Lambda Cognition

Conquering LLM Hallucination with Platonic Coding

Fri, 06 Feb 2026 00:00:00 +0000

The Hallucination Problem

Large Language Models have revolutionized software development, enabling developers to generate code, debug systems, and explore solutions at unprecedented speed. Yet, anyone who has worked extensively with AI coding assistants knows the persistent frustration: agents generate plausible-looking code that violates explicit requirements, introduce inconsistencies across sessions, and drift from the original intent over time. This phenomenon, often called “hallucination” in the context of LLMs, is not merely a technical glitch. It is a fundamental consequence of how meaning is negotiated in current AI-assisted workflows.

In traditional prompt engineering, meaning lives in the latent space of neural networks. Constraints are persuasive rather than binding. Violations are common, and correction is conversational. The system negotiates intent through examples, clarifications, and repeated iterations, but meaning remains unstable. What was clear yesterday becomes ambiguous today. What was specified explicitly gets reinterpreted implicitly. The agent appears productive, but coherence degrades over time.

This is not a problem of better prompting or more sophisticated models. It is a problem of form, or rather, the absence of explicit form. In most AI-assisted workflows, the ideal structure of the software system remains implicit. Developers and agents negotiate it repeatedly, but the negotiation never closes. The world remains open, meaning drifts, and hallucinations emerge as the natural consequence of an unconstrained semantic space.

What is Platonic Coding

Platonic Coding is a coding style grounded in a radical but simple belief:

Every software system has an ideal form, whether or not we choose to name it.

This form consists of what entities exist, what relationships are allowed, what transformations are valid, and what invariants must never be violated. Platonic Coding makes this form explicit. Specifications are not annotations on code, they are the source of truth. Code, conversations, and agent behaviors are all instantiations of an abstract structure that already exists.

The name “Platonic” reflects this philosophy: the program is a shadow; the spec is the form. Just as Plato argued that physical objects are imperfect reflections of ideal Forms, Platonic Coding treats code as an instantiation of an explicit specification. The specification defines what must be true, not what might be acceptable.

How Platonic Coding Conquers Hallucination

Hallucination in LLMs arises from semantic drift, the gradual divergence between intended meaning and actual output. In prompt engineering, this drift is inevitable because meaning is contextual, unstable, and implicit. Platonic Coding addresses this at its root by closing the semantic world.

Specs as Laws

In Platonic Coding, specifications function as abstract laws. RFCs act as axioms. Terminology defines the allowed symbols of thought. Invariants constrain all valid outputs. Status transitions encode time and evolution.

Once declared, these laws apply equally to humans, coding agents, automated generators, and validators. A system that violates its own spec is not “confused”, it is invalid. This is fundamentally different from prompt engineering, where constraints are persuasive and violations are common.

Language as Interface, Not Meaning

Natural language is flexible, expressive, and dangerous. Platonic Coding treats language as a projection layer, a reference mechanism, a human-friendly syntax, but never as the carrier of meaning itself.

Meaning lives in defined terms, canonical documents, stable references, and machine-checkable constraints. When agents converse, they are not negotiating intent, they are navigating a formally defined space. This eliminates the ambiguity that gives rise to hallucinations.

Agents as Form Instantiators

In Platonic Coding, agents are not collaborators with opinions. They are interpreters of specs, executors of lawful transformations, materializers of abstract forms. Creativity is permitted only where the law allows degrees of freedom.

If an agent output violates an invariant, the response is not refinement, it is rejection. This structural correction prevents the accumulation of errors that lead to hallucination.

Explicit Time and Memory

Intelligence that forgets is not intelligence. It is improvisation. Platonic Coding encodes time explicitly through change history, RFC lifecycle states (Draft, Active, Deprecated, Superseded), and traceable evolution of concepts.

Nothing important is allowed to disappear silently. This enables systems that can grow without collapsing under their own ambiguity. The persistent, institutional memory prevents the semantic drift that causes hallucinations.

The Five-Phase Workflow

Platonic Coding operationalizes this philosophy through a five-phase, closed-world workflow. Meaning is progressively constrained, materialized, and verified as the system moves from abstract intent to concrete code.

Phase 0: Conceptual Design & Requirements Elicitation

Clarify problem space, goals, constraints, and invariants. Explore domain knowledge and prior art. Identify core abstractions and system boundaries. Resolve ambiguity before formalization.

Phase 1: Design Specifications (RFC World Construction)

Formalize requirements as RFCs. Define entities, relations, invariants, and constraints. Establish terminology, taxonomy, and evolution rules. Create a closed, legally-defined specification space.

Phase 2: Implementation Guide (Spec → Concrete Design)

Translate RFCs into implementation-ready architecture. Fix language, framework, module boundaries, and APIs. Make all design decisions explicit and traceable. Validate against RFCs, no new meaning allowed.

Phase 3: Code Implementation (Mechanical Realization)

Write code strictly following guides and RFCs. No speculative design or undocumented behavior. Code is a realization, not a source of truth.

Phase 4: Spec Compliance Review (Reality Check)

Verify code against RFCs and implementation guides. Detect gaps, drift, and contradictions. Identify specs without code and code without specs. Produce traceable compliance reports.

This workflow ensures that meaning flows from explicit specifications through implementation guides to code, with validation at each stage. Hallucination becomes impossible because there is no room for semantic drift, every step is constrained by the laws defined in Phase 1.

Platonic Coding vs. Prompt Engineering

The contrast between Platonic Coding and prompt engineering illuminates why one conquers hallucination while the other perpetuates it.

Ontology: Prompt engineering treats the prompt as the primary object, with meaning that is contextual and unstable. Platonic Coding treats the spec as primary, with meaning that is explicit and persistent.

Authority: In prompt engineering, constraints are persuasive and violations are common. In Platonic Coding, constraints are binding and violations are detectable.

Semantics: Prompt engineering stores semantics in latent space, where drift is expected and reproducibility is fragile. Platonic Coding stores semantics in definitions, where drift is a bug and reproducibility is guaranteed by construction.

Time: Prompt engineering resets meaning with each session, relying on heuristic memory. Platonic Coding maintains explicit history with institutional memory.

The one-line contrast captures it perfectly: Prompt engineering asks how to phrase, while Platonic Coding declares what must be true.

Why This Matters

Prompt engineering scales effort. Platonic Coding scales understanding, coherence, multi-agent collaboration, and long-lived intelligence. By turning intent into law and law into structure, Platonic Coding enables systems that do not merely respond, they endure.

The conquest of hallucination is not about stricter rules or better prompts. It is about respecting the fact that software, like mathematics, already has a form, whether we choose to see it or not. We do not ask agents to guess what we mean. We define what must be true. And then we build.

In an era where AI agents are becoming integral to software development, Platonic Coding offers a path forward that preserves the creativity and exploration we value while eliminating the semantic drift and inconsistency we cannot tolerate. It is a way to close the world so that intelligence can accumulate, and so that hallucinations become impossible by construction.

Platonic Coding Skills Repository: https://github.com/caesar0301/platonic-coding-skills

For the full philosophical foundation, see the Platonic Coding Manifesto.

Composable Intelligence

Wed, 05 Nov 2025 00:00:00 +0000

From a physical point of view, everything in the world, from stones to brains, is composed of material units such as quarks and atoms. This perspective inspires us to consider intelligence from a material basis as well. In this article, I present a novel perspective on understanding intelligence, drawn from observations of biological intelligence and the limitations of neural network based AI. I call it Composable Intelligence, a new way of thinking about how intelligence might evolve or be continuously constructed from a hierarchical point of view, applicable to both biological and artificial systems.

The Framework

Building on this idea, a new framework, illustrated in the figure above, called Topological Coupling Meta Learning (TCML), is proposed to guide the engineering of such a practical system. From the bottom up, there are four foundational layers that together build intelligence:

Representative Carriers: The physical and atomic representations of concepts, facts, reasoning cues, and so on. Although they may take different forms in different intelligent systems, they must exist concretely and possess reactive capabilities, interacting with each other or with other components of the system.
Reactive Couplings: The underlying mechanism of continual and evolving learning. New knowledge or experience emerges through the construction of new instances or coupling structures. Gradual forgetting occurs through the disappearance or decay of existing couplings. In this sense, reactive coupling should be self-organizing and open ended rather than closed.
Compositional Meta Structures: Stable and reusable units formed from reactive couplings to perform higher level and more complex functions such as self-reflection and memory retention. These structures are observable, measurable, and interferable regarding functionality.
Scaling Topology: A topological structure, such as a graph, with nonlinear scaling ability built upon the meta structures. The entire system grows to be both wide and deep, enabling richer and more integrated forms of intelligence.

Representative Carriers

In Composable Intelligence, we regard intelligence as a physical and objective process, something that like everything else in the world exists within substance. The core and foundation of intelligence are materials, which I call Representative Carriers. These carriers differ across various forms of intelligence: biological neural cells, vector of artificial neural networks, or symbols in expert AI systems. Although we don’t even know everything about underlying machenism of carriers such as biological neurons, it is fundamentally vital to master how to observe, control, and enhance them.

