FEDIN: Frequency-Enhanced Deep Interest Network

• FEDIN is a CTR prediction model that extends the Deep Interest Network with a dual-branch architecture capturing both local temporal evolution and global periodic patterns.
• It employs target-aware spectral filtering by analyzing spectral entropy to differentiate genuine user interest from noise in behavior sequences.
• The model fuses time-domain and FFT-based frequency analysis, achieving statistically significant improvements in CTR prediction across multiple datasets.

Searching arXiv for FEDIN, DIN, and related frequency-enhanced recommendation papers. Frequency-Enhanced Deep Interest Network (FEDIN) is a click-through rate (CTR) prediction model that extends the Deep Interest Network paradigm with a dual-branch time/frequency architecture. Its central premise is that user click histories contain both local temporal evolution, which is most naturally modeled in the time domain, and global periodic or harmonic patterns of genuine interest, which can be isolated more reliably in the frequency domain. FEDIN’s distinguishing claim is that frequency analysis should be target-aware rather than sequence-only: instead of analyzing a user behavior sequence in isolation, it conditions spectral processing on the candidate target item, motivated by the empirical observation that target-attention spectra exhibit lower spectral entropy for positive targets and higher-entropy, noise-like behavior for negative targets (Dai et al., 3 May 2026).

1. Position within sequential CTR modeling

FEDIN is presented for sequential recommendation in the CTR setting, where the input consists of a user behavior sequence and a candidate target item, and the output is a user interest representation for downstream CTR scoring (Dai et al., 3 May 2026). The method is explicitly framed as an extension of the classic Deep Interest Network idea, but it replaces the standard single interest extractor with a dual-branch extractor comprising a time-domain branch, a frequency-domain branch, and a user interest aggregator (Dai et al., 3 May 2026).

The motivation arises from the claim that user behavior sequences are typically mixtures of long-term periodic preferences, short-term shifts, accidental or exploratory clicks, and other forms of noise. Within this framing, time-domain models are described as effective for local order and recent interactions but sensitive to pointwise noise, whereas frequency-domain analysis provides a global view of periodicity and is naturally suited to denoising (Dai et al., 3 May 2026). FEDIN is therefore positioned against sequential CTR baselines such as DIN, DIEN, SASRec, and BERT4Rec, which are described as vulnerable to noisy clicks, exploratory behavior, and non-stationary user activity (Dai et al., 3 May 2026).

The model is also situated relative to prior frequency-based recommendation work, including FMLP-Rec, FEARec, and DIFF. In this context, FEDIN’s stated criticism of existing frequency-aware approaches is that they typically treat the user sequence alone and do not incorporate the candidate item when deciding which frequency components matter (Dai et al., 3 May 2026). This suggests that FEDIN’s novelty lies less in the use of Fourier methods per se than in the target-conditioned use of spectral information.

2. Empirical basis: spectral entropy and target-conditioned resonance

A central empirical observation in FEDIN is that user attention scores exhibit distinct spectral entropy distributions when conditioned on positive versus negative target items (Dai et al., 3 May 2026). According to the paper, positive target items produce concentrated spectral peaks and lower spectral entropy, whereas negative target items yield diffuse, high-entropy spectra resembling white noise (Dai et al., 3 May 2026).

The paper defines spectral entropy as

$H(S) = -\sum p_k \log_2 p_k$

where $p_k$ is the normalized spectral energy distribution across frequency bins (Dai et al., 3 May 2026). Under this interpretation, a genuine interest pattern is structurally coherent and resonates at a small number of frequencies, while irrelevant behavior distributes energy more broadly across the spectrum (Dai et al., 3 May 2026).

This empirical result functions as the main justification for the frequency branch. FEDIN interprets low-entropy, target-conditioned spectra as meaningful interest signals and high-entropy spectra as noise (Dai et al., 3 May 2026). A plausible implication is that the model’s frequency processing is not intended merely to compress or transform sequences, but to discriminate between coherent and incoherent target-conditioned behavioral structure.

The paper’s central hypothesis follows directly from this observation: the target item acts like a frequency selector. A user sequence may contain multiple latent periodicities, but only some are relevant to a given candidate item, so the model first computes target attention scores and only then transforms those scores into the spectral domain to identify target-conditioned resonance (Dai et al., 3 May 2026).

3. Architecture and data flow

FEDIN follows an embedding-MLP CTR pipeline. Its inputs are a user behavior sequence $\mathbf{X} \in \mathbb{R}^{L \times D}$ and a target item embedding $\mathbf{X}_{\text{tar}} \in \mathbb{R}^{D}$, and it outputs a user interest representation $\mathbf{U} \in \mathbb{R}^{D}$ for CTR prediction (Dai et al., 3 May 2026). The architecture applies RevIN preprocessing to reduce distribution shift and non-stationarity in user behavior sequences (Dai et al., 3 May 2026).

