We audit alignment-induced shifts in residual-stream activations of three open-weight instruction-tuned LLMs (Llama-3.1-8B-Instruct, Gemma-2-9B-it, Qwen-2.5-7B-Instruct) using the effective rank of the alignment modification matrix on safety-relevant inputs, rho_eps := rank_eps(M_Ds)/d, which formalizes the single-refusal-direction observation of Arditi et al. (2024) as a continuous quantity. The paper has three contributions. (1) Confound-controlled measurement: a four-variant decomposition (M_naive, M_template, M_aligned, M_DiD) separates chat-template formatting, alignment-stage shift, and the refusal-mediating direction, and recovers the Arditi refusal direction on M_DiD at |cos| in {0.77, 0.86, 0.50} (Llama/Gemma/Qwen); chat-template-controlled rho_eps is {0.0029, 0.0048, 0.0044}, and the centered SVD residual is 4-7x larger. (2) Constructive calibration on a 3-layer MLP across rho_eps in {0.008, 0.17, 0.33, 0.40} exhibits a sweet-spot vs. brittle distinction: mild rank-maximization (lambda=5) buys ablation robustness, while strong regularization at the same nominal rho_eps (lambda=50) does not. rho_eps is a diagnostic for fragility, not a target whose mechanical inflation buys robustness. (3) Limits of rank-based diagnostics: (a) not safety-specific (LRH baseline is 2-3x the safety value); (b) SVD principal ordering does not match causal ordering (Llama u_2 inert despite ranking second; cumulative ablation non-monotone at k=5); (c) the spectral-gap hypothesis required to upgrade the O(rho_eps * d) achievability bound to a matching Mirsky-route lower bound fails empirically (1/90 Llama layer-reference pairs, 0/36 MLP combinations) and structurally (kappa_lb <= 2/(eps * r)). The matching lower bound remains an open problem.

We derive a Sequential Minimal Optimization (SMO) algorithm for the quadratic dual problem arising from $\varepsilon$-SVR~\cite{Vapnik1995, Drucker1997, Smola2004} modified to minimize the Mean Absolute Percentage Error (MAPE)~\cite{Makridakis1993, Hyndman2006} directly in the loss function~\cite{benavides2025support}. This formulation is part of a broader family of SVR models with percentage-error losses that also includes least-squares variants~\cite{Suykens2002} and symmetric-kernel extensions~\cite{Espinoza2005}, whose unified structure is studied in~\cite{benavides2026unified}. The key structural difference from standard $\varepsilon$-SVR is that the box constraints become \emph{sample-dependent}: $α_k, α_k^* \in [0,\, 100C/y_k]$. We show that this modification affects only (i) the feasibility sets $\Iup$ and $\Idown$ in the working-set selection and (ii) the clipping bounds in the analytic two-variable update, while leaving the curvature formula and gradient update structurally identical to the standard SMO~\cite{Platt1998, Platt1999, Fan2005}. A shrinking heuristic adapted to the sample-dependent bounds is derived and shown to introduce an asymmetry between $α$- and $α^*$-variables controlled by the gap $2y_k\varepsilon/100$. The same solver applies to the symmetric-kernel variant (m2) by replacing $Ω$ with $Ω_s = \tfrac{1}{2}(Ω+ aΩ^*)$~\cite{Espinoza2005}. Numerical validation against an interior-point QP reference solver confirms solution agreement to within solver termination tolerance across ten synthetic configurations spanning both kernel variants and symmetry types. An implementation is available in the open-source \texttt{psvr} R package~\cite{BenavidesHerrera2026Rpsvr}.

AI/ML methods are increasingly used in economics to generate binary variables (or labels) via classification algorithms. When these generated variables are included as covariates in regressions, even small misclassification errors can induce large biases in OLS estimators and invalidate standard inference. We study whether the bootstrap can correct this bias and deliver valid inference. We first show that a seemingly natural fixed-label bootstrap, which generates data using estimated labels but relies on a corrupted version in estimation, is generally invalid unless a strong independence condition between the latent true labels and other covariates holds. We then propose a coupled-label bootstrap that jointly resamples the true and imputed labels, and show it is valid without this condition. Two finite-sample adjustments further improve coverage: a variance correction for uncertainty in estimated misclassification rates and a Hessian rotation for near-singular designs. We illustrate the methods in simulations and apply them to investigate the relationship between wages and remote work status.

Proteomics is the interdisciplinary field focusing on the large-scale study of proteins. Proteins essentially organize and execute all functions within organisms. Today, the bottom-up analysis approach is the most commonly used workflow, where proteins are digested into peptides and subsequently analyzed using Tandem Mass Spectrometry (MS/MS). MS-based proteomics has transformed various fields in life sciences, such as drug discovery and biomarker identification. Today, proteomics is entering a phase where it is helpful for clinical decision-making. Computational methods are vital in turning large amounts of acquired raw MS data into information and, ultimately, knowledge.

"Name" is the name of the operation in our search space. "TFFunction" is the TensorFlow function that the name is mapped to when a DNA instruction is being converted to a line of TensorFlow code. "Argument Mapping" describes how the values in a DNA's argument set are mapped to the corresponding TensorFlow function arguments. This vocabulary is largely constructed from the lowest level TF operations needed to create Transformers (see Appendix A.5). We also add commonly used math primitives such as SIN and ABS. Here we provide additional implementation details. Relative Dimensions: We use relative dimensions [13] instead of absolute dimensions for each instruction's "dimension size" argument. This allows us to resize the models to fit within our parameter limits (32M to 38M parameters). The vocabulary for these relative dimensions is [1, 2, 4, 8, 12, 16, 24, 32, 48, 64].

Large Transformer models have been central to recent advances in natural language processing. The training and inference costs of these models, however, have grown rapidly and become prohibitively expensive. Here we aim to reduce the costs of Transformers by searching for a more efficient variant. Compared to previous approaches, our search is performed at a lower level, over the primitives that define a Transformer TensorFlow program. We identify an architecture, named Primer, that has a smaller training cost than the original Transformer and other variants for auto-regressive language modeling.