Continual learning · OOD detection

# TOOD ### Task-Aware Out-of-Distribution Score Calibration for Continual Learners Mostafa ElAraby · Samer B. Nashed · Liam Paull

CoLLAs 2026 · Oral presentation

Note: The presentation focuses on why classification retention alone does not establish reliable OOD detection. --- ## OOD detection throughout learning - A continual learner acquires new classes over time. - It must still recognize familiar inputs from earlier tasks. - It must also reject inputs outside **all classes learned so far**. > Remembering class labels does not guarantee remembering the boundary to the unknown. Note: Example: cups and plates are learned first, books and pens next. A shoe remains OOD throughout. Books become ID after their task is learned. --- ## Evaluation setting **Class-incremental learning:** disjoint class groups arrive in successive tasks.
$$\mathcal C_{\mathrm{seen},t}=\bigcup_{i=0}^{t}\mathcal C_i$$
- Classify without knowing the test input’s task. - Evaluate OOD detection after every task. - Keep evaluation OOD classes outside the learned classes throughout the stream. Note: This fixed OOD evaluation isolates deterioration in detection from the changing definition of which classes are known. --- ## Measuring OOD forgetting With tasks indexed $0,\ldots,N-1$, let $R_{t,i}$ be OOD AUROC for task $i$ at checkpoint $t$.
$$D_i=R_{i,i}-R_{N-1,i}$$
Average incremental AUROC tracks the full learning trajectory:
$$\overline R=\frac1N\sum_{t=0}^{N-1}\frac1{t+1}\sum_{i=0}^{t}R_{t,i}$$

Higher AUROC is better. Positive $D_i$ indicates deterioration.

Note: AUROC comparisons use each task's ID examples against the evaluation OOD sets. The trajectory metric is different from final-checkpoint AUROC. --- ## Classification and OOD forgetting ![Diagnostic comparison of representation change, OOD forgetting, and classification forgetting](assets/tood-slide12-0.webp)

Diagnostic plots from the supplied TOOD presentation

**Classification performance alone is an incomplete reliability measure.** Note: Read the original figure axes carefully: the diagnostic compares representation change with two forms of forgetting. It motivates examining output scales as well as features. --- ## Mechanism 1: the confidence gap ![Task-zero ID energy falls toward the OOD energy band as tasks are learned](assets/tood-slide13-0.webp) - Older tasks’ logit scales weaken relative to newer tasks. - Correct class ordering can survive while energy separation deteriorates. Note: This is the mechanism TOOD targets. The diagnostic follows an old task over a CIFAR-10 learning sequence; it is not an average across all tasks. --- ## Mechanism 2: manifold crowding ![Feature-space diagnostic illustrating crowding as additional tasks are learned](assets/tood-slide14-0.webp) New classes occupy feature-space regions that previously separated known inputs from outliers. **TOOD corrects output scores; it does not restore lost feature-space margins.** --- ## TOOD: animated overview Animated illustration of old-task ID scores drifting toward OOD scores, followed by TOOD grouping task responses, aligning their scores, and taking the strongest response

Illustration of score drift and calibration, not measured experimental data

Note: Animation supplied from LinkedIn. It illustrates the core maximum-score variant without the optional top-two margin. Calibration uses familiar examples; the input's task label is not required at prediction time. --- ## Why a global score shift is insufficient AUROC depends on sample ranking.
$$\operatorname{AUROC}(g\circ S)=\operatorname{AUROC}(S)$$
for any **strictly increasing** transformation $g$. TOOD calibrates each task’s response **before combining responses**, allowing different samples to change their order. Note: Strictly increasing is necessary here: a decreasing transformation reverses score orientation, while a non-strict transformation can introduce ties. --- ## Step 1: per-task energy Group the classifier’s logits by the classes introduced in each task:
$$E_t(x)=\log\sum_{c\in\mathcal C_t}\exp(h_c(x))$$
- One response for every task seen so far. - Preserve information obscured by a single global score. - Use the sign-reversed energy convention: **higher means more ID-like**. Note: Task partitions are known from training. The input's task identity is not supplied at inference. --- ## Step 2: mean-shift calibration Estimate each task’s mean energy $\mu_t$ on its own familiar calibration examples.
$$E_t^{\mathrm{ms}}(x)=E_t(x)+(\mu_{\mathrm{ref}}-\mu_t)$$
The newest task provides the reference. **Align the location of task scores while preserving their spread.** Note: Recompute statistics for all seen tasks under the current frozen model after each new task. Replay memory can supply the examples; otherwise use a held-out ID memory. --- ## Step 2: robust-anchor calibration Use each task’s median $\tilde e_t$ and scaled median absolute deviation $\widehat{\mathrm{MAD}}_t$:
$$E_t^{\mathrm{rob}}(x)=\frac{E_t(x)-\tilde e_t}{\widehat{\mathrm{MAD}}_t}\widehat{\mathrm{MAD}}_{\mathrm{ref}}+\tilde e_{\mathrm{ref}}$$
**Align location and spread using statistics less sensitive to outliers.**

Requires representative ID memory and a nonzero, numerically stabilized scale.