The high-level flow is described in six stages: normalize the input sequence with RevIN; extract sequential interest in the time domain; extract resonance-like interest in the frequency domain; sum the two branches; apply Top-k target attention to obtain the final user representation; and feed the representation to an MLP prediction head for CTR scoring (Dai et al., 3 May 2026). The architecture is explicitly designed to be parallelizable, so the time and frequency branches can be computed efficiently (Dai et al., 3 May 2026).

The following table summarizes the main modules described for FEDIN.

Module	Role	Key mechanism
Time-Domain Branch	Local sequential evolution	DIN-style target attention plus patching Transformer
Frequency-Domain Branch	Target-conditioned periodic interest	FFT-based target-aware spectrum filtering
User Interest Aggregator	Fusion and final selection	Summation plus Top-k Target Attention

This organization reflects the paper’s claim that local and global regularities are complementary rather than interchangeable (Dai et al., 3 May 2026). The time branch preserves temporal resolution and sequence evolution, while the frequency branch seeks coherent resonance patterns conditioned on the target item.

4. Time-domain branch

The time-domain branch is designed to preserve what DIN does well: identifying which historical behaviors are relevant to the target and modeling their temporal evolution (Dai et al., 3 May 2026). FEDIN first performs coarse filtering through target attention, but unlike standard DIN-style pooling, it retains the full weighted sequence rather than collapsing immediately to a single vector (Dai et al., 3 May 2026). The target-aware weighted sequence is given as

$$\mathbf{X}_{\text{attn}} = \text{Softmax}\!\left(\frac{\mathbf{X}_{\text{tar}}\mathbf{X}^\top}{\alpha}\right)^\top \odot \mathbf{X}$$

where $\alpha$ is a scaling factor and $\odot$ denotes element-wise multiplication (Dai et al., 3 May 2026).

This preservation of $\mathbf{X}_{\text{attn}}$ is important because it maintains temporal resolution for subsequent modeling (Dai et al., 3 May 2026). FEDIN then applies a patching Transformer: the weighted sequence is split into non-overlapping patches, padded with zeros if needed, flattened, linearly projected, and passed into a Transformer encoder (Dai et al., 3 May 2026). The output is the time-domain interest representation $\mathbf{X}_{\text{time}}$ (Dai et al., 3 May 2026).

The function of this branch is therefore twofold. First, it performs target-aware relevance selection in the spirit of DIN. Second, it models fine-grained evolution among the selected behaviors through Transformer processing over patches (Dai et al., 3 May 2026). In the paper’s terminology, this branch captures local sequential evolution, namely how user interest changes over time among target-relevant behaviors (Dai et al., 3 May 2026).

5. Frequency-domain branch and adaptive spectral filtering

The frequency-domain branch is the main novelty of FEDIN (Dai et al., 3 May 2026). It begins by computing a scalar target-conditioned relevance score for each historical behavior:

$p_k$0

which produces a length-$p_k$1 score vector (Dai et al., 3 May 2026). Rather than applying the Fourier transform to the raw sequence directly, FEDIN transforms these attention scores:

$p_k$2

where $p_k$3 denotes the FFT (Dai et al., 3 May 2026). This makes the resulting spectrum explicitly target-conditioned (Dai et al., 3 May 2026).

The transformed attention-score amplitudes are then used to modulate the spectrum of the original sequence:

$p_k$4

where $p_k$5 extracts spectral amplitude and $p_k$6 denotes broadcasting element-wise multiplication along the embedding dimension $p_k$7 (Dai et al., 3 May 2026). This mechanism reweights frequency components according to how strongly the target resonates with the behavior sequence (Dai et al., 3 May 2026).

FEDIN then applies a learnable spectral filter implemented as a complex-valued MLP:

$p_k$8

with the stated purpose of preserving amplitude-phase interactions while learning a nonlinear mapping from noisy spectral input to a cleaner interest spectrum (Dai et al., 3 May 2026). Finally, adaptive resonance scaling controls how strongly the frequency branch contributes:

$p_k$9

(Dai et al., 3 May 2026). The rationale is that not every user-item pair exhibits strong periodic structure; when the target-conditioned spectrum is clear and low-entropy, the frequency branch is amplified, and when it is weak or noisy, its influence is reduced (Dai et al., 3 May 2026).

