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Greedy Volume Maximization of Gradient Embeddings for Long-Tailed Frame-Level Bioacoustic Active Learning
Shiqi Zhang, Marius Faiß, Ariana Strandburg-Peshkin, Tuomas Virtanen
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Summary
The paper introduces BADGE-Greedy-DPP, a deterministic batch selection method for active learning in long-tailed, frame-level bioacoustic classification. It addresses the challenge of sparse, imbalanced data by constructing gradient embeddings from frame-wise prediction residuals, ensuring informative frames dominate the segment representation. The method greedily maximizes the volume spanned by these embeddings in gradient space, providing a theoretical approximation guarantee. Experiments on a spotted hyena dataset demonstrate that BADGE-Greedy-DPP outperforms existing baselines like MFFT and vanilla BADGE in both overall and rare-call-type performance.
Entities (9)
Relation Signals (7)
BADGE-Greedy-DPP → isa → Active Learning Strategy
confidence 95% · We propose BADGE-Greedy-DPP, a deterministic batch selector... Active learning can reduce this burden
BADGE-Greedy-DPP → uses → Gradient Embedding
confidence 92% · BADGE-Greedy-DPP... greedily adds the segment whose BADGE gradient embedding most enlarges the volume
BADGE-Greedy-DPP → evaluatedon → HyenaSET
confidence 90% · We evaluate on an extremely sparse and imbalanced spotted-hyena frame-level call-type classification dataset [35]
BADGE-Greedy-DPP → outperforms → Vanilla BADGE
confidence 90% · BADGE-Greedy-DPP achieves the best overall and rare-call-type performance among all compared query strategies, including... the two vanilla BADGE traversals.
BADGE-Greedy-DPP → outperforms → MFFT
confidence 90% · BADGE-Greedy-DPP achieves the best overall and rare-call-type performance among all compared query strategies, including MFFT
BADGE-Greedy-DPP → uses → animal2vec
confidence 88% · All methods use fixed animal2vec embeddings [23] and a 2-layer MLP head.
BADGE-Greedy-DPP → guarantees → Submodular Optimization
confidence 85% · because this log-volume objective is submodular, the greedy rule guarantees a batch value at least a (1-1/e) fraction of the optimum
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Abstract
Abstract:Bioacoustic call-type classification relies on costly expert annotation. Active learning can reduce this burden by selecting a small batch of segments for expert annotation and using the labeled segments for training the classifier. The setting is hard: the target calls are extremely sparse and the call-type distribution is long-tailed, so a tight budget must be spent on the few rare, informative segments. We propose BADGE-Greedy-DPP, a deterministic batch selector that greedily adds the segment whose BADGE gradient embedding most enlarges the volume spanned by the batch; because this log-volume objective is submodular, the greedy rule guarantees a batch value at least a (1-1/e) fraction of the optimum of this objective, a guarantee not provided by BADGE's existing k-means++ and MCMC DPP sampling heuristics. There is also a temporal granularity mismatch in the task. The acquisition function scores whole segments, yet the informative frames inside them are few. Uniform averaging therefore washes them out. We show that the BADGE construction naturally addresses this mismatch when applied frame-wise, as prediction residuals weight the aggregated pseudo-gradient, so confidently predicted no-call frames contribute little while a single uncertain rare-call frame can still set the segment's direction. Across 10 runs on a sparse, imbalanced hyena call-type dataset, BADGE-Greedy-DPP achieves the best overall and rare-call-type performance among all compared query strategies, including MFFT, the strongest non-BADGE baseline, and the two vanilla BADGE traversals.
