Capability-Specific Degradation Patterns in Quantized Small Language Models - Emil Rahimov (Lamintang Education and Training Centre, in collaboration with the International Association of Educators, Scientists, Technologists, and Engineers (IA-ESTE), 2026)
Post-training quantization is the default method for deploying small language models (one to four billion parameters) on consumer and edge hardware, yet its effect is usually summarized by a single aggregate accuracy score that can conceal severe failures in individual capabilities. This paper presents a capability-level analysis of four-bit quantization for seven open instruction-tuned small language models drawn from five architecture families: Qwen2.5, Llama-3.2, Gemma-2, Phi-3.5, and SmolLM2. Each model is evaluated at sixteen-bit floating point and at four-bit precision across six capabilities, namely factual knowledge, commonsense reasoning, mathematical reasoning, multilingual mathematical reasoning, code generation, and instruction following, yielding eighty-four controlled evaluations. Instead of reporting only mean accuracy, we construct a per-capability degradation map and test, using Kendall's rank correlation, whether capabilities degrade in a consistent order across architectures. The results show that degradation is strongly capability-specific: multilingual mathematical reasoning and code generation are the most fragile capabilities, with relative losses of up to fifty-seven percent, whereas commonsense reasoning is almost entirely preserved. However, the ordering of degradation is only weakly consistent across architectures, with a mean Kendall's tau of 0.29, indicating that the most and least fragile capabilities are shared but the overall ranking is architecture-dependent. Smaller models degrade more in magnitude. We conclude that small-model quantization should be evaluated per capability rather than in aggregate.