AdaBet: Gradient-Free Adaptation for DNNs

Updated 14 July 2026

AdaBet is a gradient-free layer selection method that uses persistent homology of activations to identify trainable layers for efficient on-device adaptation.
It computes normalized first Betti numbers from forward passes, eliminating the need for gradients, labels, or server-side meta-training.
Empirical results show improvements of up to 5% in classification accuracy and reductions in memory usage by 40%, making it ideal for constrained devices.

AdaBet denotes a gradient-free layer-selection method for efficient training and adaptation of deep neural networks, introduced in "AdaBet: Gradient-free Layer Selection for Efficient Training of Deep Neural Networks" (Tenison et al., 3 Oct 2025). It is designed for on-device retraining of pre-trained models under limited compute and memory resources, especially when adaptation to user-specific runtime data distributions is required. The method selects layers for retraining by analyzing the topology of their activation spaces through Betti numbers computed from forward passes alone, thereby avoiding labels, gradients, and server-side meta-training. In the supplied literature, the same label also appears in a distinct betting-based sequential-inference context, creating a terminological ambiguity that is best resolved by distinguishing the deep-learning method from later betting formulations.

1. Problem setting and motivation

AdaBet in its primary usage addresses efficient adaptation of pre-trained neural networks on edge and mobile devices, where user-specific runtime data distributions may differ from the data used in original pre-training (Tenison et al., 3 Oct 2025). On-device retraining can facilitate such adaptation, but full-model gradient-based optimization is often impractical because of the increasing depth of modern neural nets and the associated computational and memory overhead.

The method is positioned against layer-selection approaches that reduce training cost by selecting only a subset of layers for retraining. The stated limitation of existing methods is that they rely on labeled data, at least one full round of backpropagation, or server-side meta-training. The detailed summary specifically names TinyTrain and ElasticTrainer as examples of such prior approaches. AdaBet is introduced as a gradient-free, label-free, server-free layer selection method intended to remain suitable for constrained devices and privacy-sensitive or dynamic deployments.

This framing places AdaBet within parameter-efficient adaptation, but with a distinctive selection criterion: instead of using gradients or label-dependent importance estimates, it ranks layers by topological properties of their activations. A plausible implication is that AdaBet targets the layer-selection phase itself as the primary systems bottleneck, rather than only the optimization phase after a layer subset has already been chosen.

2. Betti numbers and activation-space topology

The central mathematical object in AdaBet is the Betti number, drawn from algebraic topology. Betti numbers $b_n$ count the number of $n$ -dimensional holes in a topological space, with $b_0$ denoting the number of connected components, $b_1$ the number of independent loops, and higher-order terms such as $b_2$ and $b_3$ counting higher-dimensional cavities (Tenison et al., 3 Oct 2025). The paper summary gives the generic homological definition

$b_n = \mathrm{rank}(H_n(\mathcal{X})),$

where $H_n(\mathcal{X})$ is the $n$ -th homology group of the activation space $\mathcal{X}$ .

AdaBet applies this formalism to layer activations. For each layer $n$ 0 in a pre-trained model, activations $n$ 1 are collected from one or more forward passes. The method then computes the first Betti number $n$ 2 of the activation space, using it as a proxy for layer learning capacity. The stated intuition is that layers whose activations exhibit more complex topology, reflected in higher $n$ 3, are likely to be more expressive and more suitable for finetuning.

Persistent homology is the computational device used to obtain these topological descriptors at different thresholds or scales. The supplied summary states that this makes the resulting features robust to noise and small perturbations in data. In operational terms, AdaBet relies on persistent-homology structure rather than gradient statistics such as Fisher information.

A crucial normalization step compensates for the tendency of raw $n$ 4 to correlate with activation size. For layer $n$ 5, AdaBet defines

$n$ 6

where $n$ 7 is the number of elements in the activation tensor of layer $n$ 8. Layers are then ranked by the normalized Betti number $n$ 9. This normalization is explicitly motivated by fairness across layers and by memory and compute constraints.

3. Selection procedure and retraining workflow

AdaBet operates through a forward-pass-only ranking stage followed by selective finetuning (Tenison et al., 3 Oct 2025). The workflow described in the summary has five steps.

First, for a batch or several batches of data $b_0$ 0, which may be unlabeled, the pre-trained DNN $b_0$ 1 is evaluated in forward propagation mode, and activations are collected for each candidate trainable layer. Second, for each activation set $b_0$ 2, the first Betti number $b_0$ 3 is computed using persistent homology algorithms; the summary names the Ripser library as an example. When batch sizes are small, activations may be accumulated over multiple batches before topological computation in order to improve stability.

Third, the normalized score

$b_0$ 4

is computed for each layer. Fourth, layers are sorted by $b_0$ 5, and the top- $b_0$ 6 fraction is selected for retraining, where $b_0$ 7 is a tunable parameter representing the training budget. The summary gives $b_0$ 8 as the example corresponding to selection of the top 10% of layers.

Fifth, only the selected layers are made trainable and updated using the dataset $b_0$ 9, while the rest of the model remains frozen. The summary states that any local optimizer and batch size may be used, with small batch size preferred for memory efficiency. The defining algorithmic property is that all selection relies solely on forward passes; no gradients, no labels, and no server meta-training are required.

This procedure differs from structured pruning and from gradient-based importance ranking. The selection target is not sparse weight elimination but identification of layers with high learning capacity under a resource budget.