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- Source: https://arxiv.org/abs/2607.13555v1
- Canonical: https://arxiv.org/abs/2607.13555v1
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Greedy Volume Maximization of Gradient Embeddings for Long-Tailed Frame-Level Bioacoustic Active Learning Abstract Bioacoustic call-type classification relies on costly expert annotation. Active learning can reduce this burden by selecting a small batch of segments for expert annotation and using the labeled segments for training the classifier. The setting is hard: the target calls are extremely sparse and the call-type distribution is long-tailed, so a tight budget must be spent on the few rare, informative segments. We propose BADGE-Greedy-DPP, a deterministic batch selector that greedily adds the segment whose BADGE gradient embedding most enlarges the volume spanned by the batch; because this log-volume objective is submodular, the greedy rule guarantees a batch value at least a (1−1/e)(1-1/e) fraction of the optimum of this objective, a guarantee not provided by BADGE’s existing k-means++ and MCMC DPP sampling heuristics. There is also a temporal granularity mismatch in the task. The acquisition function scores whole segments, yet the informative frames inside them are few. Uniform averaging therefore washes them out. We show that the BADGE construction naturally addresses this mismatch when applied frame-wise, as prediction residuals weight the aggregated pseudo-gradient, so confidently predicted no-call frames contribute little while a single uncertain rare-call frame can still set the segment’s direction. Across 10 runs on a sparse, imbalanced hyena call-type dataset, BADGE-Greedy-DPP achieves the best overall and rare-call-type performance among all compared query strategies, including MFFT, the strongest non-BADGE baseline, and the two vanilla BADGE traversals. 1 Introduction Manual annotation of bioacoustic datasets is expensive, especially when recordings need temporally strong annotations with onset and offset rather than only clip-level tags [31]. Active learning can reduce this effort by selecting a small batch of unlabeled audio segments for expert annotation before retraining the classifier [30, 20, 33, 27, 28, 19, 21, 18]. The difficulty in bioacoustics is that the pool is both sparse and long-tailed. Most frames contain no target sound, and the call types are imbalanced. Studies under long-tailed labels further show that minority categories stay poorly covered at tight label budgets [32, 7, 9, 5, 38, 39, 37], so a useful query strategy must keep finding the few segments that carry rare, informative content rather than re-sampling the abundant background. Most acquisition functions score a candidate by prediction uncertainty, by disagreement among a committee of models, by coverage of the feature space, or by explicit batch diversity [17, 25, 26, 10, 12, 24, 11, 4, 14, 8, 6]. Batch active learning by diverse gradient embeddings (BADGE) instead unifies uncertainty and diversity by representing each candidate with a single gradient embedding built from the model prediction [3]. These methods usually assume that each query candidate can be represented by one vector. Frame-level audio classification breaks this granularity assumption: the learner queries a whole segment, but each segment contains many frames, most of which are silent, non-target, or confidently predicted, while only a few remain uncertain. Directly averaging them into a segment vector lets the many uninformative frames wash out the few informative ones, diluting the frame-level feature that should drive acquisition. Our first contribution is a deterministic traversal for BADGE gradient-space batch selection. Original BADGE constructs each batch with either k-means++ seeding or finite-scan Markov chain Monte Carlo sampling from a fixed-size determinantal point process (MCMC k-DPP) [2, 1]. Both rules tend to select diverse samples with large gradient-embedding norms, but they are sampling heuristics and do not give a worst-case lower bound on the quality of the selected batch. We instead use greedy selection to maximize the regularized log-determinant of the selected segment embeddings, which is actually the volume they span in gradient space [16, 15]. Because this log-volume objective is monotone and submodular, at a fixed batch size the greedy traversal returns a batch whose value is at least a (1−1/e)(1-1/e) fraction of the optimum for this uncertainty-diversity proxy objective [22]. Our second contribution adapts the BADGE pseudo-gradient representation to frame-level audio active learning. Instead of uniformly averaging frame features, we construct and aggregate frame-wise pseudo-gradients weighted by prediction