policy gradient algorithms have been successfully applied to enhance the reasoning capabilities of large language models (LLMs). KL regularization is ubiquitous, yet the design surface, choice of KL direction (forward vs. reverse), normalization (normalized vs. unnormalized), and estimator ($k_1/k_2/k_3$), is scattered across the literature and often intertwined with off-policy estimation. We ask a focused question: under the off-policy setting, what weighting is required for each KL variant so that the surrogate we optimize yields the exact gradient of the intended KL-regularized objective? We answer this with a compact, unified derivation we call the Regularized Policy Gradient (RPG) view. RPG (i) unifies normalized and unnormalized KL variants and shows that the widely-used $k_3$ penalty is exactly the unnormalized KL; (ii) specifies conditions under which REINFORCE-style losses with stop-gradient are gradient-equivalent to fully differentiable surrogates; (iii) identifies and corrects an off-policy importance-weighting mismatch in GRPO's KL term; and (iv) introduces RPG-Style Clip, a clipped-importance-sampling step within RPG-REINFORCE that enables stable, off-policy policy-gradient training at scale. On mathematical reasoning benchmarks (AIME24, AIME25), RPG-REINFORCE with RPG-Style Clip improves accuracy by up to $+6$ absolute percentage points over DAPO. We extend our experiments to 8K context length, and RPG-REINFORCE with RPG-Style Clip achieves 52% accuracy on AIME25, surpassing the official Qwen3-4B-Instruct model (47%). Notably, RPG is a stable and scalable RL algorithm for LLM reasoning, realized via (a) a KL-correct objective, (b) clipped importance sampling, and (c) an iterative reference-policy update scheme. Project Page: https://github.com/complex-reasoning/RPG.

cs.LG↗
arXiv2025

R-PRM: Reasoning-Driven Process Reward Modeling

Large language models (LLMs) inevitably make mistakes when performing step-by-step mathematical reasoning. Process Reward Models (PRMs) have emerged as a promising solution by evaluating each reasoning step. However, existing PRMs typically output evaluation scores directly, limiting both learning efficiency and evaluation accuracy, which is further exacerbated by the scarcity of annotated data. To address these issues, we propose Reasoning-Driven Process Reward Modeling (R-PRM). First, we leverage stronger LLMs to generate seed data from limited annotations, effectively bootstrapping our model's reasoning capabilities and enabling comprehensive step-by-step evaluation. Second, we further enhance performance through preference optimization, without requiring additional annotated data. Third, we introduce inference-time scaling to fully harness the model's reasoning potential. Extensive experiments demonstrate R-PRM's effectiveness: on ProcessBench and PRMBench, it surpasses strong baselines by 11.9 and 8.5 points in F1 scores, respectively. When applied to guide mathematical reasoning, R-PRM achieves consistent accuracy improvements of over 8.5 points across six challenging datasets. Further analysis reveals that R-PRM exhibits more comprehensive evaluation and stronger generalization capabilities, thereby highlighting its significant potential.

cs.CL↗
arXiv2025

A Survey of Zero-Knowledge Proof Based Verifiable Machine Learning

Machine learning is increasingly deployed through outsourced and cloud-based pipelines, which improve accessibility but also raise concerns about computational integrity, data privacy, and model confidentiality. Zero-knowledge proofs (ZKPs) provide a compelling foundation for verifiable machine learning because they allow one party to certify that a training, testing, or inference result was produced by the claimed computation without revealing sensitive data or proprietary model parameters. Despite rapid progress in zero-knowledge machine learning (ZKML), the literature remains fragmented across different cryptographic settings, ML tasks, and system objectives. This survey presents a comprehensive review of ZKML research published from June 2017 to August 2025. We first introduce the basic ZKP formulations underlying ZKML and organize existing studies into three core tasks: verifiable training, verifiable testing, and verifiable inference. We then synthesize representative systems, compare their design choices, and analyze the main implementation bottlenecks, including limited circuit expressiveness, high proving cost, and deployment complexity. In addition, we summarize major techniques for improving generality and efficiency, review emerging commercial efforts, and discuss promising future directions. By consolidating the design space of ZKML, this survey aims to provide a structured reference for researchers and practitioners working on trustworthy and privacy-preserving machine learning.

cs.CR↗
arXiv2025

Kimi k1.5: Scaling Reinforcement Learning with LLMs

Language model pretraining with next token prediction has proved effective for scaling compute but is limited to the amount of available training data. Scaling reinforcement learning (RL) unlocks a new axis for the continued improvement of artificial intelligence, with the promise that large language models (LLMs) can scale their training data by learning to explore with rewards. However, prior published work has not produced competitive results. In light of this, we report on the training practice of Kimi k1.5, our latest multi-modal LLM trained with RL, including its RL training techniques, multi-modal data recipes, and infrastructure optimization. Long context scaling and improved policy optimization methods are key ingredients of our approach, which establishes a simplistic, effective RL framework without relying on more complex techniques such as Monte Carlo tree search, value functions, and process reward models. Notably, our system achieves state-of-the-art reasoning performance across multiple benchmarks and modalities -- e.g., 77.5 on AIME, 96.2 on MATH 500, 94-th percentile on Codeforces, 74.9 on MathVista -- matching OpenAI's o1. Moreover, we present effective long2short methods that use long-CoT techniques to improve short-CoT models, yielding state-of-the-art short-CoT reasoning results -- e.g., 60.8 on AIME, 94.6 on MATH500, 47.3 on LiveCodeBench -- outperforming existing short-CoT models such as GPT-4o and Claude Sonnet 3.5 by a large margin (up to +550%).

cs.AI↗
arXiv2025

Tensor Product Attention Is All You Need

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with Rotary Position Embedding (RoPE), TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducT ATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at decoding stage enables processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models. Project Page: https://github.com/tensorgi/TPA.

cs.CL↗
arXiv2024

Towards Simple and Provable Parameter-Free Adaptive Gradient Methods

Optimization algorithms such as AdaGrad and Adam have significantly advanced the training of deep models by dynamically adjusting the learning rate during the optimization process. However, ad-hoc tuning of learning rates poses a challenge and leads to inefficiencies in practice. To address this issue, recent research has focused on developing ``parameter-free'' algorithms that operate effectively without the need for learning rate tuning. Despite these efforts, existing parameter-free variants of AdaGrad and Adam tend to be overly complex and/or lack formal convergence guarantees. In this paper, we present AdaGrad++ and Adam++, novel and simple parameter-free variants of AdaGrad and Adam with convergence guarantees. We prove that AdaGrad++ achieves comparable convergence rates to AdaGrad in convex optimization without predefined learning rate assumptions. Similarly, Adam++ matches the convergence rate of Adam without relying on any conditions on the learning rates. Experimental results across various deep learning tasks validate the competitive performance of Adam++.

cs.LG↗