Understanding or designing a controllable representative carrier for a specific form of intelligence is not trivial. However, achieving this is often limited by the SOTA of inspection technologies. Even today, it is far from clear what the actual representative carriers of human brain intelligence are. Are they stored in biochemical materials? Or do they emerge from dynamic activities such as resting and active potential changes? Or perhaps they lie in the connectivity patterns of neural networks?

AI research whether through simulation or imitation provides us, at least theoretically, with a wide range of tools and resources to experiment with different designs of representative carriers. On the other hand, after decades of AI development, we have only gained practical experience with two main forms of representative carriers: symbols in expert AI systems, and embedding vectors in machine learning and modern deep neural networks. We have been blinded by short-term achievements and have ignored some of the core problems that truly deserve attention in the long run.

Reactive Coupling

Built upon representative carriers is a layer that performs Reactive Coupling. This conceptual layer is inspired by biological intelligence, where neurons can form new pathways or even new cells (a.k.a. neuroplasticity) to create memories and neural activities. In an abstract sense, a group of representative carriers together with their surrounding materials constitute a coupling structure that reacts to external stimuli. This fundamental idea challenges the current end-to-end training paradigm of artificial neural network architectures, such as GPT models.

Reactive couplings are pervasive in biological systems and intelligence, yet they remain absent in current artificial intelligent systems. One main reason is that AI development in recent decades has been confined to probabilistic and end-to-end training paradigms. I believe that future artificial general intelligence (AGI) will be constructed upon a well designed, scalable system— much like hardware chips—that exhibits complex macro behaviors emerging from numerous micro structures governed by a limited set of rules. In current stage, these micro structures or rules may be discovered by LLM-driven technologies and then be distilled to form a minimum stable set.

Another important property of reactive couplings is dynamics. They encode specific types of functionality while remaining adaptive to external changes. This forms the foundation of evolution and self-improvement, which is essential for achieving Gödel machines with self-reference.

Meta Structures and Topology

Recently, compositional generalization has attracted growing attention in the research community as a way to address the limitations of LLMs in reasoning and memorization. In the TCML framework, we propose a similar approach through compositional meta structures, which consist of groups of reactive couplings that are functionally independent.

A fascinating example of meta structures can be found in the cerebral cortex. In human brain research, functional maps of cortical areas have been drawn using fMRI and cognitive experiments. These meta structures can be probed and measured through high level methods, and can be reused to explore a vast space of topological configurations.

Under this design, we have gained another simension of scaling, i.e., topological scaling, beyond current parameter and data scalings that enpowers LLM a lot. From structural view, parameter scaling of deep neural networks is simply to increase the number of deep layers with homoteneous structure. Thus we put this as linear scaling technologies. It is also like data scaling. But with topological scaling, we step into a new era with non-linear scaling space. The scaling power is enhanced by the combination of richness of reactive coupling, dynamics of meta-structures and unlimited scaling of topological changes.

Under this design, we gain an additional dimension of scaling, i.e., topological scaling, beyond the parameter and data scaling that currently empower LLMs. From a structural perspective, parameter scaling in deep neural networks simply increases the number of layers with homogeneous architectures, which can be considered a form of linear scaling. Data scaling follows a similar principle. In contrast, topological scaling opens a new era of nonlinear scaling, where the system’s capacity grows through the richness of reactive couplings, the dynamics of meta structures, and the boundless possibilities of topological transformation.

In future articles, I will show how to design such a TCML-like system using neurosymbolic technology.

NOTE: This artical is fully written by Dr Xiaming Chen and grammarly validated and polished by ChatGPT.

Towards cognitive agentic system

Sat, 30 Aug 2025 00:00:00 +0000

Project COGENTS (COGnitive aGENTic System) is trying to build a comprehensive, modular ecosystem for building intelligent, cognitive agent systems. COGENTS provides foundational abstractions, specialized toolkits, intelligent agents, and powerful search & automation capabilities—all designed to work together seamlessly. It combines theoretical foundations with practical implementations.

COGENTS is supported and implemented by multiple interconnected subprojects, each addressing a specific aspect of cognitive agent development.

1. cogents-core

The foundational layer providing core abstractions and essential modules for all COGENTS projects.

Core Abstractions

Agent: Base classes for building custom agents (BaseAgent, BaseGraphicAgent, BaseConversationAgent, BaseResearcher)
Goal Management: Goal decomposition, conflict detection, and dynamic replanning (Goalith)
Tool Management: Centralized tool registry, execution engine, and repository system (Toolify)
Memory Management: Persistent memory capabilities (under development)
Orchestration: Global orchestration system (under development)

Key Features

Multi-Model LLM Support: OpenAI, Google GenAI, Ollama, LlamaCPP with dynamic routing
Advanced Routing: Complexity-based and self-assessment routing strategies
Observability: Built-in token tracking and Opik tracing integration
Message Bus: Inter-agent communication system
Extensible Design: Easy to add new providers and capabilities

pip install -U cogents-core

Use Cases: Building custom agents, goal-oriented planning, tool integration, LLM management

2. cogents-smith

Complete web intelligence and automation framework: extensive toolkit ecosystem, production-ready agents, multi-engine search, browser automation, and structured data extraction.

Core Capabilities

Multi-Engine Web Search: Simultaneous search across 9+ engines (Tavily, DuckDuckGo, Google AI, SearXNG, Brave, Baidu, WeChat)
Deep Research Agent: Autonomous research with iterative query refinement and source aggregation
Browser Automation: Intelligent browser control with natural language instructions
Structured Data Extraction: Extract data using Pydantic models and YAML-based schema parser
LangGraph Workflows: Advanced agent orchestration with state management

Toolkit Ecosystem (18 Specialized Toolkits in 10 Semantic Groups)

Academic Research: arXiv integration for paper discovery and analysis
Development Tools: Bash, file editing, GitHub, Python execution
Media Processing: Image analysis, video processing, audio transcription
Information Retrieval: Wikipedia, web search, knowledge extraction
Data Management: Tabular data, memory systems, document handling
Communication: Gmail integration
Human Interaction: User communication and feedback collection

Production-Ready Agents

Askura Agent: Dynamic conversational agent for structured information collection
Seekra Agent: Deep research agent for comprehensive topic investigation and report generation

Architecture Features

Semantic Organization: Intuitive grouping for easy discovery
Lazy Loading: Load only what you need
Async-First Design: High-performance concurrent operations
Error Resilience: Graceful handling of missing dependencies

pip install -U cogents-smith

Use Cases: Rapid agent development, conversational data collection, deep research, market intelligence, web data extraction, multi-modal processing

3. cogents-browser-use

AI-powered browser automation adapted from browser-use on the COGENTS stack.

Features

Natural language browser control
Intelligent web navigation
Automated interaction with web elements
Built on COGENTS core abstractions
Support for headless and headed modes

pip install -U cogents-browser-use

Use Cases: Web scraping, automated testing, data extraction, web interaction automation

4. wizsearch

Unified Python library for searching across multiple search engines with a consistent interface.

Features

Multiple Search Engines: Baidu, Bing, Brave, DuckDuckGo, Google, Google AI, SearxNG, Tavily, WeChat
Unified Interface: Single API with consistent SearchResult format
Multi-Engine Aggregation: Concurrent searches with round-robin result merging
Page Crawling: Built-in web page content extraction using Crawl4AI
Semantic Search: Optional vector-based semantic search with local storage
Full Async/Await Support: High-performance asynchronous operations

pip install -U wizsearch

Use Cases: Multi-source search, web content aggregation, semantic search, research automation

Additional Resources

DeepWiki Documentation:
- cogents-core
- cogents-smith
Philosophy: Multi-Agent Systems Talk
🌟 Acknowledgments

COGENTS builds upon and integrates with several excellent projects:

Tencent Youtu-agent for toolkit integration
browser-use for browser automation foundations
LangGraph for workflow orchestration
The open-source community for continuous inspiration and support

Data & AI 技术趋势 2025

Fri, 21 Feb 2025 00:00:00 +0000

背景

人类社会历史是螺旋前进的，科技史亦然。从1950s提出Artificial Intelligence概念至今，AI技术已经经历了多次春、冬季交替演进(AI Winter)。上一代AI技术（1970s-1980s）是基于符号（symbolic）的计算系统，以LispMacine、专家系统、日本第5代计算机系统等为代表。这类技术在知识表示、逻辑推理上有优势，但是不具备模式识别能力。此后基于统计学的MachineLearning复兴（1990s-2000s），虽然彼时AI尚不普遍，但相关的数据统计分析、大数据系统、云计算基础设施，在这一时期并行快速发展。Hinton等人2006年提出“深度学习”概念后，随着AlexNet (2012) 和AlphaGo (2015) 的成功，AI技术逐步从基于浅层统计模型（例如SVM）向深层神经网络（例如CNN）演进；Google研究人员于2017年提出Transformer架构，之后神经网络的复杂度呈指数级上升，其性能也推动了NLP和相关领域的技术变革。OpenAI 2022年基于Transformer架构实现AI的里程碑式创新（ChatGPT），再次燃起人类对AGI的热情和渴望。本文结合过去二三年的AI技术热点和发展脉络，对Data&AI前沿技术和2025年的趋势进行分析，并探讨笔者对AGI实现路径的一些思考。