--- ## Step 3: combine calibrated responses Core score:
$$S_{\mathrm{TOOD}}(x)=\max_t E_t^{\mathrm{norm}}(x)$$
Optional top-two margin, with $E_{(1)}\ge E_{(2)}$:
$$S_\lambda(x)=E_{(1)}^{\mathrm{norm}}+\lambda\left(E_{(1)}^{\mathrm{norm}}-E_{(2)}^{\mathrm{norm}}\right)$$

$\lambda=0$ gives the core score; main experiments use $\lambda=0.5$.

Note: A high response from at least one task suggests ID. The margin rewards a clear task preference. With one task, use the core score rather than a nonexistent runner-up. --- ## Calibration and inference **After each task** 1. Freeze the current learner. 2. Forward the ID memory through it. 3. Estimate and store statistics for every seen task. **For each test input** Compute task energies → normalize → maximum plus optional margin.

No retraining, no OOD calibration examples, no change to class predictions.

--- ## Experimental protocol | Dataset | Learning stream | Backbone | | :--- | :--- | :--- | | CIFAR-10 | 5 × 2 classes | ResNet-32 | | CIFAR-100 | 10 × 10 classes | ResNet-32 | | ImageNet-1K | 100 × 10 classes | ResNet-18 | - CIFAR learners: iCaRL, BiC, DER, WA, LwF. - Near- and Far-OOD evaluation following OpenOOD. - ID memory: 200 examples for CIFAR-10; 700 for CIFAR-100. Note: Main CIFAR results average three seeds. The ImageNet scalability study uses one seed. ViT-B/16 appears in additional diagnostics. --- ## CIFAR-10 results Average incremental AUROC (%) · mean ± standard deviation, three seeds | Learner | Energy | Mean Shift | Robust Anchor | | :--- | ---: | ---: | ---: | | iCaRL | 65.9 ± 1.5 | 66.5 ± 1.5 | 66.4 ± 1.4 | | BiC | 67.2 ± 1.0 | **71.6 ± 0.2** | 70.6 ± 0.3 | | DER | 61.2 ± 0.7 | **69.3 ± 0.9** | 68.6 ± 0.9 | | WA | 78.1 ± 2.3 | 78.3 ± 2.1 | 78.2 ± 2.4 | | LwF | 72.2 ± 0.5 | 73.2 ± 0.3 | 73.0 ± 0.7 | **DER: +8.1 AUROC points over uncalibrated energy.** Note: Results are averaged over the learning sequence and Near-/Far-OOD evaluation, as reported in the local blog post and supplied deck. --- ## CIFAR-100 results Average incremental AUROC (%) · mean ± standard deviation, three seeds | Learner | Energy | Mean Shift | Robust Anchor | | :--- | ---: | ---: | ---: | | iCaRL | 58.1 ± 1.3 | 58.4 ± 1.0 | 58.9 ± 1.0 | | BiC | 65.6 ± 0.5 | 68.4 ± 1.3 | **68.8 ± 1.6** | | DER | 64.6 ± 1.2 | **67.1 ± 0.5** | 66.1 ± 0.9 | | WA | **71.9 ± 0.1** | 71.7 ± 0.2 | 71.5 ± 0.1 | | LwF | **67.0 ± 1.6** | 66.7 ± 1.7 | 66.3 ± 1.6 | **Benefit depends on the learner; WA and LwF slightly decline.** --- ## ImageNet-1K: 100 tasks Average incremental AUROC (%) · single seed | Learner | Energy | Mean Shift | Robust Anchor | | :--- | ---: | ---: | ---: | | BiC | 59.2 | **65.2** | 65.1 | | WA | **70.1** | 65.7 | 65.6 | | DER | 70.2 | **71.4** | 70.5 | Mean Shift improves BiC by **6.0 points** and DER by **1.2 points**. WA falls by **4.4 points**: calibration is not a universal upgrade. --- ## Scope and limitations - Requires known training task partitions and representative ID memory. - Corrects task-wise score drift, rather than feature-space crowding. - Gains vary with the learner and its existing output correction. - Evaluate detection throughout learning, alongside classification retention. > Calibrate the response to each known task before deciding whether an input is unknown. ---

Questions & discussion

# TOOD [Paper · arXiv:2607.29592](https://arxiv.org/abs/2607.29592) [Code · tood-continual-ood](https://github.com/mostafaelaraby/tood-continual-ood) [Related presentation · GROOD](GROOD.html)

Mostafa ElAraby · Mila / Université de Montréal

Note: Source material: TOOD paper presentation.pptx and the site's TOOD publication post. Current paper metadata is verified against arXiv. Conflicting top-two ranking counts in the supplied materials are omitted; numerical results are shown directly.