A learned weighted sum of intermediate-layer activations compresses an instruction prompt into a single patch vector that, injected at an early layer, recovers task accuracy within ~2% of the full prompt.
Llms will always hallucinate, and we need to live with this
8 Pith papers cite this work, alongside 26 external citations. Polarity classification is still indexing.
8
Pith papers citing it
26
external citations · Pith
abstract
As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.
representative citing papers
Steering LLM residual streams with random sparse vectors creates detectable self-recognition fingerprints that enable over 98% accurate attribution of generated text to specific models without degrading output quality.
DisAAD trains a 1%-sized proxy model via adversarial distillation to quantify uncertainty in black-box LLMs by aligning with their output distributions.
MOSAIC generates executable scientific code without I/O test cases by combining student-teacher distillation with a consolidated context window to reduce hallucinations across subproblems.
In a closed world of sparse random facts, the minimal memory per fact equals the KL divergence between fact and non-fact score distributions, so the optimal limited-capacity strategy hallucinates a fixed fraction of non-facts.
MOSAIC is a training-free multi-agent LLM framework with rationale, coding, reflection, and debugging agents plus a consolidated context window that outperforms prior methods on scientific coding benchmarks.
Hallucinations are inevitable on an infinite set of inputs but can be made statistically negligible with sufficient training data quality and quantity.
LLMs show accuracy drops of 0.3% to 5.9% on GSM8K math problems when culturally adapted to six countries while keeping math operations identical, with statistical significance confirmed by McNemar tests.
citing papers explorer
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Prompt Compression via Activation Aggregation
A learned weighted sum of intermediate-layer activations compresses an instruction prompt into a single patch vector that, injected at an early layer, recovers task accuracy within ~2% of the full prompt.
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LLM Self-Recognition: Steering and Retrieving Activation Signatures
Steering LLM residual streams with random sparse vectors creates detectable self-recognition fingerprints that enable over 98% accurate attribution of generated text to specific models without degrading output quality.
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Estimating the Black-box LLM Uncertainty with Distribution-Aligned Adversarial Distillation
DisAAD trains a 1%-sized proxy model via adversarial distillation to quantify uncertainty in black-box LLMs by aligning with their output distributions.
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No Test Cases, No Problem: Distillation-Driven Code Generation for Scientific Workflows
MOSAIC generates executable scientific code without I/O test cases by combining student-teacher distillation with a consolidated context window to reduce hallucinations across subproblems.
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Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testing
In a closed world of sparse random facts, the minimal memory per fact equals the KL divergence between fact and non-fact score distributions, so the optimal limited-capacity strategy hallucinates a fixed fraction of non-facts.
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MOSAIC: Multi-agent Orchestration for Task-Intelligent Scientific Coding
MOSAIC is a training-free multi-agent LLM framework with rationale, coding, reflection, and debugging agents plus a consolidated context window that outperforms prior methods on scientific coding benchmarks.
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Hallucinations are inevitable but can be made statistically negligible
Hallucinations are inevitable on an infinite set of inputs but can be made statistically negligible with sufficient training data quality and quantity.
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Lost in Cultural Translation: Do LLMs Struggle with Math Across Cultural Contexts?
LLMs show accuracy drops of 0.3% to 5.9% on GSM8K math problems when culturally adapted to six countries while keeping math operations identical, with statistical significance confirmed by McNemar tests.