Transformer介绍

Transformer属于深度神经网络的架构之一，具体属于无监督的自回归预训练模型。无监督（Self-supervised）意味着不需要人工标记数据，模型自动学习中间特征表示，并具备迁移学习能力。自回归（Auto-regressive）是预训练模型的方法之一，其本质在“回归”，基于过去的数据预测未来，例如LLM预测下一个token。预训练指通过大量的随机样本对模型进行拟合，尚不具备（高效的）场景化问题解决能力，因此需要post-train阶段对模型进行微调，以适应下游问题和场景。

与AR相关的另一种预训练方法是自编码（Auto-encoding），如BERT提出的掩码语言模型，通过遮挡样本随机位置的信息，模型可结合上下文信息，学习丰富的语言符号表示，方便下游复用。

AR和AE是两种常用的生成式语言模型的预训练方法，但并非全部，例如XLNet提出排列语言模型实现双向上下文的结合，同时具备AR和AE的优势。此外，虽然强化学习和对抗学习也在某些LLM训练中（如DeepSeek-R1）发挥了重要作用，但其作为核心训练算法的模型和应用场景，仍有待进一步探索。在图计算领域，虽然AR和AE同样被用来训练图节点的低维表示，并在下游图任务中取得了不错的效果，但是Graph-native的训练方法仍在探索阶段。

AR和AE模型，在NLP领域取得了巨大成功。透过表象看本质，在当前的语言模型训练中，并未基于自然语言单位的语义（概念）进行学习，而是基于token组合的统计规律。换句话说，在token集合展开的序列空间里，实际的自然语言样本是空间的子集，Transformer通过神经网络参数捕获了这个子空间的序列模式。只要神经网络表示的参数空间足够覆盖样本序列空间，便能够成功学习子集的表示。在这个意义上，AR和AE的训练方法对于“有限元素集合的序列空间”具有普适的学习能力。

Transformer架构目前已在自然语言之外的多个领域得到实践并达到SOTA：

计算机视觉：图像分类[ViT]、目标检测[DETR]、图像生成[TransGAN]、图像分割[SETR]
生物信息学：蛋白质结构预测[AlphaFold2]、基因序列[Lee2022]、单细胞组学[Szalata2024]
时间序列分析：天气预测[FuXi]、时空动态预测[Li2024]、金融预测[Galformer]
语音处理：语音识别[Conformer]、合成[Tacotron]
多模态学习：图文生成[DALL-E]、视频理解[VideoBERT]

从以上实践可见，通过将领域内问题通过适当的方法转换成序列数据后，构建离散元素集合，Mirchandani2023总结出Transformer是通用序列模式学习器 。对于一个封闭/半封闭式的复杂系统，当系统内部具有有限状态集合、或有限状态生成规则（如明确的物理规律），Transformer能够较好地对这类系统行为建模。

技术热点和创新趋势

LLM工程优化

对Transformer极致优化背后的逻辑是大家对Scaling-law的信奉。随着训练数据规模和参数量（trilion-scale）的提升，人们期望通过工程上极致的优化，在有限资源下训练更大的模型，期待再次出现类似GPT-3的涌现时刻。

在此背景下，一方面是粗放式地堆叠计算卡，另一方面是类似DeepSeek团队对Transformer的每个部分做极致优化：计算效率（如注意力机制、长序列优化、并行训练）、内存占用（如浮点精度、注意力窗口）、推断/Inference优化（如KVCache、蒸馏、量化、wafer级加速）等。

工程优化是LLM产品化和业务化降低成本的必经之路，但单纯地追求scaling-law并不能让我们更接近AGI或human-level intelligence，这是Transformer也是神经网络算法的内在限制（见下文后LLM时代）。

所以无论Jason Huang多么大声疾呼scaling-law无比重要，研究人员也要保持理性和洞察力，理解、掌握并跨越scaling-law，寻找那把真正能打开AGI大门的钥匙。

LLM知识增强

LLM架构自身有几个显著缺陷：

知识更新成本高：这是神经网络基于参数的隐知识表示（latent knowledge representaiton LKR）的限制，无法复用、局部更新和迁移知识。理解LLM的LKR是可解释AI领域关注的重要问题之一。如何复用LKR或寻找通用知识表示，也是AGI需要攻克的技术难点之一。
生成“幻觉”：虽然LLM注意力模块是确定性的，即模型训练好后，对于任何一个注意力模块给定输入后，输出是确定的；但LLM依然有生成幻觉问题，原因是多方面的[Huang2025]，例如训练数据缺陷、错误传导、无自指导致的弱一致性等。
可解释和可控性不足：这也是神经网络架构的固有限制，几乎所有的post-train工作都只能在e2e下进行。虽然相关的LLM probing和editing技术也在研究，但尚无稳定可靠的方法论或工具。神经网络模型的过拟合和泛化，就像夜空中的启明和长庚，本为一体却又相互矛盾。

尽管如此，LLM作为自然语言处理领域的一项颠覆性技术，其价值对于社会生产力的潜在提升，也是不容忽视的。为了利用更新信息、或私有域数据，Retrieval Augmented Generation (RAG) 的工作流被提出来。从最初基于文本块向量的VectorRAG到语义表示更丰富的GraphRAG，2024可谓是RAG大年，相关技术已经成为LLM+商业化落地的基石，也是未来AI-native apps的必备技能。

同时，结合数据和算法的增强，在减小模型尺寸的同时保持LLM的有效知识密度（笔者注：有效知识密度，定义为LLM内的知识完备度与模型复杂度–等效vanilla transformer架构的参数量–的比值），为模型的推理质量、推理深度的增强铺平了道路。诚如Ilya Sutskever所言，Internet是LLM时代的化石燃料。在数据规模有限的情况下，深入理解LLM原理，磨炼算法才是正途（见下文可解释性）。

从即时推断到深度推理

自Chain of Thought提出以来，人们在优化LLM解决复杂推理问题的同时，也在不断探索如何通过计算机模拟人类思考（Turing’s imitation game）。DeepSeek的出圈，一方面是对工程极致的追求，更重要的是开源了GPT-4级、具备深度推理能力的模型训练方法，人们在享受GPT-4级免费模型的同时，研究人员再也不用猜测其内部训练机制了。

如果推断 (inference) 是对模型在训练阶段捕获的隐知识表示（token序列模式）的浅层反馈，那推理 (reasoning) 便是对这些隐性知识的深度挖掘。以自然语言为表示的推理，演绎出新的知识，最新成果例如OpenAI o1/o3-mini, DeepSeek-R1, Google Gemini Flash Thinking。Dr. Wolfe最近有篇精彩的总结文章。

对于推理机制和算法的深入研究，或许是ChatGPT引领的AI复兴留给未来AGI科技的重要资产之一，也是未来LLM商业化的核心竞争力。深度推理之于LLM，类似于PageRank算法之于搜索引擎。商业巨擘基于LLM技术对自身内部无处不在的数据Silo进行整合，基于深度推理开发出更具吸引力产品体验。近期上线的Gemini Flash Thinking with apps功能，基于整合Youtube、GoogleMap的数据，Gemini2展现出比单纯模型推理、RAG更为强大的实际问题解决能力。但因为涉及核心的业务逻辑，背后的深度推理链未来可能不会再采取开源开放的态度。

LLM可解释性

和单纯用好LLM相比，理解LLM的工作机制，深入探索知识表示、记忆、推理、遗忘等深层次和人类认知相关的基础技术，更有助于迈向AGI。因此AI开拓者们在Nature大声呼吁，我们应该注重neuroscience和AI的跨领域研究（NeuroAI），加强认知、神经科学等基础领域的教育和资金投入。

神经网络的层数越多，参数空间越大，可存储的信息越多。在神经网络中，模式以高维向量表示，在LLM中也称作隐知识表示。由于训练语料体量大，即使采用数据清理去噪，也无法获得一致性强的原始知识。实践表明，数据Bias和人为构造攻击数据，很容易对模型的行为造成影响。

在深入理解LLM机制上，Zhou2024发现参数越大、post-train阶段指令调教越多的LLM稳定性越差。在内部激活神经元不可控的前提下，针对特定领域问题的fine-tuning/filtering会加速其他领域知识的遗忘。Mahowald2024的研究揭示了LLM对Formal语言能力（指对语言规则和统计规律的掌握，如翻译）较强，但是Functional语言能力（指利用语言在现实场景应用，如推理）较弱；这与当前LLM向DeepReasoning方向演进的趋势相符。

