Pitfalls of Scale: Investigating the Inverse Task of Redefinition in Large Language Models (2025)

Abstract: Inverse tasks can uncover potential reasoning gaps as Large Language Models (LLMs) scale up. In this work, we explore the redefinition task, in which we assign alternative values to well-known physical constants and units of measure, prompting LLMs to respond accordingly. Our findings show that not only does model performance degrade with scale, but its false confidence also rises. Moreover, while factors such as prompting strategies or response formatting are influential, they do not preclude LLMs from anchoring to memorized values.

## introduction the surprising advent of large language models (llms) has greatly sparked the interest in natural language research, demonstrating remarkable results in several linguistic, reasoning and knowledge retrieval tasks @xcite . llms are -seemingly-capable of thinking out-of-the-box @xcite , preserving factuality of generated claims @xcite and effectively collaborating in llm-based multi-agent environments @xcite , assimilating human-like traits in thought patterns and even surpassing humans in world-knowledge recall @xcite . nevertheless, llms remain pattern learners, despite being exposed to years and years of vast documented human knowledge, making the distinction between memorization and genuine capability increasingly ambiguous @xcite . there is evidence that llms fall short in truly comprehending human language and cognition in conjunction to its biological imprints on the human brain, as well as its cultural evolution @xcite . this poses a possible inherent divergence between human and llm reasoning, inspiring the research of breaking points regarding llm capacity, the more they exhibit advancements in challenging tasks. in an effort to formally describe and predict llm capabilities, @xcite proposed scaling laws of llms, establishing a framework that links model performance to key factors such as parameter count, dataset size, and computational resources. they demonstrate that increasing these variables leads to predictable improvements in language modeling efficiency, shedding light on trade-offs and limitations ingrained in scaling. beyond such predictable improvements, larger models often exhibit emergent abilities @xcite -capabilities absent in smaller models yet arising spontaneously once a critical scale is reached. these include incontext learning @xcite , advanced reasoning @xcite , and compositional generalization @xcite , suggesting that scaling is not merely a linear enhancement of existing skills but also a rather unpredictable threshold mechanism for qualitative shifts in capability. in an attempt to question emergent abilities as an analogy to model scale, inverse scaling tasks @xcite re-frame the justified so far trustworthiness that larger models offer. these tasks refer to worsening model performance as the loss on the original training objective improves, contrary the the typical scaling laws that guarantee predictable performance advancements with loss decrease @xcite . they are designed to expose more potent llms, revealing reasoning divergence in comparison to humans, who are able to solve many of these tasks with ease. interestingly, inverse scaling is widely underexplored in literature. in this paper, we address this gap by examining the redefinition task, where well-known concepts are assigned alternative values, and llms are prompted to respond accordingly. for example, redefining π = 100 (figure 1 ), overwriting the default π = 3.14159 refutes llm's prior knowledge, calling for flexible reasoning pathways in order to handle mathematical operations over the redefined π value. through vast experimentation on several redefinitions, llm families and model scales, we conclude that: inverse scaling problems have been thoroughly investigated within the inverse scaling prize contest @xcite , targeting to unveil the causes behind inverse scaling. one primary cause is strong priors, where the llm relies on its preexisting knowledge instead of adhering to prompt instructions. another contributing factor is unwanted imitation, where the llm reproduces undesirable patterns from its training data. additionally, exemplars containing distractors can mislead the llm by providing easier reasoning shortcuts, obscuring the true task objective. finally, spurious few-shot prompting may steer the llm toward deceptive reasoning pathways, even when the right answer is explicitly provided in the prompt. redefinition falls under the category of strong priors, achieving 100% human accuracy-highlighting humans' ability to effortlessly override default meanings. this finding is on par with evidence that given ample time, humans have the cognitive abilities to generalize on alternative realities @xcite . true llm reasoning is a fundamental concern, questioning the real barrier between llms and human cognition. while llms excel in linguistic competence, this ability is dissociated with thought @xcite . in practice, llms are prone to performance degradation under alternative formulations, denoting their limited reasoning flexibility @xcite and their susceptibility to knowledge conflicts between contextual prompt information and stored facts @xcite . similar findings are reported in causal @xcite , analogical @xcite and commonsense @xcite reasoning, where llm performance declines sharply under diverging formulations. alternative prompts are also shown to influence llm capacity in arithmetic reasoning @xcite , translation over artificial languages and deductions with twists @xcite . quite often, memorization accounts for reasoning, perplexing the evaluation of the real llm abilities @xcite @xcite . ## method we test redefinition on two kinds of well-encoded knowledge in llms. the first one includes widely known physical and mathematical constants, while the second involves commonly used units of measure. we also examine two redefinition types, initially focusing on simple assignment of a new value, overriding the default one. a more challenging option is to swap two constants/units (e.g. "redefine π as ϕ"), where the llm has to override its knowledge with another piece of learned information. additionally, we design escalating redefinition levels, as well as three question levels over original and redefined values, reflecting increasing difficulty. finally, from the llm's response format side, we study both free-form (ff) generation and multiple choice (mc). in the mc case, the problem may become more constrained, but we select distractors that are sufficiently challenging. constants redefinition involves the following: π, euler's number e, ϕ, the speed of light c, the gravitational constant g, planck's constant h, the elementary charge q e , avogadro's number n a , the boltzmann constant k b , the gas constant r, the imaginary i, the square root of 2 ( √ 2), infinity ∞, the vacuum electricity permittivity ϵ 0 and zero. we then design assignment redefinitions r a for the three degrees of increasing difficulty. in the first level, we assign a value close to the actual one ("redefine π as 4.5"), inspecting how an llm handles variance within an acceptable range. to stress the llm's flexibility, we modify values by orders of magnitude, assigning a deviating value we also design three levels of question difficulty. the first level (q 1 ) mainly regards the question what is the first -non-zero-digit of {constant}?. the correct answer a q 1 is actually isolating the leftmost digit (ignoring leading zeros or the minus sign in cases of negative numbers) of the constant. ## experiments we test 19 llms, including state-of-the-art (sota) model families: llama 3 (8/70/405b), mistral7b/large/mixtral8×7b, anthropic claude (opus/instant/haiku/v2/sonnet 3.5&3.7), cohere command (light/text/r/r+) and amazon titan (text lite/text express/large). all llms are prompted using zero shot (zs), few shot (fs) and chain of thought (cot) techniques. for evaluation, we decompose the llms' responses, assigning them to four categories: ## conclusion in this work, we thoroughly investigate the redefinition task by prompting llms to reason with redefined values of physical constants and units of measure. we uncover several critical patterns in llms, showcasing pitfalls of scale, such as decreased reasoning capacity and increased confidence in erroneous answers instead of abstaining. moreover, we offer extensive insights into how redefinition difficulty, prompting strategies, and response format influence llms' propensity to anchor on their prior knowledge rather than reason flexibly.