Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs. Existing sparse attention and KV-compression methods typically decide which tokens or heads to preserve from runtime attention scores, observation windows, calibration prompts, or learned gates, making head diagnosis input-dependent and costly to deploy. We propose Autonomy-of-Heads (AoH), a data-free method that identifies retrieval and streaming heads from the spectral geometry of query-key projections. AoH defines the kernel attention operator $M_h = W_K^{h\top}W_Q^h$ and uses its effective-rank as a weight-space measure of head function: concentrated spectra indicate a small number of dominant query-key matching directions and are associated with retrieval heads, whereas diffuse spectra indicate the absence of a dominant global matching direction and are associated with streaming heads. We further derive an efficient $d_\text{head}$-dimensional computation that avoids constructing the full $d_\text{model}\times d_\text{model}$ matrix. We conducted extensive experiments across models demonstrating that at 50\% sparsity, AoH retains 96.5\% of Full Attention performance on average while reducing prefill and decode latency by up to 41.4\% and 66.0\%, respectively, and KV-cache memory by 50.0\% at 256K tokens.

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