事实上，由于训练数据内部知识的不一致性，造成LLM内部的知识冲突，Xu2024表明这种冲突是普遍存在、且内生的，需要更加底层的变革。因此，LLM是弱一致性（weak-consistency）模型。和一致性相关有个著名的Gödel不完备定理，其表示对于任意的formal system，完备性（completeness）和一致性（consistency）无法兼而有之。Pérez2021证明Transformer一定约束下是turing-complete，而turing-complete system是formal system。由此可见，LLM在一定约束下满足Gödel不完备定理，在追求知识量（高完备性）的前提下，势必会破坏知识表示的一致性：这如同紧箍咒，定位了通用单一LLM模型的能力边界。因此笔者认为，这也预示着MoE架构比当下流行的通用单一模型更有前景。

除此以外，即便LLM是个黑盒，其对自然语言模式、尤其对基于语言的逻辑推理的捕获，让人们不禁好奇：这种类人思考的机制的本质是什么？在NeuroAI领域，结合LLM和大脑fMRI数据的研究，Mischler2024和Kumar2024揭示了LLM工作机制和人脑皮层的神经信号处理在宏观上的相似性。虽然仍处于初期研究阶段，该领域的研究或许是下一代AGI技术的突破所在。

后LLM时代：两种潜在的AGI路径

它山之石可以攻玉。近年来，人们经过对LLM及Transformer架构的深入研究，在通过工程化增强LLM实用性的同时，也逐步认识到其内在局限性。从AI概念提出至今，人们不断对“机器如何模拟人类”的想法进行实践，经典的研究领域包括认知框架（Cognitive Architectures）、形式系统（Formal systems）、心智理论（Theory of Minds）、世界模型（World Models）等。虽然这些领域的问题在实践中尚未得到完全的解决，但其思想沉淀对AGI研究依然有所启示。

基于当前数据规模和算力提升，我们应该重新审视AI的发展历程，汲取前人思想和实践经验，从宏观视角探索潜在的AGI实现路径。笔者以为，当下有两个潜在的AGI实现路径值得关注：世界模型和神经符号AI（Neuro-symbolic AI）。

世界模型的思想与AI发展一脉相承，其核心思想从第一性原理出发，通过描述世界的状态和行为，并定义状态和行为之间的联系，来构建AI模型/系统。世界模型可以用于解决各种问题，如智能体在环境中的规划、决策、行为等。Han2018首次系统介绍了相关概念，并基于vision-memory-controller架构的二维小车游戏展示了世界模型的潜力。LeCun2022提出了基于能量模型EBM和JEPA架构的世界模型实现思路，并在视觉表征、自动驾驶领域得到了实践。李飞飞带队创业成立WorldLabsAI，专注于大世界模型(Large World Models，LWMs)，去年12月发布了空间智能计算的第一个成果Generating 3D worlds。Google于2025年1月宣布在DeepMind内部成立专门的WorldModeling团队，以解决世界模型问题。该领域仍处于起步和布局阶段，但其前景令人期待。

神经符号AI是另一个让人兴奋的方向。基于统计模型的机器学习和以LLM为代表的纯神经网络架构，是1990s以后的主流方法，在持续学习、可解释性、常识知识等方面存在缺陷。当前AI研究者的技术栈已鲜有符号AI的影子。符号AI在知识表示、逻辑推理、可解释性等方面有天然优势。在人类的科技理论中，通过领域语言（DSL）而非自然语言表述是普遍的，例如数据符号、逻辑符号、电路符号、编程语言等。基于DSL能够对领域内问题进行精确定义并推理，这也是符号AI的魅力所在。在LLM普遍头疼的数字加减问题，在数据DSL里是最基本的运算。例如Google AlphaGeometry通过神经符号AI解决IMO几何数据问题，新版V2实现了首次超越人类、84%的问题解决率。

在未来的AGI探索中，笔者认为LLM、世界模型、神经符号AI都将是核心技术，并且思想上相辅相成，在世界知识表征、逻辑推理、持续学习、Active Inference等方面实现完全不同于当前AI的范式。

总结

本文围绕当前Data&AI研究领域，对LLM相关的思考、研究、未来世界模型、神经符号AI等方向进行了总结。因为笔者研究视角和精力限制，并未能对当前所有技术趋势进行总结，例如多模态MLLM、Agentic框架也是2025年的热点研究领域，读者可以继续探索AGI的世界。

Neurosymbolic AI - Part II

Sat, 08 Feb 2025 00:00:00 +0000

Background

Self-reference, one of the most important concepts for understanding human consciousness, is both a fundamental aspect and a powerful tool for advancing future AI systems. Its profound implications are explored in Douglas Hofstadter’s books Gödel, Escher, Bach and I Am a Strange Loop. These two works, spanning nearly thirty years, showcase the author’s evolving thoughts on self-reference, transitioning from empirical observations in cognitive science to a deeper, more introspective philosophical perspective. In Hofstadter’s philosophy, self-reference is central to understanding the concept of “I”.

In cognitive science, self-reference is closely tied to conscious experiences such as memorization, reasoning, prediction, and decision-making. The sense of “I” is considered to arise from the interplay of sensory feedback within our biological subsystems and the cerebral neural network—mechanisms, unfortunately, that still remains largely unexplored. This lack of understanding, however, does not impede the development of AI; on the contrary, it fuels our curiosity about the potential to replicate human consciousness within a mechanical framework.

Meanwhile, self-reference poses challenges in mathematics and computer science. It disrupts the foundations of mathematics through Gödel’s incompleteness theorems (1931) and renders Turing’s Halting Problem undecidable (1936), both of which rely on self-referential constructs (e.g., the Gödel sentence) to derive contradictions. These results underscore the inherent limitations of all formal systems, such as mathematical logic and Turing machines, and have sparked decades of debate (see Lucas-Penrose Argument, 1961-2003) over whether computer can truly emulate human intelligence. This question remains a pivotal consideration as today we are marching toward artificial general intelligence (AGI).

Self-reference and AGI

Self-awareness, a fundamental aspect of future agentic systems, is deeply tied to self-reference. If we aim to build human-like agents to serve our civilization, their “mental” world must be self-consistent while mastering vast knowledge and skills. The flip side of this is the risk of multiple conflicting personalities, which can lead to dilemmas and inconsistencies. These, in turn, may result in unintended reasoning processes and unpredictable behavior.

Current large language models can simulate role-playing scenarios through prompts such as “assume you are a [role]…,” indicating a lack of self-consistency and self-reference in general problem-solving contexts. This limitation is one of the key sources of LLM hallucinations.

Gödel’s incompleteness theorems establish that consistency and completeness cannot be achieved simultaneously. Gödel’s insights suggest that creating AGI requires more than just accumulating data and refining neural networks; it necessitates an understanding of the fundamental principles that shape logic, mathematics, and cognition [1].

From a theoretical standpoint, we can make the following assertions regarding AI and self-reference today:

A formal system adheres to Gödel’s incompleteness theorems.
A Turing machine is a formal system.
Neural networks are not Turing-complete.
However, transformers and recurrent neural networks (RNNs) have been proven to be Turing-complete under specific theoretical conditions [3].

This suggests that the balance between completeness and consistency remains a crucial factor in transformer-based AI systems. Historically, Turing’s paradox demonstrated the impossibility of a universal proving machine, an insight that reshaped computing history and led to the development of modern, versatile computers.

By analogy, we propose a bold prediction: large, unified language models represent an intermediate stage in the evolution of AI architectures. The next-generation mainstream approach is likely to be Mixture of Experts (MoE) models, systems that enhance predictive accuracy (consistency) by incorporating expert models with specialized but limited completeness in specific domains. These architectures may provide a more balanced trade-off between completeness and consistency, pushing AI development forward.

Self-reference and Attention

The attention mechanism, a fundamental aspect of human intelligence for processing contextual information, is a crown jewel of AI science. After years of exploration by researchers worldwide in the field of natural language processing, the success of the Transformer model (2017) is twofold. First, it effectively captures the attention mechanism through an efficient multi-head attention (MHA) structure, enabling scalable models that can be trained on internet-scale data with parallel processing. Second, it demonstrates remarkable generality in modeling sequential data within closed or semi-closed complex systems, such as natural language, global weather patterns, and protein structures.

This generality in modeling sequential data is particularly significant. According to the second law of thermodynamics, our physical world operates as a vast three-dimensional closed system with a temporal direction, resulting in a unidirectional flow of information, i.e., a sequential system. Since human consciousness emerges from interactions with the external world, our memory, reasoning, and even emotions are deeply tied to temporal sequences in physical reality. In this sense, mastering a powerful framework for modeling sequential data is crucial for the advancement of human-like AI architectures.

Transformer models perform attention modeling through a combination of positional encoding and self-attention mechanisms. The positional encoding encodes the position of each token in the sequence, while the self-attention mechanism allows the model to focus on different parts of the sequence to enhance the information representation.

Encoding self-reference in a Transformer model remains a challenge due to the absence of a dedicated module for capturing the sense of “I”. In role-playing games of large language models, a character’s sense of self is simulated through a segment of tokens representing its internal state—akin to a memory cache—prepended to each query. This mechanism helps maintain consistency in the character’s internal state by feeding information into the attention modules.

In the MoE architecture, an alternative approach to self-reference involves employing a dedicated expert model that encapsulates the concept of “I”. The output of this shared self-reference expert receives greater weight when the input aligns with the system’s global internal state. However, this method may diminish the knowledge coverage of other non-shared experts, ultimately reducing the generality of global training.

