ConceptTime: building self-grounded concept bottlenecks from prediction surprise for interpretable time series classification

Core problem: how can a time series classifier simultaneously be accurate, interpretable, and capable of calibrated abstention when evidence is insufficient. The authors argue that existing methods cannot satisfy all three at once, and that the obstacle is structural rather than engineering-related.

• Application scenarios: time series classifiers deployed in risk-sensitive domains such as healthcare, wearable sensing, environmental monitoring, and industrial telemetry need to allow inspection of the basis for decisions and to defer judgment when evidence is weak (Introduction).

• Shortcomings of existing methods: black-box classifiers pursue only accuracy; post-hoc explanation methods only describe outputs without constraining the decision process; interpretable-by-design methods are closest to the goal, but concept annotations are scarce and expensive on sequence data (Introduction).

• Core observation (chicken-and-egg problem): meaningful temporal concepts require knowing segment boundaries in order to be defined, while meaningful boundaries require knowing what concepts to look for in order to be drawn. Prior methods decouple the two steps—first segmenting with fixed windows or thresholds, then learning concepts—each sacrificing one of the three properties (Introduction).

• The paper's hypothesis: the same self-supervised signal can both locate boundaries and describe segments. A frozen probabilistic predictive model gives the distribution of the next observation; the mismatch between prediction and realized signal (predictive surprise) is a natural boundary location, and its predictive statistics simultaneously characterize segment behavior (Introduction).

• The paper proposes: ConceptTime—closed-loop segmentation and concept discovery with a single frozen autoregressive Gaussian density model (ARGDM); concepts are anchored by behavior relative to expectations rather than appearance, and prototype distance directly yields a fidelity score for abstention, without manual annotation, language models, or domain experts (Abstract).

Concept bottleneck models (CBM)

• Koh et al.'s CBM [28]—predictions pass through inspectable, intervenable intermediate concepts, but the original form requires concept annotations; subsequent label-free work mines concepts with vision-language models [45, 66, 53, 50].
• Time series CBM—Wu et al. [62] use predefined statistical summaries as clinical signal concepts; van Sprang et al. [57] use CKA-aligned concepts for prediction; Ferfoglia et al. [16] use Signal Temporal Logic predicates. The paper notes that these methods all start from a specified vocabulary and do not address how to simultaneously discover concepts and their boundaries when both duration and pattern identity are unknown.

Adaptive chunking and discrete tokenization

• BLT [46] and EntroPE [1]—BLT places boundaries at next-token entropy peaks, and EntroPE adapts this to time series (thresholding class entropy); others learn boundaries with reinforcement learning [64] and content-aware compression [4].
• TOTEM, VQShape, Chronos [55, 59, 5]—represent time series as discrete tokens using learned codebooks or value quantization. The paper notes that these methods address where to split or how to encode, but do not answer whether the predictive signal used to choose boundaries can also describe segment behavior.

Prototypes, shapes, and post-hoc methods

• Prototype/shapelet classifiers [67, 43, 21, 15, 60, 33]—use representative subsequences and local shapes for explanation. The paper notes that shape alone loses distinctions: visually identical flat segments mean different things after calm versus after a spike.
• Post-hoc explainers (TimeX, TimeX++, ShapeX, etc. [48, 34, 8, 23])—find influential regions via saliency or perturbation; the paper notes that their explanations describe the behavior of an existing classifier, whereas a concept bottleneck requires the classifier to predict based on the exposed concepts.

Selective prediction and concept-level uncertainty

• Common signals—softmax confidence [18], ensemble disagreement [29], distance-based OOD scores [30, 54, 36, 37]; in vision there are concept models that implement abstention via uncertainty heads, calibration networks, or stochastic concept layers [26, 35, 58, 27, 52].

Baselines and benchmarks: classification comparisons against ROCKET, MiniRocket, InceptionTime, TS-TCC, TimesNet, PatchTST, GPT4TS, CrossFormer, TSLANet, EntroPE, MLP (black-box/chunking class) and catch22, ProSeNet, VQShape, TOTEM (interpretable class); OOD and faithfulness comparisons against softmax, TOTEM/VQShape prototype distances, GradientSHAP, TimeX, TimeX++; benchmarks are UCI-HAR, Epilepsy, Sleep-EDF, UEA 10 datasets, FD-A to FD-D (Section 4.1).

Positioning: the authors state that ConceptTime uses a single frozen Gaussian density model for both segmentation and concept discovery, without concept annotations or language priors, and prototype distance simultaneously provides a fidelity score for abstention; in the UCI-HAR ablation, predictive moment features are 45.0 percentage points higher than raw morphology features (87.7% vs. 42.7%, Section 2).

