avatarAnthony Alcaraz

Summarize

Augmenting Large Language Models with Hybrid Knowledge Architectures

Tracing Vector Relevance with Symbolic Chains: A Balanced Approach for Robust Reasoning in Retrieval-Augmented Generation

Retrieval augmented generation (RAG) refers to a paradigm in which large language models (LLMs) are enhanced by integrating relevant information from external knowledge sources. This approach produces outputs that are significantly more accurate, relevant, and informative compared to standalone LLMs.

The key insight behind RAG is that while pretrained LLMs encapsulate a lot of implicit knowledge acquired through their vast training datasets, their knowledge remains static and prone to false inferences when applied to downstream tasks. Connecting LLMs to external knowledge repositories that can provide up-to-date, trustworthy information tailored for specific applications vastly improves performance.

For instance, an LLM may generate erroneous medical advice if not conditioned on accurate health data. Linking the LLM to structured medical databases prevents this while allowing dynamic responses based on the latest statistics and guidelines.

However, the design of what knowledge sources complement LLMs remains an open research question. A key tension highlighted is whether to rely on structured knowledge graphs with discrete symbols and formally defined relationships or unstructured text corpora that contain information in free-flowing natural language.

Structured knowledge graphs provide organized knowledge with clear semantics and support logical reasoning which enhances explainability and trustworthiness. But manually encoding human knowledge into symbolic frameworks can be extremely labor-intensive and often infeasible at scale.

In contrast, unstructured text corpora require little explicit modeling but lack formal verifiability and reasoning capabilities.

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I. Symbolic and Sub Symbolic Representations

Comparing Representations

When designing the knowledge component for RAG systems, a key consideration is how to represent the stored information — using explicit symbolic models or implicit sub-symbolic vectors.

As outlined, symbolic systems use discrete graph structures with defined semantic relationships, like an “apple” node connected to a “fruit” node. This offers interpretability and traceability. In contrast, sub-symbolic systems employ numerical vector embeddings based on implicit patterns within data. This provides flexibility in handling ambiguity.

Equations for Similarity Calculations

In the context of symbolic knowledge graphs, the calculation of similarities between concepts or entities is a critical task. Taxonomy-based similarity measures, such as the Leacock-Chodorow similarity, are particularly useful in this regard. These measures typically rely on the hierarchical structure of a taxonomy (like a tree) where concepts or entities are organized according to their levels of abstraction or specificity.

The Leacock-Chodorow similarity, specifically, is a measure based on the shortest path that connects two concepts in a taxonomy, normalized by the maximum depth of the taxonomy. This method takes into account both the distance between the concepts and the depth of the taxonomy, providing a more nuanced similarity measure compared to simple path-length-based methods.

In mathematical terms, the Leacock-Chodorow similarity between two concepts is calculated as:

This measure is particularly relevant in natural language processing, information retrieval, and semantic analysis, where understanding the degree of relatedness between concepts is crucial. By integrating such a similarity measure into a symbolic knowledge graph, it becomes possible to perform more refined and context-aware queries, enhance the accuracy of information retrieval systems, and improve the overall understanding of the relationships between different concepts in a knowledge domain.

Whereas sub-symbolic vectors use similarity metrics like cosine distance:

The cosine similarity (or cosine distance) is a commonly used metric to measure the similarity between two vectors in this space. It assesses how close or far apart two vectors are in terms of their orientation, regardless of their magnitude. This is particularly useful in text processing, as it allows for the comparison of words, sentences, or documents based on their semantic content rather than their specific word composition.

Balancing Representations in RAG Architectures

Ideally, RAG systems should harness symbolic knowledge representations where explainability is mandatory, while utilizing sub-symbolic techniques for ambiguous or complex domains. Unified frameworks may employ attention mechanisms to anchor vectors to related symbolic concepts for traceability. Combining symbolic graphs and sub-symbolic vectors can provide structured knowledge without compromising flexibility or continuity with new data. RAG is well positioned to integrate discrete and distributed data semantics into coherent, robust and trustworthy generative applications.

II. The Case for Symbolic Systems

Explicit Semantics

  • Human-interpretable symbols: Symbolic systems are based on discrete concepts like “apple” and defined relationships like “is-a-type-of”. This aligns with human cognition, unlike sub-symbolic numeric representations.
  • Clear meaning: The symbols directly convey meaning. We can interpret that an apple node connected to a fruit node indicates an apple is a fruit. There is no inherent meaning in a numeric apple vector.
  • Data modeling: The use of explicit symbols and typed relationships allows systematically modeling entities and their logical associations, forming structured data frameworks.