A more advanced and human-like integration of self-reference would embed it directly within the attention mechanism itself. Achieving this requires reimagining and innovating attention structures within AI architectures. In neuro-symbolic AI, the attention module can take different forms, such as a sub-graph correlation matrix rather than a conventional vector distance matrix. In this context, the core aspect of self-reference, when represented as a graph, can be directly embedded within the correlation matrix. This mechanism will be explored in greater depth in future blogs.

Summary

In this blog, the concept of self-reference in the context Godel’s incompleteness theorems and its implications for AI are explored. It is shown that self-reference is central to guide and advance future AI systems, such as agentic or robotic systems.

References

[1] Gödel: Incompleteness Architect – Limits of Knowledge in AI Era

[2] Gödel’s Incompleteness Theorem is Not an Obstacle to Artificial Intelligence

[3] Attention is turing-complete. Journal of Machine Learning Research, 2021, link

Neurosymbolic AI - Part I

Sat, 11 Jan 2025 00:00:00 +0000

Background

The success of LLMs has triggered a new wave of prosperity of AI researches. The market, supply chains and end-users have been educated in a unprecedented depth about AI capabilities in this wave. This is another fresh start toward the future of intelligent world.

Project LaCogito was initiated to explore the foundational architecture of next-generation AI—an AI system characterized by self-explanation, self-reference, and unlimited extensibility for diverse real-world contexts via active inference [3]. Positioned at the forefront of innovation, LaCogito aims to identify and develop the essential core technologies, service capabilities, and market opportunities based on the first principles of intelligence.

The foundational idea behind LaCogito was conceived as a system designed to fuse multi-source data and enable interactive, autonomous knowledge mining, akin to Wolfram Alpha, even before the announcement of ChatGPT. I was deeply impressed by the scale and multidimensionality of the data supporting Wolfram Alpha and its Cloud services. To unravel its underlying technologies, I explored a wide range of disciplines, from the semantic web to category theory to neural networks. Despite these efforts, I ultimately failed to build such a system.

The sudden emergence of ChatGPT, however, reignited hope by demonstrating a practical AI system aligned with this vision. Yet, the more I delved into understanding how large language models (LLMs) operate, the stronger my desire grew to revolutionize the design of an AI system. My vision centers on key principles: self-reference with consistent cognition, self-explanation through concrete and precise concept representation, active inference derived from interactions with the external world, and continuous learning for evolution.

In a series of posts, I will outline the fundamental concepts underpinning this ideal future AI system. In this post, I will depict the essentials and solutions to support AI systems with self-explanation.

What is Self-Explanation

Self-explanation is a key aspect of research into explainable AI models, enabling us to understand how AI systems operate and to control their behavior when necessary. At the heart of self-explanation lies the representation of concepts. Grasping the importance of conceptual representation in artificial intelligence is comparable to understanding the role of the space-time dimension in Einstein’s theory of relativity.

In traditional semantic web, a concept is recorded as a symbol (e.g., ‘Love’ in English and ‘愛’ in Chinese). In artificial neural networks (ANN), a concept is encoded in the vectors (e.g., 1001001010101 in LLM). As for biological neural networks, memorial formation and storage of a concept still remain mysterious (cognitive science and systems biology, two related promising areas to uncover this).

From my perspective, AI systems capable of self-explanation should possess the following characteristics:

Controllable Concept Formation: This applies regardless of whether the conceptual representations are explicit or implicit.
Traceable Logical Reasoning: The reasoning should be based on clearly defined conceptual relationships.

Cerebral vs. ANN Intelligence

To analyze the differences in conceptual representations, it is essential to consider the encoding and decoding processes. When comparing cerebral and artificial neural networks, irrespective of their actual structures, concepts in the brain are functionally encoded within a multi-modal, heterogeneously featured, and highly dimensional space, while they are conveyed by hidden layers in ANN with a vast amount of parameters.

Empirically, when stimulated by specific external signals (e.g., a familiar scene or an old object), the human brain can rapidly reconstruct a concept and its related associations within milliseconds. These associations can encompass both symbolic information (e.g., a piece of literature) and non-symbolic information (e.g., emotions or feelings) . However, despite these empirical insights, a sufficiently robust theoretical foundation for cerebral encoding, decoding, and their interactions remains lacking.

In contrast, artificial neural networks (e.g., transformers) perform encoding through pre-training, embedding concepts into network weights that are tightly linked to network topology. In this process, vectors primarily serve as transmission mediums to collect and compress contextual information layer by layer via attention heads, weights, and residual pathways. This implies that concepts are stored within the network’s transformations rather than in the vectors themselves [2].

A significant limitation of this approach is the distributed and implicit correlation across the entire network, involving numerous active parameters that are still largely unknown and uncontrollable in the global parameter space. This globally correlated representation gives rise to challenges such as hallucinations, difficulties in ad-hoc updates to pre-trained models, and inefficiencies in reusing encoded knowledge. Techniques like Reinforcement Learning with Human Feedback (RLHF) or Direct Preference Optimization (DPO) provide only limited solutions to these issues, as their end-to-end and result-oriented guidance and optimization approaches fail to address the root causes effectively.

Recent researches [1,2] comparing brain intelligence and the mechanisms of LLMs offer a valuable opportunity to explore how intelligence is “generated”. Current findings reveal some intriguing similarities between the brain and LLMs, such as cascading information processing (e.g., cerebral cortex regions vs. transformer layers) and contextual knowledge integration (e.g., cortex neuron connectivity vs. transformer attention heads). However, it remains unclear whether they share the same underlying mechanisms. The lack of effective technologies to trace cerebral neural activities during thought processes limits our understanding of possible counterparts to transformer’s embeddings, attention transformations, residual optimizations, and more. Nevertheless, continued progress in cognitive and brain sciences is essential to unraveling the complexities of cerebral intelligence.

Neuro-symbolic AI

Another potential solution for developing self-explainable systems is the integration of symbolic technologies. Traditional symbolic AI faced significant inefficiencies during the previous “AI winter” (late 1980s to 2000), particularly in iconic symbolic processing (e.g., LISP machines) and frame-based expert systems. However, adversity often fosters innovation. The decline of purely symbolic approaches, coupled with the potential challenges of pure neural-network AI, has paved the way for the emergence of promising neuro-symbolic AI.

In this novel framework, a General Symbol (GS) represents a concept in various forms, such as a sequence of words, a 3D geometric shape, a sound, or even a physical sensation (potentially embedded as smaller models). Neural networks are not directly involved in encoding all knowledge. Instead, they are trained to perform specific tasks, such as routing paths to particular concepts, encoding complex non-symbolic concepts, or understanding and mastering the intrinsic relationships among them.

Together, these general symbols and their interconnections form the foundational knowledge base of AI. The sheer scale and complexity of such a symbolic knowledge base may surpass human capacity for manual upkeep. To address this, agentic bots with specific goals can be designed to assist humans in managing and maintaining the knowledge base effectively.

Summary

In this post, I have outlined the essentials and a potential solution, i.e., neuro-symbolic AI, for explainable AI systems. The next posts will delve into two other fundamental principles: self-reference and active inference.

References

[1] Contextual Feature Extraction Hierarchies Converge in Large Language Models and the Brain, Nature Machine Intelligence, 2024, link

[2] Shared functional specialization in transformer-based language models and the human brain, Nature Communications, 2024, link

[3] Generating meaning: active inference and the scope and limits of passive AI, Trends in Cognitive Sciences, 2024, link

Ontology Framework

Thu, 18 Apr 2024 00:00:00 +0000

概述

本文总结当前主流的语义网络（知识图谱）领域的本体描述框架，包括理论，语言和系统。其中本体论介绍相关理论发展，以及大家对其形而上学的争论；本体工程介绍若干基础和领域的本体概念集；本体语言介绍典型的知识表示语言及其发展过程。最后展望在大语言模型变革下的本体论技术发展趋势。

简史

符号知识系统的发展，从最初的通用问题解决器GPS 到最近的语义网络和知识图谱，经历了多次的基础理论迭代和系统发展，这里简要总结（Wikipedia通过ChatGPT总结生成）。

~1959

General Problem Solver (GPS) System，由Allen Newell & Herbert A. Simon提出关于规划和分解解决问题的数据结构。
Advice Taker，John McCarthy提出，提倡使用predicate calculus进行常识推理。

1960s

Resolution Method，John Alan Robinson提出，提出利用一阶逻辑进行自动化定理证明。
Situation Calculus，John McCarthy and Pat Hayes提出，对场景和因果知识通过逻辑表示。

1970s

逻辑编程和Prolog，提出了一种将Horn子句映射成目标约减过程的解法，并发展了系统化的计算机语言。
Frame Concept，Marvin Minsky提出，可认为一次重要的发展节点，消弭了长期关于知识的基于本体论的静态表示和基于逻辑推理的过程知识表示，提出Frame概念表示本体及问题解决策略。Frame概念受到面向对象理念发展的影响，二者有诸多相似之处。目前主流的知识表示语言，与Frame概念一脉相承。

1980s

KEE，Intellicorp公司提出知识工程环境，在以frame概念为基础的知识表示之上，增加了规则引擎。
KL-ONE，一种frame语言，包含了规范预发和自动推理引擎。
Cyc，Doug Lenat创立的Cyc公司，后发布过OpenCyc，其目标为基于frame的知识表示，构建一个常识推理系统。
知识表示假设，Brian C. Smith首次提出知识表示假设(Knowledge Representation Hypertheses)，对于如何表示知识进行了理论化表述，引用原文：

Any mechanically embodied intelligent process will be comprised of structural ingredients that a) we as external observers naturally take to represent a propositional account of the knowledge that the overall process exhibits, and b) independent of such external semantic attribution, play a formal but causal and essential role in engendering the behavior that manifests that knowledge.

