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Multi-LLM Answer Synthesis

Modern systems can query several LLMs (or one LLM with diverse prompts) and fuse their outputs into a superior answer. For example, the Conceptual Boolean Operations framework issues the same query to multiple providers, then applies Semantic XOR (and related operations) to compare responses. Conceptual XOR extracts the unique concepts each model brings (while AND finds consensus, OR the union, and NOT gaps). The system then prompts an “aggregator” LLM to synthesize a final answer: e.g. using the XOR analysis to “incorporate the best elements from both responses” into a “BEST POSSIBLE answer. In code, the get_best_possible_answer method explicitly 1) runs XOR on each pair of responses, 2) picks the best base answer, 3) enhances it with unique points from others, and 4) outputs the combined answer. For more than two responses, a multi-way XOR step identifies each model’s unique contributions, guiding a unified synthesis pass.

Compared to simple prompt ensembling (multiple prompts on one model), multi-LLM synthesis leverages model diversity. Prompt-ensembling methods like DiVeRSe or AMA generate many variations and then use a verifier or voting to pick an answer. For example, DiVeRSe generates 100 answers from 5 different prompts and uses a neural “voting verifier” to score each completion. In contrast, Boolean XOR-based synthesis merges semantic content across different models rather than sampling one model, aiming to leverage complementary strengths.

A related strategy is Mixture-of-Agents (MoA): one LLM acts as an aggregator of proposals from others. In a classic MoA, “proposer” models generate candidate answers and an “aggregator” model synthesizes them. For example, one can feed multiple answers into a final GPT prompt that fuses their ideas. The recent trend of self-MoA shows that even sampling multiple outputs from a single strong model (then aggregating) can outperform mixing diverse LLMs. In all these ensemble/agentic schemes, techniques like weight-averaging or routing (selecting which model to ask based on task) are also used.

Retrieval-Augmented Generation (RAG) is another complementary approach: it retrieves relevant documents and feeds them to a single LLM. Unlike answer fusion, RAG augments context rather than combining model outputs. One can combine RAG with multi-LLM by retrieving facts first or in parallel, then asking each model (or the aggregator) to answer with that evidence. In practice, a classifier or heuristic can decide when to invoke web search: e.g. queries needing up-to-date facts or having low confidence answers trigger retrieval. For instance, an internal classifier might tag “Who won the 2023 Nobel Prize?” as requiring web search, while “Explain quantum entanglement” stays in-model. When search is triggered, a standard RAG pipeline is used: query a search API, retrieve and rank docs, insert them into the prompt, then generate an answer. This hybrid strategy leverages the models’ reasoning strengths but falls back to retrieval for novel or precise data.

Bias in Automated Judging

When using an LLM to judge or rank candidate answers, care must be taken to avoid bias. Studies find that LLM-judges tend to lean positive (label an answer correct if unsure) – and this bias is stronger in smaller models. Likewise, judge models often favor verbose or familiar styles. Mitigations include shuffling answer order (to avoid position bias) and using an ensemble of judge models (“jury” rather than a single judge). In practice, one can prompt multiple different LLMs (or multiple prompts on one LLM) for quality scores and average their judgments. For example, Cohere AI found that a panel of smaller judges “outperforms a single large judge” with less bias and cost. Similarly, using LLM judges of varying sizes (e.g. GPT-4 Turbo plus a 7B open model) helps reduce individual model’s idiosyncrasies. In short, treat the judging ensemble like any model ensemble: diversity and blind evaluation (shuffling) help mitigate bias. Evaluators should also compute robust metrics (e.g. Cohen’s Kappa) to ensure judges align well.

Cost-Quality Tradeoffs

Using multiple LLMs inevitably raises costs. A good framework tracks spending per step. In the logical-gate-test implementation, a complete XOR analysis (two responses + boolean analysis + synthesis) runs in $0.05–0.15 per query. In one example, “initial responses” might cost ~$0.03–0.08, with XOR analysis and synthesis each ~$0.02–0.05. These numbers came from using OpenAI/Anthropic models at typical rates. To manage costs, the system allows selecting or capping providers. For instance, environment variables can enable/disable certain LLM APIs or limit the total number used. One might exclude the most expensive models or set MAX_PROVIDERS_PER_QUERY=3 to restrict calls. In practice, workflows can be tiered: run a cheaper model first and only call a bigger model or extra passes if needed. In the logical-gate CLI, flags like --cost-summary or --providers give fine control over provider usage. The goal is to raise quality above a single SOTA model, but only incurring extra cost when the multi-model analysis adds value.

