Zixi Li, Youzhen Li
Learning-rate steps are usually treated as hyperparameters. This paper isolates a local beliefspace calculation: when an update is modeled as a projected forward step on the probability simplex, admissibility means contractivity in the natural KL/Bregman geometry. Under this model, the upper bound of an admissible step is not a tuning slogan but a formula.
Zixi Li
We present TreeGPT, an attention-free neural architecture that explores the potential of pure TreeFFN encoder-decoder design for structured reasoning tasks. Unlike traditional transformer approaches that rely on attention mechanisms, TreeGPT employs bidirectional TreeFFN components that process sequences through adjacent connections in parallel, aiming to achieve computational efficiency while maintaining reasoning capabilities. Our approach centers on a TreeFFN Encoder-Decoder mechanism: $$\text{Encoder TreeFFN (L} \rightarrow \text{R)} + \text{Decoder TreeFFN (R} \leftarrow \text{L)} \rightarrow \text{Parallel Processing}$$ where the encoder processes left-to-right dependencies while the decoder handles right-to-left patterns, both using simple neighbor-to-neighbor connections. This design eliminates attention computation while maintaining sequence modeling capabilities. We evaluate our approach on the ARC Prize 2025 dataset, where TreeGPT achieves 99\% validation accuracy using 3.16M parameters. The model converges within 1500 training steps and demonstrates 100\% token-level accuracy on selected evaluation samples. Our preliminary results suggest that for certain structured reasoning tasks, specialized TreeFFN architectures may offer advantages over attention-based approaches. While these findings are encouraging, we acknowledge that further investigation across diverse tasks and datasets would be valuable to establish the broader applicability of attention-free designs.
Yuhui Sun, Xiyao Wang, Zixi Li et al.
Large language models (LLMs) demonstrate strong generalization across a wide range of language tasks, but often generate outputs that misalign with human preferences. Reinforcement Learning from Human Feedback (RLHF) addresses this by optimizing models toward human preferences using a learned reward function and reinforcement learning, yielding improved alignment but suffering from high computational cost and instability. Direct Preference Optimization (DPO) simplifies the process by treating alignment as a classification task over binary preference pairs, reducing training overhead while achieving competitive performance. However, it assumes fixed, single-dimensional preferences and only supports pairwise supervision. To address these limitations, we propose Multi-Preference Lambda-weighted Listwise DPO, which allows the model to learn from more detailed human feedback and flexibly balance multiple goals such as helpfulness, honesty, and fluency. Our method models full-ranked preference distributions rather than binary comparisons, enabling more informative learning signals. The lambda vector controls the relative importance of different alignment goals, allowing the model to generalize across diverse human objectives. During inference, lambda can be adjusted without retraining, providing controllable alignment behavior for downstream use. We also introduce a learned scheduler that dynamically samples performant lambda configurations to improve robustness. Notably, our method requires only 20GB of GPU memory for training, making it suitable for compute-constrained settings such as academic labs, educational tools, or on-device assistants. Experiments on 1B-2B scale models show that our method consistently outperforms standard DPO on alignment benchmarks while enabling efficient, controllable, and fine-grained adaptation suitable for real-world deployment.
Zixi Li
What is reasoning? This question has driven centuries of philosophical inquiry, from Aristotle's syllogisms to modern computational complexity theory. In the age of large language models achieving superhuman performance on benchmarks like GSM8K (95\% accuracy) and HumanEval (90\% pass@1), we must ask: have these systems learned to \emph{reason}, or have they learned to \emph{pattern-match over reasoning traces}? This paper argues for a specific answer: \textbf{reasoning is iterative operator application in state spaces, converging to fixed points}. This definition is not merely philosophical -- it has concrete architectural implications that explain both the failures of current systems and the path to genuine reasoning capabilities. Our investigation begins with a puzzle (OpenXOR), progresses through theory (OpenOperator), and culminates in a working solution (OpenLM) that achieves 76\% accuracy where state-of-the-art LLMs achieve 0\%. This is not about criticizing existing systems, but about \emph{understanding what reasoning requires} and \emph{building architectures that provide it}.
Zixi Li
We propose the \textbf{Asterisk Operator} ($\ast$-operator), a novel unified framework for abstract reasoning based on Adjacency-Structured Parallel Propagation (ASPP). The operator formalizes structured reasoning tasks as local, parallel state evolution processes guided by implicit relational graphs. We prove that the $\ast$-operator maintains local computational constraints while achieving global reasoning capabilities, providing an efficient and convergent computational paradigm for abstract reasoning problems. Through rigorous mathematical analysis and comprehensive experiments on ARC2 challenges and Conway's Game of Life, we demonstrate the operator's universality, convergence properties, and superior performance. Our innovative Embedding-Asterisk distillation method achieves 100\% accuracy on ARC2 validation with only 6M parameters, representing a significant breakthrough in neural-symbolic reasoning. \textbf{Keywords:} Abstract Reasoning, Adjacency Structure, Parallel Propagation, Asterisk Operator, Convergence, Universal Approximation
Zixi Li
We introduce Pointer, a novel architecture that achieves linear $O(NK)$ complexity for long-range sequence modeling while maintaining superior performance without requiring pre-training. Unlike standard attention mechanisms that compute $O(N^2)$ pairwise interactions, our approach uses layer-wise pointer chaining where each layer's pointer selection depends on previous layer's pointer positions, creating explicit long-distance connections through pointer chains. We demonstrate that this architecture achieves $2$--$10\times$ speedup on long sequences compared to standard transformers, maintains $>95\%$ accuracy on copy tasks at distances up to 2048 tokens, and learns interpretable pointer patterns that reveal structured dependency modeling. Our experiments on efficiency benchmarks, long-range dependency tasks, and interpretability analysis show that Pointer offers a compelling alternative to attention mechanisms for scenarios requiring efficient long-range modeling without pre-training dependencies.