2000~

Semantic Web，由W3C组织提出，又称Web 3.0，基于RDF、OWL等标准化技术实现。Knowledge Graph也属于这一技术领域。Berners-Lee在1999年这样表达自己对于语义网络的Vision（结合当前AIGC的发展仍然具有启发性）：

I have a dream for the Web [in which computers] become capable of analyzing all the data on the Web – the content, links, and transactions between people and computers. A “Semantic Web”, which makes this possible, has yet to emerge, but when it does, the day-to-day mechanisms of trade, bureaucracy and our daily lives will be handled by machines talking to machines. The “intelligent agents” people have touted for ages will finally materialize

本体论

关于本体论(Ontology)的基本定义，在发展过程中一直备受争议。总结起来有两种递进意义下的定义。侠义地，本体论指概念及其关系的集合。广义地，本地论指以高度语义化的表达描述关于客观世界的知识。

Russell & Norvig给出的结构化表示（structural representation）可以认为是一种狭义的定义：

facts about particular objects and event types and arrange the types into a large taxonomic hierarchy analogous to a biological taxonomy.

Tom Gruber也给出类似的定义：

An ontology is a description (like a formal specification of a program) of the concepts and relationships that can formally exist for an agent or a community of agents.

Gruber（1993）试图给出更一般的定义：

Ontologies are also not limited to conservative definitions — that is, definitions in the traditional logic sense that only introduce terminology and do not add any knowledge about the world. To specify a conceptualization, one needs to state axioms that do constrain the possible interpretations for the defined terms.

Feilmayr & Wöß (2016) 对Gruber的定义进行了更清晰的说明

An ontology is a formal, explicit specification of a shared conceptualization that is characterized by high semantic expressiveness required for increased complexity.

这也是我们采用的广义定义，主要特征包含通用性、语义化、强表达力。需要说明的是，Ontology一词被广泛使用，通常根据上下文可能代表概念词表、分类系统、元数据、以及语义网络等不同含义，因此我们很难给出统一的使用限制。在AI领域里，我们推荐Feilmayr & Wöß的定义作为广义的AI Ontology概念。

本体工程

本体工程（Ontology Engineering）属于应用本体论的范畴。在信息学领域，以Sowa的 Conceptual Graph（ISO标准化为Common Logic）、W3C标准化的Semantic Web相关技术为代表，通过系统化和标准化，实现本体论所定义的对世界知识的语义性表达。

本体工程的产物，本文中也称之为本体模型，即定义了概念及其关系的集合。和大语言模型的基础模型和微调模型类似，本体模型也包含基础本体模型（Foundation ontology or Upper ontology）和领域本体模型（Domain ontology）。常见的基础本体模型有BFO、 Dublin Core、GFO、Cyc、SUMO、UMBEL、FOAF、DOLCE等。WordNet也被大多数研究者认为是基础本体模型，但是在实际应用中，wordnet通常被作为语言学工具学习领域本体模型。

在本体工程中，只有开放合作，才能实现不同领域专家知识的连接和共享。因此标准化的工作至关重要。目前相关标准包括W3C RDF/RDFS资源定义框架、OWL知识表示语言、SPARQL 查询语言。以及ISO Common Logic标准（ISO/IEC 24707:2007），定义了一套逻辑编程语言的框架，有助于不同的知识表示语言能够相关转化；其中也定义了一些方言，例如逻辑交换格式CLIF、概念图交换格式CGIF等。CL标准具有通用性，其他基于逻辑的语言（例如 OWL）可以转化为CL定义的抽象语法和语义。

与此同时，W3C发起了Linked Data项目，旨在基于标准化定义，实现不同本体模型的对齐和关联，实现全人类共同拥有和受益的语义网络。

本体论语言

这部分我们再回顾本体论框架下的知识表示语言（Knowledge Representation Languages, KRL）的发展。回顾这些历史，有助于我们在当下技术发展阶段，进一步发展出表达力更强、更易于计算的KRL。典型的语言包括CASL、CycL（Cyc项目）、KIF（基于S表达式的一阶逻辑语言）、Olog、OntoUML、OWL等。

在众多KRL当中，有一类语言基于Frame概念，至今方兴未艾，也深刻影响了OWL的标准化制定，这一类语言包括KRL（第一个通用的Frame语言）、KL-ONE、Loom、RDFS、OIL、DAML （基于RDF的标记语言）、以至OWL。其中OWL的标准化设计，受到了DAML+IOL的深刻影响。

未来

在基于Transformer的大语言模型的深刻技术变革中，本体论相关技术以其强逻辑性、可解释性，有潜力实现对大语言模型隐式知识表达的融合和创新。近两年已有不少有趣的工作和项目出现，例如知识图谱和LLM的结合应用[3]、基于LLM的Ontology Learning[4]等，这方面未来值得花篇幅单独介绍。

另一方面，本世纪以来，人类在软件工程化（例如数据计算和信息提取领域），实现了长足进步，尤其在开源软件社区蓬勃发展的驱动下。早期以标记符号为主的知识表示语言（例如OWL）开始展现出不足，尤其是对于计算型知识（Computational Knowledge）的表达表现出较大局限性。如何实现基于标准化、又发展标准化的新的KRL，能够充分利用当前已有的软件生态以及计算硬件，是构建未来的高科技实力组织，并且实现通用人工智能的关键环节之一。

参考

[1] https://en.m.wikipedia.org/wiki/Ontology_(information_science)

[2] https://en.m.wikipedia.org/wiki/Ontology_language

[3] Neuhaus, Fabian. (2023). Ontologies in the era of large language models – a perspective. Applied Ontology. 18. 399-407. 10.3233/AO-230072.

[4] Hamed Babaei Giglou etc., LLMs4OL: Large Language Models for Ontology Learning, https://arxiv.org/abs/2307.16648

Zen of Lisp Language

Sun, 10 Dec 2023 00:00:00 +0000

S-expr and evaluation

A lisp program is a set of s-expressions. The basic of s-expressions are lists and atoms. An atom is a non-list or the empty list. Lists are delimited by parentheses and contain any number of whitespace-separated elements. Each element is itself an s-expression.

Given a bunch of text as input, the lisp reader (compiler) translates text into s-expressions that can be evaluated into Lisp forms. However, not every s-expression is valid to be evaluated into Lisp forms. Lisp evaluation introduces a second-level syntax to determines which s-expression can be treated as Lisp forms. The syntax rule is simple. Any atom or list that has a symbol as its first element is a legal Lisp form.

Atoms can be divided into two categories: symbols and everything else. A symbol, evaluated as a Lisp form, is considered the same of a variable and evaluated to the current value of the variable (How do variables get their values?). Certain symbols represents variables that can be evaluated into constant values or the symbols themselves. For example, symbol PI is evaluated to a constant float number. Symbol T and Nil, the canonical truth and falsity, are self-evaluating in the sense that variables they name can be assigned the value of the symbol itself. Another class of self-evaluating symbols are keyword symbols (whose name starting with :). When the reader interns such a name, it automatically defines a constant variable with the name and with the symbol as the value.

Another large category of atoms being self-evaluating are numbers, strings, and numeric expression like ratio. When such an expression is passed to the notional evaluation function, it’s simply returned.

All legal list forms start with a symbol, but three kinds of list forms are evaluated in different ways. They are function call forms, macro forms, and special forms.

Function

Lisp function syntax supports various kinds of parameter-passing methods. These methods which are familiar in other languages are location indexed arguments, optional arguments, named arguments by keywords, and varying length arguments.

The first symbol of the list as Lisp forms is function name. The remaining elements of the list should be well-formed Lisp forms and evaluated one after another into values passed into the first element of function.

In Lisp, RETURN-FROM is not bound to function; it is tied to a code BLOCK. BLOCK is a special operator. When defining a function, DEFUN automatically initiates a new block with the same name of function. So we always return from a function by calling (RETURN-FROM :funcname :values). Note that the function is changed the same time that RETURN-FROM’s first argument should be changed as well.

The FUNCTION operator is used to get the function object from function name. The function name is not quoted. A syntax sugar is #'.

lisp (foo 1 2 3) === (funcall #'foo 1 2 3)

Special forms

A group of operators defined in Common Lisp to do things that functions can not. For example, the flow control operator IF changes the order of remaining element evaluation orders in function call. Instead IF operator evaluates the first remaining element and performs encoded logic in IF operator of branch controlling. Other special operators are like QUOTE, which takes a single expression and simply returns it, unevaluated; and LET, which is used to create new variable bindings.