Handling Long Contexts

Different LLMs have widely varying context windows (from ~4K to 200K tokens). A synthesis system must manage these limits. One approach is context compression: distill or trim inputs to fit. The boolean framework implements Adaptive Context Compression: it dynamically reduces tokens by focusing on consensus answers and unique points. For example, if responses are very long, the system might first run a consensus AND to find overlapping content, then use XOR to capture only new bits, effectively compressing the payload. If still over limit, hierarchical reduction splits the task in tiers (process subsets of responses, then merge). In practice, you may set a context limit flag (e.g. --context-limit 4000) and the system will try lightweight Boolean summarizations before running the main analysis. In contrast, if one model has a huge context (like 100K tokens) it might absorb full answers directly, so the system can choose whichever model’s context fits best. Ultimately, context strategies include chunking long inputs, summarizing intermediate outputs, or using retrieval to bypass lengths.

Automatic Answer Scoring

Beyond binary judging, we can rank multiple answers using automatic metrics. One method is Elo rating: conduct pairwise “battles” judged by an LLM, and update scores accordingly. For example, the EloBench framework engages many LLMs (GPT-4, GPT-3.5, Google Gemini, etc.) in head-to-head comparisons using GPT-4 as a judge. Over many comparisons it produces a calibrated Elo leaderboard of model quality. This can be adapted to answer quality: treat each answer as a “player” and compare them. In practice, one can use a strong model (e.g. GPT-4 Turbo or even a smaller one) to directly rate each answer on a scale, or to decide pairwise which answer is better. Several open tools and APIs facilitate this. For instance, EleutherAI’s open Evals framework can prompt an LLM-judge to score answers against rubrics, and Microsoft’s EloBench code provides scaffolding to run GPT-4-as-judge tournaments. Because open-source LLMs (like Llama-2 or Mistral) can serve as cheaper judges, one can run many comparisons cheaply. In sum, automatic ranking often uses an LLM judge to assign quality scores or win/lose outcomes, then aggregates them (e.g. via Elo or simple voting) to choose the top answer.

Role of Small Models (≈7B)

Smaller locally-hosted models (7B parameters) can play key supporting roles. They are far cheaper to run and can be used for pre-filtering or sanity checks. For example, a 7B model can first attempt a quick answer or classification: if it seems confident and correct, skip querying the big models. Or small models can act as lightweight judges or error detectors. In evaluating answers, a 7B model (like Llama-2-7B or Mistral-7B) might flag obvious hallucinations by checking factual consistency or simple logic. These models often over-penalize uncertainty (tending “positive” in doubt), so their judgments should be used cautiously – for example only to catch glaring issues, not as sole arbiters. One could also use a 7B to classify queries: e.g. decide if a query is “factual” vs “creative” to route it to a specialized pipeline. Finally, an ensemble of small models (a “jury”) can judge aspects like style or tone cheaply. While large models offer the best accuracy, small local models allow for cost-effective gating, filtering, and additional checks that improve the multi-LLM workflow without the expense of scaling all steps on GPT-4-class systems.

In summary, a robust multi-LLM system queries diverse models, analyzes their answers via semantic XOR/AND/OR/NOT comparisons, and synthesizes a final answer that leverages each model’s strengths. It compares favorably to simple RAG or voting schemes by explicitly reasoning about content overlap. Retrieval is invoked when needed via classifiers or confidence checks. Bias is mitigated by shuffling and by using multiple judges. Costs are managed by limiting providers and operations. Long contexts are tamed by adaptive compression. And automatic ranking (Elo or judge scores) can select the best answer without human oversight. Altogether, this pipeline aims to exceed any single SOTA model by combining them intelligently, while balancing quality gains with practical considerations.

Sources: The above draws on the logical-gate-test repository’s Boolean fusion framework, along with recent literature on LLM ensembles, RAG, prompting techniques, and evaluation biases.

Citations

https://learnprompting.org/docs/reliability/ensembling?srsltid=AfmBOookUGK71Ttyh2TgSGk3G3dKISU0sndL-R9TSPft4kvnE23A9a6h#:~:text=,complex%20and%20not%20covered%20here

https://arxiv.org/html/2406.12624v2#:~:text=taker%20models%20in%20terms%20of,as%20%E2%80%98Yes%E2%80%99%20and%20%E2%80%98Sure%E2%80%99%3B%205

https://www.atla-ai.com/post/judge-or-jury-whats-the-right-approach-for-llm-evaluation#:~:text=Finally%2C%20the%20paper%20found%20reduced,which%20isn%E2%80%99t%20always%20the%20case

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