Why the Valuable Capabilities of LLMs Are Precisely the Unexplainable Ones

This paper proposes and argues for a counterintuitive thesis: the truly valuable capabilities of large language models (LLMs) reside precisely in the part that cannot be fully captured by human-readable discrete rules. The core argument is a proof by contradiction via expert system equivalence: if the full capabilities of an LLM could be described by a complete set of human-readable rules, then that rule set would be functionally equivalent to an expert system; but expert systems have been historically and empirically demonstrated to be strictly weaker than LLMs; therefore, a contradiction arises -- the capabilities of LLMs that exceed those of expert systems are exactly the capabilities that cannot be rule-encoded. This thesis is further supported by the Chinese philosophical concept of Wu (sudden insight through practice), the historical failure of expert systems, and a structural mismatch between human cognitive tools and complex systems. The paper discusses implications for interpretability research, AI safety, and scientific epistemology.

Via Negativa for AI Alignment: Why Negative Constraints Are Structurally Superior to Positive Preferences

Recent empirical results have demonstrated that training large language models (LLMs) with negative-only feedback can match or exceed standard reinforcement learning from human feedback (RLHF). Negative Sample Reinforcement achieves parity with PPO on mathematical reasoning; Distributional Dispreference Optimization trains effectively using only dispreferred samples; and Constitutional AI outperforms pure RLHF on harmlessness benchmarks. Yet no unified theoretical account explains why negative signals are so effective. This paper proposes such an account: positive preferences and negative constraints are structurally asymmetric. Positive preferences ("which is better") encode continuously coupled, context-dependent human values that cannot be exhaustively specified -- leading models to learn surface correlates such as agreement with the user (sycophancy). Negative constraints ("what is wrong") encode discrete, finite, independently verifiable prohibitions that can converge to a stable boundary. This asymmetry -- rooted in Popper's falsification logic and the epistemology of negative knowledge -- explains both the sycophancy failure of preference-based RLHF and the surprising effectiveness of negative-signal methods. We argue that alignment research should shift its center of gravity from "learning what humans prefer" to "learning what humans reject," and offer testable predictions for this framework.

Continuous Subspace Optimization for Continual Learning

Continual learning aims to learn multiple tasks sequentially while preserving prior knowledge, but faces the challenge of catastrophic forgetting when acquiring new knowledge. Recently, approaches leveraging pre-trained models have gained increasing popularity to mitigate this issue, due to the strong generalization ability of foundation models. To adjust pre-trained models for new tasks, existing methods usually employ low-rank adaptation, which restricts parameter updates to a fixed low-rank subspace. However, constraining the optimization space inherently compromises the model's learning capacity, resulting in inferior performance. To address the limitation, we propose Continuous Subspace Optimization for Continual Learning (CoSO) to fine-tune the model in a series of subspaces rather than a single one. These sequential subspaces are dynamically determined through the singular value decomposition of gradients. CoSO updates the model by projecting gradients into these subspaces, ensuring memory-efficient optimization. To mitigate forgetting, the optimization subspaces of each task are set to be orthogonal to the historical task subspace. During task learning, CoSO maintains a task-specific component that captures the critical update directions associated with the current task. Upon completing a task, this component is used to update the historical task subspace, laying the groundwork for subsequent learning. Extensive experiments on multiple datasets demonstrate that CoSO significantly outperforms state-of-the-art methods, especially in challenging scenarios with long task sequences.