Macro forms A macro is a function that takes s-expressions as arguments and returns a Lisp form that’s then evaluated in place of the macro form. The macro expansion occurs at compile time when the macro input s-expressions don’t need to be well-formed Lisp forms.

Closure

Lexical scoping var is similar to scoped variables in other languages like Java and C. A common pattern of using lexical var is in closure. The key of understanding closure is that it is the binding, not the value of the variables, that’s captured. Thus the closure can change and persist the value between calls of the closure.

Variables

CL is a dynamically typed and strongly typed language in the sense that all type errors will be detected.

All values in CL are conceptually references to objects. Assigning a new value to variable changes what object the variable refers to but has no effect on the previously referenced object. All variable assignment is creating a new binding to the assigning object but has no effect on the previously bound object. This is the basic law of CL variable syntax.

Special operators LET and LET* are usually used to bind variables.

Two types of variables: lexical scoping vars, and dynamic (global) vars.

Dynamic variable

Operator DEFVAR and DEFPARAMETER are two ways to create dynamic or global variables. Global vars are conventionally with names that start and end with *. DEFPARAMETER always assigns the initial value to the named variable while DEFVAR does so only if the variable is undefined. If you specifically want to reset a DEFVARed variable, you can either set it directly with SETF or make it unbound using MAKUNBOUND and then reevaluate the DEFVAR form.

Lexical and dynamic vars have different scope and extent in the sense that scope refers to space while extent refers to time. Lexical vars have lexical scope but indefinite extent. Dynamic vars have indefinite scope since they can be referred to from anywhere by dynamic extent.

LET operator can shadow dynamic var during the execution of the binding form, and recover the original binding to the dynamic var after finishing executing the lexical binding form.

Constant

DEFCONSTANT, the var name can be used only to refer to the constant; it can’t be rebound with any other binding form.

Redefinition of DEFCONSTANT is allowed, but this doesn’t change the value.

Conventionally, using names as constant starting and ending with +.

Assignment

Macro SETF is used to assign a new value to a binding. It can examine the form of the place it’s assigning to and expand into appropriate lower-level operations to manipulate that place.

(seft place form)

Assigning a new value to a binding has no effect on any other bindings of that variable. And it doesn’t have any effect on the value that was stored in the binding prior to the assignment.

References

Forms and functions
- Symbols as Forms: http://www.lispworks.com/documentation/HyperSpec/Body/03_abaa.htm
- Function Forms http://www.lispworks.com/documentation/HyperSpec/Body/03_ababc.htm
Data structure
- Enhanced data structure and functions: alexandria https://alexandria.common-lisp.dev/draft/alexandria.html
Sharpsign
- Syntax: https://mr.gy/ansi-common-lisp/Sharpsign.html
CLOS & MOP Spec
- https://clos-mop.hexstreamsoft.com/

Zen of Javascript Language

Mon, 18 Sep 2023 00:00:00 +0000

背景

我比较喜欢研究计算机语言理论。所有的计算机语言来自于历史上诸多计算机学者和工程人员的努力。每种语言都有生而为之的特征。每年都有诸多计算机语言诞生，而追寻每种语言背后的故事以及了解它们的与众不同的特点，很有意思。这是What X surprises me系列文章之一，记录某种语言的设计特点在我的认知中带来某种惊讶或惊喜。有点钟书先生《管锥编》异曲同工之意。这篇有关Javascirpt的语言特点，对比的背景是Java/CPP/Python等。

基础

灵活的变量声明范围：var声明范围为function or script scoped，let和const是block-scoped
声明提升：var可提升，默认为undefined; let和const不可提升，否则抛出referror

控制流

throw可以抛出任意类型
Boolean和literal true/false判定不同，if (Boolean) 为true
loop break: break label语法方便快速跳出更外层的loop；类似的continue label语法
for语法：for…in对object属性名进行遍历，或者对可便利变量如array values进行遍历； for…of对object所有可遍历属性的值进行遍历，针对不同属性调用不同的遍历器。

函数

func参数都是基于值传递，即更改参数值不影响外部传入参数；但是如果传入参数是obj或 arr，修改obj属性或者arr value会同样修改外部对象属性。逻辑上并不矛盾，基于参数传递，可以理解为obj地址为参数值。
Closure功能比较强大并且随处可见。Closure生命周期能够超越定义它的外部函数，进入调用函数生命周期，成为真正意义的clousure。
arguments: func参数以array-like方式存储在arguments中，例如arguments[0], length, callee (等价于func name)。
Arrow function (=>): 更短的函数声明，不绑定this，同时没有arguments, super, new.target等；在arrow function出现以前，所有函数须有绑定的this。

操作符

Comma为操作符之一，二元操作符，用于for loop condition
Array的[]操作符，既是索引操作符根据index获取值，同时也是属性操作符根据值获取 index。

对象与类

JS建立在一套简单灵活的Object概念之上
Object是引用类型reference type，因此两个不同object永不相等。
Object和Class是两个相似但不同的概念，不像其他语言中一个是另一个的实例化。
Object可以通过变量+初始化列表定义，变量名即为Object名称。
Object可以通过定义构造函数、并通过New创建。构造函数绑定this，arguments等内置 \变量。在这个意义上，大部分函数都可以认为是object构造函数。Object可以通过
Object.create(ObjectName) 构造实例
Object可以定义函数类型的属性。
Object可以定义getter和setter，二者同样为属性，属性名为函数名
Function constructor定义的Object和Class在大多数情况下作用相同，如定义属性、 \静态函数属性等，而Class可以定义private属性、methods，这是object所不具备的。
Class也可以通过声明class类型的变量定义，变量名即为Class名称。
Class构造函数通过constructor()定义，literally
Class private变量通过#varname定义

其他

Typed array是个奇怪的名称，更具体应该是typed buffer或者typeless array。和通常意义上的array并无相似之处，是一组特定长度的连续的内存空间。
任何类型都可以成为迭代器Iterator，只需要1）实现next() 方法；2）返回值包含value 和done属性。注：这种有点类似python和go的duck typed接口声明，是一种很灵活的类型扩展机制。
JS支持一种简洁生成迭代器的函数，声明为function*和yeild关键字。和Python yeild类似，但是没有后者简洁。
Iterables：特指支持for…of的遍历语法对象。一个对象如果想成为iterables，需要增加Symbol.iterator实现，其实现内容通常为function* 定义的生成迭代器。

Knowledge Representation - Part I

Sat, 27 May 2023 00:00:00 +0000

Intro

An efficient representation of knowledge/logics lies at the core of knowledge computing engines. This requirement is also one of vital pieces of future artificial general intelligence (AGI). Recent success of Transformer architecture in natural language field [1], especially with Large Language Models like GPT-4 and LLaMA series, inspires us that neural networks (NNs) with Attention mechanism are efficient at condensing information and logics encoded in sequential tokens. However these models still remain as a black box about learned inner representation of knowledge (KR). The main reason comes from the token vectorization and high dimensional nature of neural networks with a vast amount (tens to hundreds of billions) of parameters and deep layers.

We can imagine LLM as a higher dimensional space that absorbs token occurrence patterns as vectors, and implicit complex logics encoded in their computational relations. Nevertheless we encounter a challenge to interpret, extract and reuse those mastered patterns as explicit knowledge outside a trained model. Also, the representation of specific knowledge piece or logical relation remains unstable as for changes of training context, neural network structure, or the involvement of finetuning techniques. Even models trained against the same datasets at differing times remain incomparable when considering their inner representations.

Hypothesis-1. LLM illustrates the capability to absorb world knowledge as well as reasonable logics, because it masters not the world knowledge per se, but the rules of knowledge organization depicted by natural languages.

A portion of community endeavor is put into reversing engineering the black box by prompt engineering [2], single neuron interpretation [3], network structural analysis [4] etc. We argue that the first principle thinking should be applied to ask the basic and core questions,

What are we really talking about when saying knowledge representation?
And what is the straightforward way to represent knowledge?

The answer for the first question is addressed below by several proposed principles about KR. Our answer of the second one is proposed here as “SYMBOLIC”, with a footnote that the concepts of representation and reasoning should be treated independently. Human race has gained abilities to exchange complicated information between each other and convey knowledge between generations after the invention of mnemonic symbol systems. This also enhances our logical reasoning with a ‘inner speech’ mechanism [6], usually driven by symbolic native language. In this sense the symbolic is still a native way of KR.

Limitations of LLM in KR

We have accumulated a large amount of knowledge in different forms, while the symbolic conveys a significant portion (other forms like pictures, sounds, sculptures). It is convenient and efficient to speak or write with mnemonic symbols. What the LLM captures well is the pattern of token sequences, grammar and logics being encoded by token organization (location in sentence, occurrence frequency, relative long- and short-range dependency and so on). Nevertheless there are many other forms of vital symbolic knowledge that cannot fit into the token-sequence model, thus LLM does not deal well with, such as arithmetic equations, physical theories, spatial relations.

