Minimum-eigenvalue spectral pruning

Integrate this as a post-training structured-pruning procedure for a linear, convolutional, or MLP layer; the selected objects are output channels, input channels, attention heads, or MoE experts. First run B calibration examples through the frozen model and record each candidate's activation signature. For channel i, set m_i=A[:,i]/(||A[:,i]||_2+epsilon), and initialize C=delta I_B. Initialize x_i=k/d, choose tau after normalizing the signatures, and repeat 50-200 projected ascent steps. At each step form M=C+sum_i x_i m_i m_i^T, compute S=expm(-M/tau)/trace(expm(-M/tau)), compute q_i=m_i^T S m_i, compute the entropy contribution h_i=log((1-x_i+epsilon)/(x_i+epsilon)), set g_i=q_i-mu h_i, update y=x+eta g, and project y onto the capped simplex {z:0<=z_i<=1, sum_i z_i=k} with sorting-based water filling. Anneal tau and optionally mu, then retain the k largest x_i and fine-tune. The paper-derived quantities are the affine Gram matrix and soft minimum-eigenvalue gradient; estimate the spectrum with Lanczos for diagnostics. Test on CIFAR-10 ResNet-20 or a small Transformer, pruning 50% of channels against magnitude, random, and norm-greedy baselines at equal fine-tuning FLOPs. Measure accuracy, activation Gram minimum eigenvalue, and redundancy. Success means equal or better accuracy at fixed sparsity and a larger post-pruning minimum eigenvalue. For MoE, compare against load-balanced top-k routing at identical active-expert FLOPs and measure perplexity.