residuals. This maps each segment into BADGE gradient space. Because residual magnitudes are large near the decision boundary and close to zero on confidently predicted no-call frames, a few uncertain frames, even a single uncertain rare-call frame, can determine the segment’s gradient direction. The resulting representation aggregates frames by informativeness rather than by frame count, so it is better suited to sparse, long-tailed frame-level queries. We evaluate on an extremely sparse and imbalanced spotted-hyena frame-level call-type classification dataset [35]. All methods use fixed animal2vec embeddings [23] and a 2-layer MLP head. Across 10 independent runs, BADGE-Greedy-DPP achieves the best overall and rare-call-type active-learning quality among all compared strategies, including the strongest non-BADGE baseline, mismatch-first farthest traversal (MFFT) [29, 36], and two vanilla BADGE traversals. Its margin is largest on the rarest classes, consistent with the exploration hypothesis behind the greedy volume objective. 2 Method 2.1 Active-Learning Framework and BADGE Embeddings We work in a standard pool-based active-learning loop. Let LrL_r be the labeled set of audio segments and UrU_r the unlabeled pool at annotation round r. Each segment is a 10 s clip divided into T fixed-length frames, and each frame may carry any subset of 1010 call-type labels (multi-label). A classifier trained on LrL_r predicts these frame labels. The query rule ranks the unlabeled segments in UrU_r, and the top B segments (the per-round budget) are labeled by an expert at the frame level and moved from UrU_r to Lr+1L_r+1. A useful query rule prioritizes segments whose labels should improve the next classifier, either because the current prediction is uncertain or because the segment covers a poorly represented region. For segment i and frame t, the classifier produces a posterior vector it∈[0,1]10p_it∈[0,1]^10 and a penultimate-layer feature vector ith_it. Following BADGE [3], we form a pseudo label (termed a hallucinated label in the original BADGE study) by thresholding the current prediction as ^it=[it>0.5], y_it=I [p_it>0.5 ], (1) where [⋅]I[·] is the element-wise indicator, equal to one where the posterior exceeds 0.50.5 and zero otherwise. This pseudo label only builds the query representation; it is not a training target. We use it as the temporary label in a frame-wise pseudo binary-cross-entropy loss and take the gradient with respect to the final classification-layer weights. For a sigmoid multi-label head, this frame-wise gradient has the form (it−^it)⊗it(p_it- y_it) _it. We aggregate these frame-wise gradient embeddings as i=1T∑t=1T(it−^it)⊗it,G_i= 1T _t=1^T (p_it- y_it ) _it, (2) where ⊗ is the outer product. We flatten iG_i into a vector ϕi=vec(i) φ_i=vec(G_i), the segment representation used for selection. Unlike a segment-wise gradient built from a pooled segment feature and a segment-presence pseudo label, which assigns one residual to the whole segment and is blind to where frame-level uncertainty occurs, (2) keeps a separate residual for each frame. The residual it−^itp_it- y_it is largest near the decision threshold, and ith_it records where that uncertainty sits in feature space, so each frame enters the sum in (2) weighted by its own residual magnitude. The aggregation over frames is therefore uncertainty-weighted rather than a uniform mean. Boundary frames dominate iG_i, while frames the model predicts confidently (residual near zero), including the abundant no-call ones, contribute almost nothing. A segment with only a few informative frames thus keeps a distinctive embedding direction. The factor 1/T1/T scales every frame alike and serves only to keep the log-determinant objective (3) in a stable numerical range; it does not change the relative weighting among frames. Acquisition then operates on these per-segment embeddings to bound query-stage compute and candidate-embedding storage, while predictions and supervision stay frame-level. We change only the traversal rule applied to these embeddings. 