Many experiments have shown that LLM fails to calculate addition and multiplication of arbitrary large numbers, much less complicated mathematical theorem understanding. The core reason is that the arithmetic operator, say ‘plus’ or ‘+’, is not just a symbol, but also embodies calculating rules predefined in math. A sequential regression model heavily relying on sample occurrences can not master this kind of implicit knowledge well.

Hypothesis-2. LLM presents superb capabilities in pattern capturing and summarization, while showing an intrinsic weakness to involve the encoded implicit knowledge in symbols.

In the natural language scenario, we are always surprised by the knowledge scale and grammatical generation of LLM, while ignoring the scale of substantial related samples in training datasets and their connections with the generated output. Another explanation for arithmetic weakness of LLM is that we are unable to have a training dataset containing a full arrangement of all possible number calculation.

General Principles of KR

For general concept of knowledge, interpretability, reusability and integration are fundamental practicable demands in our daily usage. We argue that, in a similar sense, knowledge representation in cognitive computing or AGI systems should possess these natures as well. Concretely,

Interpretability, a foundation stone for explainable knowledge systems. We are able to trace the source and reasoning process for output conclusion. It is a vital part to construct paradigm of knowledge discovery, differing from knowledge squeezing and summarization, Hypothesis-1.

Reusability, transferring summarized or discovered knowledge ingredients across different AI systems. In LLM, we assume that complex (implicit) relational dependencies between explicit knowledge ingredients are fetched (Hypothesis-2), similar to the neural pathways created in creatural brains when some direct psychological interactions are built. However, these learned implicit knowledge is locked as black-boxed representations.

Integration, exemplified as a kind of ‘knowledge protocol’ between systems. Almost every branch of our theories owns a suite of symbol framework to present its assumptions, axioms, theorems, deductions etc. This plays an indispensable role in either people communication or system/theoretical framework interaction.

Knowledge Intermediate Representation

To address the challenges observed in LLMs, we suggest that representation should be separated from communication and reasoning processes in knowledge-intensive systems, and a concept of Knowledge Intermediate Representation (KIR) is proposed to fulfil above principles. Some explicit and flexible structures, for example hypergraph, are preferred for KIR. Recent progress in multimodal graph learning [5] also confirms the importance and powerfulness of selecting a suitable presentation paradigm in a sense of fusing multimodal data sources.

We compare the methodology of KIR with graphical reasoning such as large graph model (LGM) or probabilistic graph reasoning (PGS) with current state-of-the-art LLM technique, as illustrated in above figure. Here we consider the interdisciplinary knowledge presented in symbols, such as natural languages, system control instructions and physical theories. We treat the input human-readable symbols as a human-system interaction interface, defined as the communication part. In left LLM way, all symbolic knowledge in training samples are converted into token sequence and fed into the neural model, where its encoder-decoder structure with attention mechanism is efficient at training parallelly and capturing the long-term dependencies between tokens. Its limitation is coupling of representation and reasoning, and challenges to fulfil those KR principles depicted above.

In our proposed methodology, the general KIR part is introduced, as the right line in above figure. It embodies the principles of interpretation, reusability and integration for KR in a declarative method. A Lisp-like declarative language is recommended. Under the hook, each list expression with a functor and variables could embody both the implicit and explicit knowledge, which is also efficiently handled by other computational techniques, such as symbolic regression [7]. Similar consideration is also made in the project OpenCog Hyperon for MeTTa language [8]. KIR is the kernel of our framework, playing a role like ‘inner speech’ for a cognitive process [6], memorizing ingredients in an artificial mind model (An interesting example is the generative agents from [9] whose KIR is natural language for memorization).

During the reasoning phase, given user’s prompts, tokens are generated recursively by the LLM fine-tuned targeting at specific task. This sequence-in-sequence-out manner constrains LLM’s application in scenarios that the information cannot be transformed into token sequence properly. For example, when human looking at a video of a flock of birds hovering above the forest, birds’ flying patterns and landing location would be inferred and predicted with our born sense of space and understanding of spatial relation of birds, sky and forests. However, it is hard for LLM to formulate these spatial knowledge. Although some showcases imply that LLM can answer space-concept-related physical reasoning question, it is because that similar sequences describing related problems are present in the training set and encoded in the hyper-parameter space.

To conquer this limitation, we propose graph-modeled equivalent (e.g. hypergraph) of KIR before performing reasoning. Also in the birds-hovering example, we could embody the spatial relation of different objects in edges, as well as physical knowledge encoded in edge-bundled functors. Ektefaie etc. [5] employ a unified graph model to perform multimodal learning, which shares the similar idea. In the reasoning procedure, the problem is formulated as partial substitution of masked subgraphs, in other words, performing subgraph matching given a variable-embedded graph (variable grounding). We categorize techniques into two groups, searching paradigm and graph neural network (GNN) paradigm. Both could meet our requirements, but have differences in the scale of searching space and computing efficiency.

Contd. We leave the discussion of graph-centric paradigm and its integration with KRI in next part.

Summary

This article shows a blueprint of my project LaCogito towards general cognitive/knowledge computing infrastructure. It summarized my recent thinking about KR and expected related principles to develop a knowledge-intensive system. After a technical deduction, KIR seems to pave a new way to integrate both explicit and implicit knowledge in a unified framework. Also graph-centric architectures have shown potentials to perform reasoning on KIR base.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

[1] Lin T, Wang Y, Liu X, Qiu X. A survey of transformers. AI Open. 2022 Oct 20.

[2] White, J., Fu, Q., Hays, S., Sandborn, M., Olea, C., Gilbert, H., Elnashar, A., Spencer-Smith, J. and Schmidt, D.C., 2023. A prompt pattern catalog to enhance prompt engineering with chatgpt. arXiv preprint arXiv:2302.11382.

[3] Dai, D., Dong, L., Hao, Y., Sui, Z., Chang, B. and Wei, F., 2021. Knowledge neurons in pretrained transformers. arXiv preprint arXiv:2104.08696.

[4] Li, M. and Zhang, Q., 2023. Does a Neural Network Really Encode Symbolic Concept?. arXiv preprint arXiv:2302.13080.

[5] Ektefaie, Y., Dasoulas, G., Noori, A., Farhat, M. and Zitnik, M., 2023. Multimodal learning with graphs. Nature Machine Intelligence, pp.1-11.

[6] Alderson-Day, B. and Fernyhough, C., 2015. Inner speech: development, cognitive functions, phenomenology, and neurobiology. Psychological bulletin, 141(5), p.931.

[7] Cornelio, C., Dash, S., Austel, V., Josephson, T.R., Goncalves, J., Clarkson, K.L., Megiddo, N., El Khadir, B. and Horesh, L., 2023. Combining data and theory for derivable scientific discovery with AI-Descartes. Nature Communications, 14(1), p.1777.

[8] Goertzel, B., 2021. Reflective Metagraph Rewriting as a Foundation for an AGI” Language of Thought”. arXiv preprint arXiv:2112.08272.

[9] Park, J.S., O’Brien, J.C., Cai, C.J., Morris, M.R., Liang, P. and Bernstein, M.S., 2023. Generative agents: Interactive simulacra of human behavior. arXiv preprint arXiv:2304.03442.

Acknowledge of images, ‘awesome-transformer-nlp’ attributed to project awesome-transformer-nlp

Lambda Cognition

Conquering LLM Hallucination with Platonic Coding

The Hallucination Problem

What is Platonic Coding

How Platonic Coding Conquers Hallucination

Specs as Laws

Language as Interface, Not Meaning

Agents as Form Instantiators

Explicit Time and Memory

The Five-Phase Workflow

Platonic Coding vs. Prompt Engineering

Why This Matters

Composable Intelligence

The Framework

Representative Carriers

Reactive Coupling

Meta Structures and Topology

Towards cognitive agentic system

1. cogents-core

Core Abstractions

Key Features

2. cogents-smith

Core Capabilities

Toolkit Ecosystem (18 Specialized Toolkits in 10 Semantic Groups)

Production-Ready Agents

Architecture Features

3. cogents-browser-use

Features

4. wizsearch

Features

Additional Resources

🌟 Acknowledgments

Data & AI 技术趋势 2025

背景

Transformer介绍

技术热点和创新趋势

LLM工程优化

LLM知识增强

从即时推断到深度推理

LLM可解释性

后LLM时代：两种潜在的AGI路径

总结

Neurosymbolic AI - Part II

Background

Self-reference and AGI

Self-reference and Attention

Summary

References

Neurosymbolic AI - Part I

Background

What is Self-Explanation

Cerebral vs. ANN Intelligence

Neuro-symbolic AI

Summary

References

Ontology Framework

概述

简史

本体论

本体工程

本体论语言

未来

参考

Zen of Lisp Language

S-expr and evaluation

Function

Special forms

Closure

Variables

Dynamic variable

Constant

Assignment

References

Zen of Javascript Language

背景

基础

控制流

函数

操作符

对象与类