Yiyang Jia

Bochen Lyu, Yiyang Jia, Xiaohao Cai et al.

Safety alignment in large language models (LLMs) is fragile in part because it is often shallow: fine-tuning mainly reshapes the model's behavior near the first few output tokens. We argue that this phenomenon can be understood through autoregressive consistency, the tendency of next-token prediction to preserve and extend the current response trajectory consistently. By analyzing the learning dynamics of safety alignment, we show that autoregressive consistency can concentrate alignment updates on early tokens, offering a mechanistic explanation for shallow safety alignment. The same mechanism also predicts a broader class of attacks on LLMs: attacks that induce harmful continuation states at arbitrary positions in the output trajectory. As a concrete example, we introduce random insertion attack, which inserts a short harmful span into an otherwise safe refusal trajectory and exploits autoregressive consistency to sustain the resulting harmful branch, thereby bypassing safety alignment. Notably, a short harmful span can redirect the generation to be harmful even after a long refusal prefix, highlighting autoregressive consistency as a potential broader failure mechanism. This suggests that safety alignment should also break harmful autoregressive consistency throughout the output trajectory. We therefore propose adversarial safety alignment, an initial framework based on worst-case harmful continuation states, and instantiate it with random worst-insertion training. Overall, our results suggest that autoregressive consistency should be treated as a central consideration in both safety alignment and attack design.

Luciano Floridi, Yiyang Jia, Fernando Tohmé

This paper presents a formal, categorical framework for analysing how humans and large language models (LLMs) transform content into truth-evaluated propositions about a state space of possible worlds W , in order to argue that LLMs do not solve but circumvent the symbol grounding problem.

Yiyang Jia, Guohong Peng, Zheng Yang et al.

In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning. For the first three topics, we primarily review research in the past five years, updating and expanding on the previous survey by Shiebler et al.. The fourth topic, which delves into higher category theory, particularly topos theory, is surveyed for the first time in this paper. In certain machine learning methods, the compositionality of functors plays a vital role, prompting the development of specific categorical frameworks. However, when considering how the global properties of a network reflect in local structures and how geometric properties are expressed with logic, the topos structure becomes particularly significant and profound.

Yiyang Jia, Chengxu Zhou

Control policies in deep reinforcement learning are often implemented with fixed-capacity multilayer perceptrons trained by backpropagation, which lack structural plasticity and depend on global error signals. This paper introduces the Self-Motivated Growing Neural Network (SMGrNN), a controller whose topology evolves online through a local Structural Plasticity Module (SPM). The SPM monitors neuron activations and edge-wise weight update statistics over short temporal windows and uses these signals to trigger neuron insertion and pruning, while synaptic weights are updated by a standard gradient-based optimizer. This allows network capacity to be regulated during learning without manual architectural tuning. SMGrNN is evaluated on control benchmarks via policy distillation. Compared with multilayer perceptron baselines, it achieves similar or higher returns, lower variance, and task-appropriate network sizes. Ablation studies with growth disabled and growth-only variants isolate the role of structural plasticity, showing that adaptive topology improves reward stability. The local and modular design of SPM enables future integration of a Hebbian plasticity module and spike-timing-dependent plasticity, so that SMGrNN can support both artificial and spiking neural implementations driven by local rules.

Bochen Lyu, Yiyang Jia, Xiaohao Cai et al.

Transformers can acquire Chain-of-Thought (CoT) capabilities to solve complex reasoning tasks through fine-tuning. Reinforcement learning (RL) and supervised fine-tuning (SFT) are two primary approaches to this end, yet their underlying mechanisms and differences remain theoretically unclear. In this work, we examine these aspects specifically for learning $k$-sparse Boolean functions with a one-layer transformer and intermediate supervision that is akin to CoT. In particular, we consider $k$-sparse Boolean functions that can be recursively decomposed into fixed 2-sparse Boolean functions. We analyze the learning dynamics of fine-tuning the transformer via either RL or SFT with CoT to identify sufficient conditions for it to provably learn these functions. We verify that these conditions hold for three basic examples, including $k$-PARITY, $k$-AND, and $k$-OR, thus demonstrating the learnability of both approaches. Notably, we reveal that RL and SFT exhibit distinct learning behaviors: RL learns the whole CoT chain simultaneously, whereas SFT learns the CoT chain step-by-step. Overall, our findings provide theoretical insights into the underlying mechanisms of RL and SFT as well as how they differ in triggering the CoT capabilities of transformers.

Yiyang Jia, Zheng Wei, Zheng Yang et al.

Understanding the complex and stochastic nature of Gene Regulatory Networks (GRNs) remains a central challenge in systems biology. Existing modeling paradigms often struggle to effectively capture the intricate, multi-factor regulatory logic and to rigorously manage the dual uncertainties of network structure and kinetic parameters. In response, this work introduces the Probabilistic Categorical GRN(PC-GRN) framework. It is a novel theoretical approach founded on the synergistic integration of three core methodologies. Firstly, category theory provides a formal language for the modularity and composition of regulatory pathways. Secondly, Bayesian Typed Petri Nets (BTPNs) serve as an interpretable,mechanistic substrate for modeling stochastic cellular processes, with kinetic parameters themselves represented as probability distributions. The central innovation of PC-GRN is its end-to-end generative Bayesian inference engine, which learns a full posterior distribution over BTPN models (P (G, Θ|D)) directly from data. This is achieved by the novel interplay of a GFlowNet, which learns a policy to sample network topologies, and a HyperNetwork, which performs amortized inference to predict their corresponding parameter distributions. The resulting framework provides a mathematically rigorous, biologically interpretable, and uncertainty-aware representation of GRNs, advancing predictive modeling and systems-level analysis.