Overall approach: ConceptTime decomposes classification into stages whose training signals do not overlap—a self-supervised density model produces all representations, clustering yields a nonparametric concept vocabulary, and a lightweight transformer head consumes labels; the path from raw signal to concept activations is fully deterministic and inspectable (Section 3).

Problem setting and ARGDM

• The input is a multivariate sequence with T steps and C channels; the ARGDM and concept vocabulary are fitted on an unlabeled corpus Du (in experiments, training inputs are used without labels) (Section 3.1).
• The ARGDM is a 4-layer causal Transformer that predicts a diagonal Gaussian distribution for the next step p_θ(x_t+1|x_{≤ t}), trained with a stepwise Gaussian NLL plus a calibration regularizer that forces the predictive variance to match the actual residual energy; the authors state that without calibration the variance degenerates into a free parameter and the downstream signatures lose interpretability (Section 3.2).
• The per-step surprise is the negative log-likelihood s_t of the realized signal under the predictive distribution; it is highest when the model is confident but predicts wrongly, exactly the regime-change points the segmenter should mark (Eq. 2).

Length-constrained adaptive segmentation

• Given the surprise sequence and a target number of segments K, dynamic programming places K−1 boundaries to maximize cumulative surprise under a per-segment length constraint [Lmin, Lmax], with complexity O(TK) (Eq. 3).
• The length constraint prevents two failure modes: single-segment degeneration on flat surprise and tail collapse where boundaries cluster at peaks (Section 3.3).

Predictive geometric signatures

• Each segment is compressed into a 2C+13-dimensional signature, all derived from ARGDM outputs, with no neural component between signal and signature (Section 3.4).
• Three feature families: predictive moments (2C+1 dimensions: mean prediction, variance, log length), residual morphology (8 dimensions: FFT peak frequency, autocorrelation, etc. computed on standardized residuals), and surprise trajectory (4 dimensions: characterizing the position and distribution of surprise within the segment).
• Signatures are standardized using 99th-percentile truncated statistics estimated on Du, preventing a single segment's outliers from overwhelming other dimensions.

Nonparametric concept vocabulary

• A diagonal-covariance GMM is fitted on the standardized signatures, with M ∈ {8, 16, 32}; the authors state this range is small enough for the concept transition matrix to be readable and large enough to ensure class separability (Section 3.5).
• Segments are mapped to prototypes via temperature-scaled soft assignment, with distance being the Mahalanobis distance weighted by component covariance (Eq. 4); the concept tensor Π ∈ R^{K×M} stacks the assignments of each segment.
• The authors state that the entire path (ARGDM, standardizer, GMM) never sees labels, so concepts are immune to the concept-leakage failure mode [42].

Classifier and fidelity score

• A lightweight classifier gψ (about 10^3–10^4 parameters) maps Π to class logits and is trained with cross-entropy; it is the only component with label supervision (Section 3.6).
• The fidelity score F(x)=exp(−1/(Kτ)∑_j d_j), i.e., the exponentiated mean of each segment's distance to its nearest prototype, with τ set to the median segment-prototype distance on Du; high F indicates the input can be described by the vocabulary, low F indicates a mechanism the vocabulary cannot cover.
• The authors emphasize that F answers a different question from softmax: softmax asks whether the classifier is confident, while F asks whether the input can be described in concept space—the latter being a representation-level question the classifier itself cannot pose (Section 3.6).

Experimental Setup

• Datasets: UCI-HAR (7352 train/2947 test, 9 channels, 6 classes), UCI Epilepsy (9200/2300, single channel, binary classification), Sleep-EDF (25612/8910, Fpz-Cz channel, 5 classes), 10 datasets from the UEA archive, Fault Diagnosis FD-A to FD-D (8184/2728, 3 classes, 4 transfer domains) (Table 5, 6).
• Configuration: ARGDM is a 4-layer causal Transformer (d=128, λcal=0.25, 50 epoch); (Lmin, Lmax)=(8, 40); K and the signature family are selected by validation set accuracy; the classifier is a 2-layer Transformer (dcls=64); results are the mean of 3 seeds (Section 4.1).
• Baselines: black-box methods ROCKET, MiniRocket, InceptionTime, TS-TCC, TimesNet, PatchTST, GPT4TS, CrossFormer, TSLANet, MLP; interpretable methods catch22, ProSeNet, VQShape, TOTEM; adaptive chunking controls ConceptTime-Static, EntroPE (Section 4.1).
• Metrics: classification accuracy (full labels, 1%, 5% label budgets); OOD detection AUROC; deletion faithfulness AUC (lower is more faithful); selective prediction AURC/E-AURC.

