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Notation

Single source of truth for symbols used across SUPREME's READMEs and algorithmic specifications. Matches the notation in the paper (Section 2.1 and Algorithm 1).

Seeds and counts

Symbol Meaning
$I$ number of training seeds
$J$ number of unlearning seeds per training seed (default $J = 1$; the SUPREME paper uses $J = 1$)
$K$ number of evaluation seeds per unlearning seed (default $K = 1$)
$i$ training-seed index, $i \in \{1, \dots, I\}$ (paper, 1-indexed) or $\{0, \dots, I-1\}$ (codebase, 0-indexed)
$j$ unlearning-seed index, $j \in \{1, \dots, J\}$ (paper) or $\{0, \dots, J-1\}$ (codebase)
$k$ evaluation-seed index, $k \in \{1, \dots, K\}$ (paper) or $\{0, \dots, K-1\}$ (codebase)
$s_t$ training seed; paper uses $s_t \leftarrow i$
$s_u$ unlearning seed; paper uses $s_u \leftarrow (i-1) J + j$
$s_e$ evaluation seed; paper uses $s_e \leftarrow (i-1) J K + (j-1) K + k$

Independence requirement

Nested repetitions require distinct seed identities at each level:

  1. All $I$ training seeds are mutually distinct.
  2. All $I \cdot J$ unlearning seeds, one per $(s_t, j)$ pair, are mutually distinct.
  3. When $K > 1$, all $I \cdot J \cdot K$ evaluation seeds, one per $(s_t, j, k)$ triple, are mutually distinct.

The paper's formulas $s_u \leftarrow (i-1) J + j$ and $s_e \leftarrow (i-1) J K + (j-1) K + k$ give distinct identities by construction. The scripts use the sparser $s_u = s_t \cdot 1000 + j$ (and $s_e = s_u \cdot 1000 + k$ when $K > 1$). Use distinct nonnegative indices $j,k < 1000$ to avoid collisions; counts alone do not constrain arbitrary user-supplied indices. When $J = 1$, the scripts use $s_u = s_t$; when $K = 1$, they use $s_e = s_u$.

Distinct seeds do not make nested results marginally independent: unlearning runs share their original model, and evaluation repetitions share their unlearned model. Treat repetitions as conditionally independent only under the relevant sampling assumptions. See seed protocols and variance interpretation.

Datasets and partitions

Symbol Meaning
$D, D'$ training and test datasets
$D_f, D_r$ forget and retain partitions of $D$, with $D_r := D \setminus D_f$
$D'_f, D'_r$ forget and retain partitions of $D'$
$C$, $c$ set of forget targets (classes for fullclass/subclass, ratios for random_); a single target $c \in C$
$\tau$ scenario type $\in \{\text{targeted}, \text{random-sample}\}$

Models

Symbol Meaning
$M_\text{init}$ model with initial parameters (randomly initialised or pre-trained)
$M_o$ model trained on the full training set $D$
$M_r$ retrained baseline, trained from scratch on the retain set $D_r$
$M_u$ unlearned model, output of applying an unlearning method to $M_o$

Unlearning methods and evaluation

Symbol Meaning
$A$, $a$ set of unlearning methods; a single method $a \in A$
$E$ set of evaluation metrics
$P$ set of devices (GPUs)
$\epsilon^\text{tot}$ total training epochs per training run (repo-specific; e.g., 200 for Cifar100, 40 for Cifar20)

Operations

Symbol Meaning
$\text{Train}(D, s)$ train from scratch on $D$, seeded by $s$, full schedule
$\text{Sample}(D, c, s)$ uniformly sample a size-$\lceil c\lvert D\rvert \rceil$ subset of $D$ using seed $s$ (random-sample scenario only)
$a(M_o, D_f, D_r, s)$ apply unlearning method $a$ to $M_o$, seeded by $s$
$\text{Evaluate}(M_u, M_r, D'_f, D'_r, E, s)$ compute the metrics in $E$ on $M_u$ against $M_r$, seeded by $s$