2.2 Greedy DPP Traversal in Gradient Space The traversal aims to select a batch of unlabeled segments whose gradient embeddings span a large volume. For a candidate selected set S, let S _S be the matrix whose rows are the vectors ϕj:j∈S\ φ_j:j∈ S\. We score the selected set with the regularized log-determinant objective F(S)=logdet(λ+S⊤S),F(S)= ( + _S _S ), (3) where λ>0λ>0 is a small regularizer. Up to a constant, F(S)F(S) is the volume spanned by the selected gradient embeddings, the quantity a DPP rewards [16]. We build the batch greedily, at each step adding i⋆=argmaxi∉SΔ(i∣S),i = _i∉ S (i S), (4) with marginal gain Δ(i∣S) (i S) =F(S∪i)−F(S) =F(S∪\i\)-F(S) =log(1+ϕi⊤(λ+S⊤S)−1ϕi), = \! (1+ φ_i ( + _S _S )^-1 φ_i ), (5) obtained from the matrix determinant lemma. Equation (5) is the volume increase from adding candidate i to the current batch. It has a direct geometric reading: a candidate scores high when its gradient still has a large component outside the span of the already selected gradients, measured by the quadratic form ϕi⊤(λ+S⊤S)−1ϕi φ_i ( + _S _S )^-1 φ_i. The selector therefore favors segments that expand the span of the selected gradients over those that reinforce directions already well covered. We call this behavior exploration in BADGE gradient space. In addition, F is monotone and submodular in the selected set [15, 22, 34]; at a fixed batch size, deterministic greedy selection therefore achieves a (1−1/e)(1-1/e) lower bound on the optimum of this regularized log-volume proxy for batch uncertainty and diversity. What’s more, BADGE already encodes uncertainty through the pseudo-gradient construction [3], we do not need to introduce an additional weight between uncertainty and exploration. At each active-learning round, we train the classifier with the same architecture on the current labeled set, compute (2) for all unlabeled segments, select B segments greedily with (5), and request their labels. 3 Experimental Setup Table 1: Train-pool prevalence of 10 call types, sorted by segment prevalence. Segment prevalence is the fraction of 10 s segments with at least one frame of the type; frame prevalence is the fraction of 0.5 s frames carrying it. Call type Segment (%) Frame (%) feeding (fed) 8.267 5.887 regular groan (grn) 4.194 1.204 other (oth) 3.978 0.676 whoop (whp) 2.398 0.935 squeal (sql) 1.847 0.413 giggle (gig) 1.408 0.259 alarm rumble (rum) 1.273 0.303 squitter (str) 0.771 0.219 snore (snr) 0.444 0.247 growl (gwl) 0.425 0.072 Table 2: Main active-learning results over 10 runs; metrics are defined in Section 3.2. N-AULC, Rare-N-AULC, F-mAP, and F-rmAP are percentages, and QT is in seconds. ‘*’ averages reaching runs only, and ‘–’ means no run reached the reference. Bold marks the best effectiveness values, highest FS-Rch, and lowest FS-Bud. Method N-AULC Rare-N-AULC F-mAP F-rmAP R-Enr FS-Bud FS-Rch QT Random 41.3 ± 1.8 24.5 ± 2.9 48.3 ± 2.2 33.5 ± 3.2 1.03 ± 0.09 – 0% 0.00 ± 0.00 Entropy 52.1 ± 1.2 38.0 ± 3.2 60.3 ± 1.1 50.7 ± 2.5 4.57 ± 0.21 – 0% 115.60 ± 19.65 Farthest Traversal 49.9 ± 0.5 38.5 ± 0.6 55.9 ± 0.7 44.3 ± 1.6 2.32 ± 0.09 – 0% 125.16 ± 3.60 Disagreement 54.9 ± 0.7 40.9 ± 2.3 62.4 ± 0.8 53.7 ± 2.0 8.59 ± 0.17 2880 ± 164* 50% 355.32 ± 19.51 MFFT 55.5 ± 0.7 43.6 ± 2.2 63.2 ± 0.6 55.4 ± 2.0 8.72 ± 0.24 2533 ± 339* 90% 427.46 ± 78.40 Vanilla BADGE (KMeans++) 54.2 ± 1.0 43.7 ± 1.8 62.3 ± 0.4 55.5 ± 1.1 5.74 ± 0.33 2880 ± 164* 50% 125.30 ± 40.12 Vanilla BADGE (MCMC DPP) 53.0 ± 1.8 40.9 ± 3.2 61.7 ± 1.2 53.8 ± 2.8 5.36 ± 0.64 2925 ± 150* 40% 768.99 ± 17.86 BADGE Greedy DPP (proposal) 56.7 ± 0.9 47.4 ± 1.7 64.3 ± 0.6 58.6 ± 1.3 10.41 ± 0.26 2040 ± 126 100% 141.96 ± 9.77 Figure 1: Active-learning curves on the hyena frame-level call-type task. Lines show mean test mAP across 10 runs. Colored bands show min-max ranges across runs, not confidence intervals. The dashed black line and gray band show the mean and min-max range of the separate full-supervised reference. We evaluate on a hyena frame-wise multi-label call-type classification task built from preliminary version of the HyenaSET dataset [35]. The data are tracking-collar recordings from a spotted hyena clan of 19 spotted hyenas (Crocuta crocuta) in the Masai Mara National Reserve in Kenya, collected by the Mara Hyena Project, Michigan State University, and the Max Planck Institute of Animal Behavior, and contain significant collar and environmental noise. We use the fully annotated sections, where call type, onset, and offset are marked, giving about 205 hours of audio with 10 call types. The recordings are cut into non-overlapping 10 s segments, each split into 20 frames of 0.5 s. The task is sparse and long-tailed. Under 10%10\% of frames contain an annotated call. Table 1 reports the segment and frame prevalence of every call type; both span a strong long tail, from the most common type down to the three rarest, growl (gwl), snore (snr), and squitter (str). We split the segments into train, validation, and test sets in a 70/15/15 ratio, stratified by segment-level call-type label. Each method is evaluated over 10 independent runs with different random seeds. A run starts from a randomly sampled seed set of 300 labeled segments and adds nine active-learning rounds of B=300B=300 segments each, reaching a final labeled budget of 3000 segments. 