The direct mapping between symbolic knowledge constructs and human-understandable semantics is what makes symbolic systems inherently interpretable, as highlighted.

Structural Inferencing

  • Logical deductions: The schema of well-defined concepts and relations enables logical deduction. For example, the transitive property allows inheriting fruits’ properties down to apples by virtue of “apples are fruits”.
  • New fact inference: Chains of deductions facilitate inferring new facts from existing structured knowledge. Logical reasoning over symbolic systems can reveal non-explicit connections.
  • Reasoning workflows: Constructing and evaluating chains of reasoning is streamlined when relying on formally defined symbols and relationships. This supports explainable expert systems.

The deductive reasoning afforded by symbolic logic serves as the basis for explainable automated reasoning — a key requirement for trustworthy AI.

Explainability

  • Query provenance: Mapping of query results back to the originating nodes and connections provides visibility into why certain answers are obtained.
  • Traceability: Following step-by-step paths linking queried symbols to retrieved information ensures operations are transparent.
  • Auditability: The ability to formally track each inference trail makes symbolic systems more rigorously auditable. Debugging issues is straightforward given the human legibility.

The combination of encoding structurally traceable knowledge and formally defined reasoning patterns drives explainability in symbolic systems — a pivotal consideration for credible and responsible AI.

III. The Case for Sub-symbolic Systems

Handle Ambiguity

  • Distributed representations: Sub-symbolic systems are based on vector embeddings locating concepts as directions in a high-dimensional vector space. This distributed representation can gracefully handle ambiguity.
  • Reconcile contradictions: Closely oriented vectors reconcile contradictions which strict symbolic logic cannot. Minor vector deviations can reflect nuanced differences or contradictions without breaking.
  • Domain flexibility: Vector orientations fluidly adapting to new data makes sub-symbolic systems intrinsically capable of resolving real-world ambiguity and inconsistencies across domains.

The distributed and malleable nature of vectors provides an efficient way to reconcile ambiguity and change — a core requirement for robust AI.

Learn from Data

  • Automated encoding: Vector spaces can be generated automatically by algorithms like Word2Vec or GloVe. These create vector representations capturing semantic meaning from unlabeled text at scale.
  • Unsupervised learning: Without human oversight, vector embeddings can be derived using self-supervised learning on vast corpora like Wikipedia or domain-specific datasets.
  • Scalability: The unsupervised methodology lends itself to scalable embedding creation from ever-growing data, unlike cost-prohibitive manual modeling.

Automatically distilling vector spaces from large datasets provides a scalable way to encode world knowledge — a major driver of performant LLM applications.

Similarity Calculations

  • Math over symbols: Unlike symbolic systems, sub-symbolic vector spaces rely on mathematical similarity measures like cosine distance rather than logical operations over discrete symbols.
  • Analogy detection: Cosine similarity can systematically identify analogies like the king is to queen as man is to woman. This analogical reasoning is inaccessible to symbolic systems.
  • Pattern recognition: Mathematical similarity helps uncover clusters and patterns within vector embeddings, enabling powerful temporally complex inferences hard to capture via symbolic logic.

The capacity to statistically reason over vectors provides the analogical thinking and pattern recognition integral to general artificial intelligence.

IV. Why RAG Needs Both

Complementary Strengths

  • Hybrid knowledge: A hybrid knowledge store combining structured symbolic graphs and unstructured vector spaces provides explanatory capacity where required while retaining flexibility where needed.
  • Situational methods: Symbolic semantics maintain trust in explainable deductions while vector similarities add adaptable analogical thinking — together surpassing either’s individual capability.
  • Check and balance: Vectors can provide probable directional inference to guide symbolic logic, which in turn verifies and grounds vectors to prevent divergence.

Hybrid symbolic-subsymbolic architecture allows RAG systems to achieve both rigid accuracy and fluid adaptability. An integrated approach would use vector search to identify relevant areas of the knowledge graph for contextual exploration.

For instance, when asked for art recommendations, vector similarity can first retrieve nodes like an artwork or artist vector close to the query vector. Attention then focuses symbolic activity on that region — traversing connected artists, styles and influences. This ultimately produces a response marrying sub-symbolic pattern relevance with symbolic explanatory coherence.

Likewise in a patient diagnosis application, vector similarity may link symptoms to disease areas in a medical ontology. Subsequent symbolic inference can deduce related risk factors through the ontology relationships. The doctor finally receives disease suggestions with logically traced rationales.

In both cases, vector similarity acts as the heuristic guiding searches over symbolic space while symbolic chains provide explanatory accounts of inferences. Like our brain using emotions to direct logical trains of thought, RAG systems require an analytical vector-driven impulse to trace interpretable symbolic paths.

