cs.LGOct 27, 2026

CADENCE: Distributional Next-Transaction Forecasting for Business Cash-Flow Underwriting

Authors: Alexander Wu, Jingchao Huang

Organizations: Slope

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Abstract

Recurring cash flows are the backbone of cash-flow underwriting: they separate durable revenue from one-off deposits, expose standing obligations, and ultimately determine ability to pay. For small businesses, recurrence is both indispensable and hard to estimate, because much of their income arrives as ambiguous transfers, most payment streams are short, and schedules follow calendar conventions that frequency-domain methods treat as noise. We present CADENCE, Calendar-Aware Distributional Event Network for Cash-Flow Estimation, a compact causal Transformer that treats each transaction as a token and predicts the amount and a full, nonparametric timing distribution of every cash flow's next payment. Inheriting transaction semantics from an external labeler and a frozen text encoder keeps CADENCE compact yet general across the long tail of small-business counterparties, while predicting a calibrated distribution rather than an opaque embedding makes its outputs interpretable enough to feed existing underwriting models and power credit decisions. Ablations confirm the role of each design choice, with counterparty semantics driving recall on short histories, calendar inputs driving timing accuracy, and no-event supervision driving precision. Against the production FFT baseline, CADENCE improves one-day timing accuracy by 93.3% and next-event F1 by 6.7%, while producing calibrated distributions that serve directly as a confidence gate for downstream decisions. In an end-to-end credit evaluation on production applications, replacing FFT recurrence features with CADENCE features raises KS by 4.8%, raises the approval rate at a fixed loss rate by 18.2%, and lowers the loss rate at a fixed approval rate by 13.1%.

Figures & tables

Figure 1: CADENCE end to end for one example payroll stream. Each transaction becomes one event token that combines LLM-derived semantic labels with structural, amount, timing, and calendar fields. A causal Transformer reads the stream’s tokens, and from the final hidden state a time head predicts a calibrated distribution over the days to the next payment, including no event, while an amount head predicts its size. Decoding the distribution yields the underwriting features. The dashed region replaces the FFT recurrence estimator.
 FFT baselinePRAGMATREASURECADENCE
DataNone (fit per stream)24B consumer banking events6B card transactions47M business bank transactions
ObjectiveSpectral period estimateMasked modeling (encoder)Next transaction (decoder)Next event per stream (decoder)
SemanticsNoneSubword embeddings learned from scratchLearned merchant embeddingsLLM labels and frozen text embeddings
CalendarNone; fixed-period sinusoidsTimestamps as tokensNot reportedCalendar inputs; day-resolution output
OutputPeriod and strength scoresEmbedding; binary repeat-next-month taskEmbedding; next card transaction, any merchantCalibrated next-payment distribution and amount
Timing uncertaintyNoneNot predictedSingle log-normalCategorical over days, with no-event class
Table 1: CADENCE compared with the FFT baseline and transaction foundation models.
GroupInputEncoding
SemanticCounterparty (shared across the stream)Frozen BGE-small with learned projection
 Category, subcategory, payment railLearned embeddings
StructuralAccount slotLearned embedding
AmountSigned amountSigned logarithm
TimingGap since previous eventLog days and Time2Vec
CalendarDay of week, day of monthLearned embeddings
Table 2: Components of an event token.
Figure 2: Transactions as tokens. Slope TransFormer converts a raw bank descriptor into a canonical counterparty, category, subcategory, and payment rail. Each transaction then becomes a single event token: semantic inputs come from the labels, while account, amount, timing, and calendar inputs come from the raw transaction fields. A linear layer projects the token to the model width of 192.
Figure 3: Next-event prediction for one stream, illustrated with a schematic biweekly Friday payroll whose December payment was made early, on a Wednesday, before the holiday. Each past payment becomes a token, a causal Transformer summarizes the history at the last event, and two heads predict a distribution over the days until the next event, including an explicit no-event class, and the next amount. Because the model sees calendar position, it expects the schedule to return to Friday 16 days later rather than repeat a fixed 14-day interval that would land on a Wednesday. The distribution is then decoded into the recurrence features used in underwriting.
ResultRelative change
Timing within one day+93.3%
Next-event F1+6.7%
Credit-application KS+4.8%
Approval rate at fixed loss rate+18.2%
Loss rate at fixed approval rate−13.1%
Table 3: Headline results relative to the FFT baseline.
Figure 4: Direct next-payment performance, normalized so that the FFT baseline equals 100 and higher is better.
Events in historyOne-day timingNext-event precisionNext-event recall
3–5+101%+38%+510%
6–10+79%+9%+46%
11–25+78%+2%+17%
More than 25+68%<1%+7%
Table 4: Relative change versus the FFT baseline by history length, measured at a fixed recurrence threshold.
Figure 5: Four shapes of the predicted next-event distribution on validation streams: (A) a monthly payment shifted past a weekend, (B) a second-Wednesday-of-the-month payment with peaks at four and five weeks, (C) a midweek expense with irregular spacing and peaks seven days apart, and (D) an irregular stream on which the model is correctly unconfident. The strip above each panel shows the stream’s past events relative to its last event, bars show the predicted probability of the next event on each day, gray shading marks days that had already elapsed without an event at the reference date, and the orange marker shows when the next event actually occurred.
Figure 6: Calibration of the predicted distribution on validation streams. Left: predicted versus realized probability that the next event lands within one day of the most likely date. Right: predicted versus realized probability that a next event occurs within the 200-day horizon. The diagonal marks perfect calibration.
Figure 7: Why the forecast horizon must clear the quarter. Left: on-schedule gaps of 80 to 100 days between consecutive payments in regular quarterly streams; because three calendar months span 89 to 92 days, 70% exceed 90 days. Middle: a quarterly sales-tax stream scored by an earlier model with a 90-day horizon, whose daily distribution peaks one day from the actual payment while the pooled no-event outcome outranks every individual day. Right: a quarterly sales-tax stream scored by CADENCE with a 200-day horizon, which places its peak on the day of the actual payment, 91 days after the last, and leaves little probability for no event.
AblationKey metricRelative change
Remove calendar inputsExact-day timing accuracy−21%
Remove counterparty semanticsRecall on streams with 3–5 events−17%
Remove terminal no-event examplesNext-event precision−19%
Table 5: Key effect of each ablation relative to the full CADENCE model.
Figure 8: Selected ablations relative to the full CADENCE model. Calendar inputs drive exact-day timing, counterparty semantics drive short-history recall, and no-event supervision drives precision.
Figure 9: Downstream credit-application lift from CADENCE recurrence features relative to FFT recurrence features.
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