3.1 Representation, Model, and Compared Methods Following common active-learning practice, we freeze the audio representation and vary only the query strategy. All methods use fixed animal2vec embeddings [23] and a 2-layer MLP head. This isolates the selection rule from representation-learning effects. The classifier is trained with binary cross-entropy loss and Adam, with model selection and early stopping on validation macro average precision (mAP). The compared query strategies are Random, Entropy, Farthest Traversal, Disagreement, MFFT [29, 36], vanilla BADGE (k-means++) [3, 2], vanilla BADGE (MCMC DPP) [3, 1], and BADGE-Greedy-DPP. Entropy, Farthest Traversal, and Disagreement operate on the same frame-level predictions, and MFFT applies mismatch-first farthest traversal. All BADGE variants use the same pseudo-gradient embedding construction in (2); they differ only in the traversal step, which selects a batch by k-means++, MCMC DPP, or our greedy log-det rule. For BADGE-Greedy-DPP, we fix the regularizer to λ=10−6λ=10^-6 as a small ridge term for invertibility and numerical stability. We also train a full-supervised reference model that uses the same protocol (data splits, animal2vec representation, MLP head, loss, optimizer, early-stopping rule, and test metric). Figure 2: Final segment-level enrichment of the three rare call types relative to their train-pool prevalences, compared across all query strategies. The dashed line at 1.0 corresponds to prevalence-matched selection. Error bars show standard deviation over 10 runs. 3.2 Metrics Our primary metric is N-AULC, which summarizes the whole learning curve instead of only the last labeled budget. We compute N-AULC as N-AULC=1b9−b0∑k=19(bk−bk−1)mk+mk−12,N -AULC= 1b_9-b_0 _k=1^9(b_k-b_k-1) m_k+m_k-12, (6) where bk=300+k⋅300b_k=300+k· 300 is the cumulative labeled budget after round k for k=0,…,9k=0,…,9, and mkm_k is the test mAP at round k. Thus, N-AULC is the budget-averaged test mAP over the learning curve and the higher the better. We compute Rare-N-AULC analogously by applying the same formula to the rare-call-type mAP over gwl, snr, str. At 3000 labeled segments, final mAP (F-mAP) and final rare-call-type mAP (F-rmAP) summarize endpoint performance. Rare macro enrichment (R-Enr) averages, over gwl, snr, and str, the ratio between selected-set and train-pool segment prevalence. FS-Bud records the first cumulative labeled budget when a run reaches the mean test mAP of the same-protocol full-supervised reference, and FS-Rch records the fraction of runs that do so. FS-Bud means and standard deviations use reaching runs only. QT sums the total query-stage wall-clock time over the nine active-learning rounds. 4 Results Table 2 and Fig. 1 show that BADGE-Greedy-DPP is the best active learner among the methods compared here. It attains the highest N-AULC (56.7%±0.9%56.7\%± 0.9\%), final mAP (64.3%±0.6%64.3\%± 0.6\%), and rare-call-type metrics. The closest competitor is MFFT; BADGE-Greedy-DPP exceeds it by +1.2+1.2 points in N-AULC, +3.8+3.8 points in Rare-N-AULC, and +1.1+1.1 points in final mAP. For reference, same-protocol full-supervised runs reach 62.2%±1.5%62.2\%± 1.5\% final mAP. Under Holm-corrected exact permutation tests [13], BADGE-Greedy-DPP improves over MFFT, vanilla BADGE (k-means++), and vanilla BADGE (MCMC DPP) by +1.2+1.2, +2.5+2.5, and +3.7+3.7 points in N-AULC (corrected p=1.60×10−3p=1.60× 10^-3, 4.87×10−54.87× 10^-5, and 3.79×10−53.79× 10^-5), and by +3.8+3.8, +3.7+3.7, and +6.5+6.5 points in Rare-N-AULC (corrected p=3.57×10−4p=3.57× 10^-4, 3.57×10−43.57× 10^-4, and 3.79×10−53.79× 10^-5). 4.1 Rare Call-Type Performance The rare-class gains reflect more than stronger overall performance. In Table 2, BADGE-Greedy-DPP has the highest Rare-N-AULC, final rare-call-type mAP, rare macro enrichment, and final count of selected segments carrying at least one rare-call-type label (496.8±11.3496.8± 11.3). Figure 2 shows the per-class pattern. Disagreement and MFFT over-sample gwl and str (mean enrichments of 14.00×14.00× and 9.97×9.97× for Disagreement, 13.51×13.51× and 10.19×10.19× for MFFT) but stay weak on snr, with mean snr enrichments of only 1.81×1.81× and 2.46×2.46×. BADGE-Greedy-DPP is more balanced across the tail, with 12.24×12.24×, 9.23×9.23×, and 9.76×9.76× enrichment for gwl, snr, and str; this is consistent with rewarding underrepresented directions in BADGE gradient space. 4.2 Full-Supervised Reference and Efficiency Trade-Off Table 2 also reports FS-Bud and FS-Rch, which quantify label efficiency and reliability against the full-supervised reference. BADGE-Greedy-DPP is the only method that reaches the mean reference in all 10 runs, doing so after 2040±1262040± 126 labeled segments (3.94%±0.24%3.94\%± 0.24\% of the full train set); MFFT reaches it in 90% of runs at 2533±3392533± 339 segments (4.89%±0.66%4.89\%± 0.66\%). 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