Binding vectors and symbols also resolves subtleties. Class imbalance where few malaria cases exist relative to common colds can skew predictions. But symbolic rules noting malaria’s severe symptoms can correct vectors overemphasizing frequency.

This demonstrates the integration necessary for truly reliable AI.

V. Imposing Constraints on Embeddings

Non-Negativity Constraints

Imposing non-negativity constraints restricts entity embeddings to only positive values, often between 0 and 1. This induces sparsity in the representation, so that the embedding explicitly models the positive characteristics of the entity. Any negative values are pushed to 0 instead.

This is useful because most real-world entity properties tend to be explicit rather than implicit. For example, we would encode the fact that “penguins can swim” but generally not encode the infinite set of things penguins cannot do. Sparse non-negative embeddings align better with this natural positivity of real-world semantics.

Entailment Constraints

Entailment constraints encode expected logical rules like symmetry, inversion, transitivity directly as restrictions on the relation embeddings in the knowledge graph. For example, the “employed_by” relationship may have a constraint to enforce symmetry — if A is employed_by B, then B employs A.

By directly embedding these rules, the knowledge graph embeddings learn to comply with the desired logic patterns that match reality. This prevents illogical reasoning and alignments better with human deductive patterns.

Soft Confidence Constraints

Strict entailment in embeddings can become brittle. So soft constraints with slack variables allow some flexibility to account for uncertainty or exceptions. These constraints encode the degree of confidence in a rule based on the evidence.

For example, a 99% confidence may be assigned to the symmetry expectation for the “married_to” relation. This introduces some slack for potential unmatched facts but still mostly enforces the logic. Softer constraints add flexibility while retaining useful inductive biases.

VI. Invoking Focused Graph Algorithms

Post Vector-Search Symbolic Exploration

The vector similarity phase aims to rapidly narrow down potential relevance from a huge space to minimize pointless exploration. But it can still leave some inaccuracy.

Applying graph algorithms afterwards for structured analysis allows precisely following connections between the identified entities.

For example, vector search may first link a patient’s symptoms to certain disease vectors. Shortest path algorithms can then traverse medical ontologies to retrieve highly pertinent intermediate concepts like risk factors ultimately influencing disease likelihoods.

This staged approach harness strengths of both methods. Vectors enable heuristic identification then Give symbols precision.

Interleaved Vector and Symbolic Search

An alternative is a parallel yet synchronized approach where vectors highlight potentially relevant regions while algorithms explore within those subgraphs.

The vector and symbolic processes can communicate to mutually guide and enhance each other, almost like a pair of AI assistants collaborating.

For instance, centrality might first identify key entity nodes, vector matching then finds semantics-adjacent nodes for graph traversal originating there. Each result refines the next search iteration.

This allows dynamic interleaving, preventing hard staged boundaries. Tight integration permits leveraging both techniques simultaneously in a coordinated dance that mingles their strengths.

The Quest for Human-like Intelligence Demands Symbolic-Subsymbolic Unification

As we reflect on the complementary strengths of symbolic knowledge graphs and sub-symbolic vector representations, it becomes evident that creating RAG systems reaching human intelligence necessitates tightly integrating these two knowledge fabrics rather than choosing one over the other.

The human mind itself processes information by interlinking concrete concepts and logical reasoning with distributed activations making intuitive connections. Achieving this versatile yet robust cognitive profile requires AI to emulate the mind’s ability to reconcile structured theories with fluid neural patterns into a dynamic tapestry of thought.

Binding symbolic semantics with sub-symbolic vectors is key to producing this versatile reasoning. Just as our subjective intuitions often spawn logical deliberations which in turn steer back emotions, RAG systems must engage vectors to direct structured symbolic explorations whose inferences subsequently validate and enhance sub-symbolic activity.

The companies that focus innovations on explicitly interlinking explicit graphs with fluid vectors will lead the advent of next-generation AI that melds unflinching logic with insight, and explanation with exploration.

These dual-knowledge RAG systems promise to transform numerous enterprise and societal domains by bringing trustworthy yet creative decisions. In professions from medicine to public policy, AI can deploy tactical rules derived from accumulated structured knowledge while adapting strategy with sub-symbolic vectors tracking new complex dynamics. RAG allows prescriptive analytics guided by descriptive revelations.

As researchers compel bold new AI to both justify and dream, structured knowledge graphs will provide the steady scaffolding for vector spaces to reveal surprising bridges. And like human intelligence, the synergy promises imagination and innovation tempered with accountability and ethical responsibility.

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