4. Experimental evaluation

The empirical evaluation reported for AdaBet covers sixteen pairs of benchmark models and datasets and focuses on on-device vision tasks (Tenison et al., 3 Oct 2025). The datasets are Stanford Dogs, Oxford-IIIT Pets, CUB-200-2011, and Flowers102. The evaluated pre-trained models are ResNet50, VGG16, MobileNetV2, and ViT-B16, all pre-trained on ImageNet. Baselines are Full Training, Vanilla Transfer Learning, ElasticTrainer, PruneTrain, and Fisher Information. Unless otherwise noted, all methods are evaluated under the same selection budget, $b_1$ 0. The infrastructure is NVIDIA Tesla V100 GPU with TensorFlow and Ripser.

Category	Items
Datasets	Stanford Dogs; Oxford-IIIT Pets; CUB-200-2011; Flowers102
Models	ResNet50; VGG16; MobileNetV2; ViT-B16
Baselines	Full Training; Vanilla Transfer Learning; ElasticTrainer; PruneTrain; Fisher Information

The principal reported result is that AdaBet achieves the highest average accuracy, 76.26%, across the evaluated models and datasets at $b_1$ 1. The summary further states an average gain of 5% more classification accuracy over the best gradient-based baseline, identified as ElasticTrainer in the detailed comparison. Performance is described as especially strong on challenging fine-grained tasks such as CUB.

Systems-level gains accompany the accuracy result. Peak memory usage is reduced by about 40% on average, and by up to 76% for ViT compared to full training, because the selection stage avoids backpropagation. The selection step is reported to be 45% faster than ElasticTrainer’s gradient and dynamic-programming-based selection, and per-epoch training is about 11% faster than full training. The per-epoch cost is described as comparable to Fisher Information and Transfer Learning, but with substantially higher accuracy.

The summary also reports favorable optimization behavior: AdaBet converges as fast or faster than baselines, reaches lower final loss, and remains stable as $b_1$ 2 varies. Layer rankings are described as consistent across batches and random seeds, and the method is reported to be not sensitive to batch size when activation accumulation is used.

5. Operational properties, ablations, and interpretation

The ablation studies emphasize three operational properties of AdaBet (Tenison et al., 3 Oct 2025). First, normalization of Betti numbers by activation size yields the best trade-off. Second, partial selection controlled by $b_1$ 3 is effective: even small $b_1$ 4, such as 10% of layers, can match or surpass full fine-tuning. Third, the method works well with small batches through activation pooling over several mini-batches, which is highlighted as important for low-memory devices.

These results motivate the interpretation of the first normalized Betti number as a practical proxy for layer learning capacity. The paper does not claim a universal theorem equating topology and generalization; rather, it operationalizes a ranking signal that is inexpensive to compute and empirically effective. This suggests that topological complexity in activation space can serve as a usable indicator of retraining utility when gradient computation is too costly or labels are unavailable.

A frequent misunderstanding would be to view AdaBet merely as another compression or pruning technique. The summary instead presents it as a selection method for retraining: it identifies which layers should remain trainable under a constrained budget, while leaving the rest frozen. Another possible misconception is that its “importance” measure is a substitute for Fisher information in the same gradient-based family. The defining distinction is that AdaBet’s ranking is computed from activation topology using forward passes alone.

The method’s practical significance follows from this combination of properties: it is label-free, server-free, and forward-pass-only, yet tunable through $b_1$ 5 to trade off accuracy against memory and speed. The public code release at https://github.com/Nokia-Bell-Labs/efficient_layer_selection indicates an implementation intended for reproducible evaluation.

6. Terminological scope and distinct betting-based usages

The supplied literature also uses the label “AdaBet” in a separate line of work on horizon-aware anytime-valid testing and confidence sequences for bounded means under a strict deadline $b_1$ 6 (Taga et al., 20 Mar 2026). In that formulation, the core object is a betting or $b_1$ 7-process,

$b_1$ 8

with rejection determined by the stopping time

$b_1$ 9

and the method is cast as a finite-horizon optimal control problem on the state space $b_2$ 0. The summary describes a phase diagram in which Kelly betting, fractional Kelly, and aggressive betting are preferable in different regions, and it further reports a universal Deep Q-Network policy trained on synthetic distributions.

This betting-based usage is mathematically disjoint from the deep-learning AdaBet. The former concerns wealth processes, Ville’s inequality, deadline-aware sequential tests, and DQN-based action selection; the latter concerns persistent homology of neural activations, normalized Betti numbers, and selective finetuning of DNN layers. A plausible implication is that “AdaBet” should be read as a context-dependent label rather than a single unified methodology.

The broader betting literature in the supplied corpus reinforces this distinction. "Bayesian logistic betting strategy against probability forecasting" models forecast exploitation through Bayesian logistic regression and a capital process in the game-theoretic probability framework (Kumon et al., 2012). "Interactive rank testing by betting" introduces i-bet, an adaptive martingale-based test in randomized experiments with rejection when wealth crosses $b_2$ 1 (Duan et al., 2020). "Multi-Armed Sequential Hypothesis Testing by Betting" describes a multi-arm extension of betting-based sequential testing with oracle-style log-optimality criteria and a UCB-like allocation algorithm (Sandoval et al., 18 Mar 2026). These methods share betting language and wealth-process constructions, but not the activation-topology machinery of the DNN AdaBet.

For encyclopedic usage, the clearest resolution is therefore to treat AdaBet primarily as the gradient-free layer-selection method of (Tenison et al., 3 Oct 2025), while noting that later summaries in the sequential-testing literature also attach the same label to a separate betting-based framework (Taga et al., 20 Mar 2026).