Main Results

Classification accuracy (%, from Table 1, Full column; see main text for the 1% column):

Swipe horizontally to read the table

Method	Category	HAR Full	Epilepsy Full	Sleep-EDF Full	UEA Full
MiniRocket	Black-box	97.31	98.26	85.91	73.80
TSLANet	Black-box	95.41	97.26	81.51	75.35
ROCKET	Black-box	93.91	97.15	76.38	72.30
TOTEM	Interpretable	83.83	94.56	67.75	52.99
VQShape	Interpretable	72.24	90.43	59.95	59.82
catch22	Interpretable	58.87	88.34	71.36	43.29
ConceptTime-Static	This paper	83.27	95.47	73.36	67.82
ConceptTime-Dynamic	This paper	88.91	98.39	78.15	71.82

• The authors state that ConceptTime-Dynamic is the strongest interpretable method on all 4 benchmarks and at all label ratios, with advantages ranging from 1.5 percentage points (Epilepsy full labels) to over 30 percentage points (HAR vs. catch22).
• Under full labels, the authors reach or exceed the black-box baselines on Epilepsy (98.39% is higher than all black-box methods in the table), and lag by 2–8 percentage points on the remaining benchmarks; under 1% labels, they exceed all black-box baselines on Epilepsy (97.91% vs. TSLANet 95.41%).
• Ablations show the gains come from the predictive geometry rather than adaptive chunking alone: replacing with equal-length windows drops HAR by 5.64 points and Epilepsy by 2.92 points; replacing with EntroPE segmentation drops by 4.5–8.5 points; replacing with the catch22 shape descriptor drops HAR by 30 points and UEA by 28 points (Section 4.2).

Cross-Domain Transfer (FD-A to FD-D, Table 2)

• What was measured: target-domain accuracy on 12 directed condition pairs. Direct (zero-shot direct application) averages 67.61%; fixing the source vocabulary and training the classifier with only 5% target labels (Source-Mθ) rises to 91.09%; training the density model also on unlabeled target-domain data (Target-Mθ) rises a further 3.28 percentage points to 94.37%, the highest mean in Panel A, ranking first in 7 directions.
• Comparison: TSLANet (masked reconstruction pretraining + full-model fine-tuning) averages 90.76%, leading in 3 directions; Source-Mθ leads in 2 directions.
• Vocabulary adaptation (Panel B): with the source density model frozen, refitting the standardizer and GMM on the target domain raises the mean from 91.38% to 91.74% (improving in 7 of 12 directions, with a maximum gain of A→D +4.67 points and a maximum drop of B→A −2.75 points); training both the density model and the vocabulary on the target domain gives 90.48%.

Selective Prediction and Faithfulness

• OOD detection (Figure 3): on HAR under 3 levels of Gaussian noise and 3 shuffle perturbations, fidelity outperforms max-softmax and the prototype distances of TOTEM/VQShape under all 6 conditions, with AUROC rising from 0.864 to 0.992 as the noise factor goes from 0.5→2.0, while the other scores are close to random. The authors state this shows that prototype-based OOD detection is not a free property of codebook methods.
• FD real condition shift (Table 13): fidelity has the best mean on 4 metrics, but AUROC is only 0.666±0.187, FPR95 reaches 0.719±0.343, and the directions vary widely.
• Deletion faithfulness (Figure 4, Appendix E.3): deleting segments step by step in order of fidelity, fidelity has the lowest deletion AUC on Epilepsy (0.804), while GradientSHAP leads on HAR (0.411 vs. fidelity 0.418); both outperform random deletion. The authors state that TimeX and TimeX++ cannot outperform random when explaining concept bottleneck classifiers.
• Selective prediction (Table 14): on Epilepsy, the E-AURC of fidelity (0.01032) is better than all TOTEM/VQShape scores, but ConceptTime's own max softmax is lower (0.00117).

