The human ability to translate diverse perceptual and linguistic inputs into structured behavior has been thought to rest on learning robust representations of concepts. The rapid advancement of transformer-based large language models (LLMs) has surfaced a diversity of computational ingredients relevant for model building - architectures, fine-tuning methods, and training datasets among others - yet it remains unclear which are most crucial for developing human-like conceptual representations. Further, most current benchmarks are ill-suited to measuring representational alignment, making LLMs' scores on them unreliable for assessing whether they are progressing as cognitive models. We address these limitations by evaluating over 75 models on a triplet similarity task, a method well established in cognitive science for measuring conceptual representations, using concepts from the THINGS database. We find that instruction fine-tuning and larger attention head dimensionality are among the strongest predictors of human alignment, while activation function choice, multimodal pretraining, and parameter size have limited influence on alignment. Correlations between alignment scores and existing benchmark scores reveal that while some benchmarks (e.g., BigBenchHard) better capture representational alignment than others (e.g., MUSR), none fully accounts for the variance in human-model alignment, demonstrating their insufficiency. Taken together, our findings highlight key computational ingredients for advancing LLMs as models of human conceptual representation and address a key gap in LLM evaluation.

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