Other Ablations and Analyses

• Signature family (Table 3): on HAR, predictive moments alone reach 87.7%, 45.0 points higher than raw morphology; on Epilepsy, distribution features are strongest (97.2%), and the residual-aware signature is highest overall (98.0%); on Sleep-EDF, the combination of all 4 families is best (78.3%).
• Vocabulary size (Table 3): M=128 is highest on all 3 datasets; at M=32, the gap from each dataset's best value is within 2.2 percentage points, so the authors default to M=32.
• Boundary signal (Table 3): the differences among entropy, KL, and surprise do not exceed 1.8 percentage points; the authors default to surprise.
• Unlabeled data scale (Table 8): under 1% labels on Epilepsy, going from 1% to 100% unlabeled raises accuracy by 1.72 points, while going from 50% to 100% raises it by only 0.03 points.
• Density model scale (Table 9): Tiny (about 110 thousand parameters) has the highest mean on both datasets, but the authors state that its gap from Default is small relative to seed fluctuation, and the relative advantage is uncertain.
• Matched-label control (Table 10): after aligning label and unlabeled data access, MiniRocket leads on HAR under both budgets; on Epilepsy, CT-FullU is highest at 1% labels and CT-LabelOnly is highest at 5%.

Limitations and future directions noted by the authors

• Vocabulary size must be fixed in advance (Conclusion, Limitations and Future Work).
• The meaning of each learned prototype depends on human interpretation after training (Conclusion, Limitations and Future Work).
• Hierarchical vocabularies can capture patterns at different granularities (Conclusion, future direction).
• Online updates can help the vocabulary adapt as signal patterns change (Conclusion, future direction).
• Low-fidelity segments can guide active relabeling, identifying samples that need human review (Conclusion, future direction).
• The authors plan to explore whether these concepts can help discover operating conditions, localize anomalies, and support inspectable decisions (Conclusion).

Scope of the experiments

• The benchmarks tested are UCI-HAR, Epilepsy, Sleep-EDF, the UEA 10 datasets and FD 4 operating conditions, 17 benchmarks in total (Section 4.1); main results are means over 3 seeds (Appendix Table 7 gives standard deviations).
• The synthetic perturbation experiments for OOD detection are done on HAR (Gaussian noise and shuffle, Figure 3); real distribution shift detection is done on 12 directed operating-condition pairs of FD, with mean AUROC 0.666 and FPR95 0.719 in fidelity (Table 13).
• Deletion faithfulness is evaluated on two datasets, Epilepsy and HAR (Figure 4); selective prediction (AURC/E-AURC) is evaluated only on Epilepsy (Table 14).
• The unlabeled data size sweep is conducted only on Epilepsy; the authors explain this is because the preliminary sweep on UCI-HAR covered only one seed (Appendix C.2).
• The cross-domain transfer experiments use 4 operating conditions and 12 directed pairs of FD, with a few-shot setting of 5% target labels (Table 2, Appendix D).

A methods paper on interpretable time series classification: addressing the difficulty of simultaneously achieving accuracy, interpretability, and abstention in risk-sensitive domains, the authors propose the concept bottleneck framework ConceptTime.

• Problem: the authors argue that time series concept bottlenecks involve a circular dependency between segmentation and concept definition; prior methods circumvent it with fixed windows or expert-annotated vocabularies, each sacrificing one of the three properties.
• Method: a frozen autoregressive Gaussian density model (ARGDM) predicts the observation distribution at each step, and predictive surprise locates segment boundaries via length-constrained dynamic programming; segments are characterized by signatures composed of predictive moments, residual morphology, and surprise trajectory, and clustered by GMM into concept prototypes; a lightweight classifier is trained on the concept tensor, prototype distance serves as a built-in fidelity score, and no manual annotation or language model is needed throughout.
• Classification results: on 17 benchmarks the authors claim it outperforms all interpretable baselines; Epilepsy full labels 98.39% (higher than all black-box methods in the table), 1% labels 97.91% (higher than all black-box baselines, Table 1); on HAR and Sleep-EDF with full labels it trails the best black-box baseline by several points.
• Transfer results: on the 12 directed condition pairs of FD, training a density model on the target domain plus 5% target labels averages 94.37%, higher than TSLANet's 90.76% (Table 2).
• Abstention and faithfulness: fidelity achieves the highest AUROC of 0.992 on HAR synthetic-perturbation OOD detection, outperforming softmax and TOTEM/VQShape prototype distances; deletion faithfulness is best on Epilepsy (AUC 0.804) and second to GradientSHAP on HAR; however, on FD real condition-shift detection the average AUROC is only 0.666.
• Authors' conclusion: the authors argue that anchoring concepts in predictive surprise rather than manual annotation allows interpretability, label efficiency, and reliable abstention to emerge together; limitations are that the vocabulary size must be preset and prototype meanings rely on post-hoc human interpretation.