The paper states that the frequency branch is dominated by FFT operations and runs in $\mathbf{X} \in \mathbb{R}^{L \times D}$0 time, which is cheaper than standard self-attention’s $\mathbf{X} \in \mathbb{R}^{L \times D}$1 on long sequences (Dai et al., 3 May 2026). This complexity claim is significant because it connects the model’s denoising and periodicity-detection goals to an efficiency argument rather than treating frequency modeling as purely representational.

6. Fusion, optimization, and empirical results

After obtaining $\mathbf{X} \in \mathbb{R}^{L \times D}$2 and $\mathbf{X} \in \mathbb{R}^{L \times D}$3, FEDIN fuses them by summation:

$\mathbf{X} \in \mathbb{R}^{L \times D}$4

(Dai et al., 3 May 2026). It then applies Top-k Target Attention:

$\mathbf{X} \in \mathbb{R}^{L \times D}$5

where non-top-$\mathbf{X} \in \mathbb{R}^{L \times D}$6 scores are masked to $\mathbf{X} \in \mathbb{R}^{L \times D}$7 before Softmax so that only the strongest signals contribute (Dai et al., 3 May 2026). The paper states that this reduces dilution from weak or conflicting interests and avoids the “seesaw phenomenon” known in multi-task or multi-interest settings (Dai et al., 3 May 2026).

The experimental setup reported in the paper uses Adam with learning rate $\mathbf{X} \in \mathbb{R}^{L \times D}$8, batch size $\mathbf{X} \in \mathbb{R}^{L \times D}$9, embedding dimension $\mathbf{X}_{\text{tar}} \in \mathbb{R}^{D}$0, maximum sequence length $\mathbf{X}_{\text{tar}} \in \mathbb{R}^{D}$1, and the FuxiCTR framework (Dai et al., 3 May 2026). The excerpt does not provide an explicit loss formula, although it frames the task as CTR prediction and states that the final representation is passed to an MLP prediction head (Dai et al., 3 May 2026). A plausible implication is that FEDIN follows a standard supervised binary classification setup for CTR, but the exact formula is not quoted in the provided material.

FEDIN is evaluated on three public datasets—Tmall, Taobao, and Alipay—split by global timeline, using AUC and GAUC as the primary metrics (Dai et al., 3 May 2026). The compared baselines are Sum Pooling, DIN, DIEN, SASRec, BERT4Rec, GRU4Rec, BST, and DIFF, with DIFF adapted from next-item prediction to target-aware CTR prediction by replacing its ranking output layer with an MLP head incorporating the candidate item embedding (Dai et al., 3 May 2026).

The reported main results are summarized below.

Dataset	FEDIN	Best baseline
Tmall	0.9658 GAUC, 0.9666 AUC	DIN: 0.9547 GAUC, 0.9518 AUC
Alipay	0.9335 GAUC, 0.9320 AUC	GRU4Rec: 0.9268 GAUC; SASRec: 0.9312 AUC
Taobao	0.9740 GAUC, 0.9729 AUC	DIN: 0.9689 GAUC, 0.9664 AUC

The gains are reported as statistically significant at $\mathbf{X}_{\text{tar}} \in \mathbb{R}^{D}$2 (Dai et al., 3 May 2026). The paper also states that FEDIN is more stable across datasets, especially when behavior data are sparse or noisy, and attributes this stability to the compensatory role of the frequency branch when time-domain modeling becomes unstable (Dai et al., 3 May 2026).

Ablation results further support the model design. Removing the time-domain branch, the frequency-domain branch, target-aware frequency attention, or frequency scaling all causes performance degradation (Dai et al., 3 May 2026). In particular, the “w/o Freq-Domain TA” result is used to argue that conditioning frequency analysis on the target item is critical, while “w/o Freq-Domain Scaling” indicates that adaptive trust in frequency information is beneficial (Dai et al., 3 May 2026). In synthetic noise experiments on Taobao, using both drop noise and replace noise with corruption ratios $\mathbf{X}_{\text{tar}} \in \mathbb{R}^{D}$3, the paper reports that the frequency branch is substantially more robust than the time-domain branch as noise increases (Dai et al., 3 May 2026).

7. Relation to neighboring frequency-domain models and naming distinctions

FEDIN belongs to a broader line of work that applies frequency-domain reasoning to recommendation, but it should be distinguished from other frequency-enhanced architectures. The paper explicitly places FEDIN in a line of frequency-based recommendation work including FMLP-Rec, FEARec, and DIFF, while arguing that those approaches analyze the user sequence alone and do not condition spectral selection on the target item (Dai et al., 3 May 2026).

A common source of confusion arises from the similarity between FEDIN and FEARec. FEARec, introduced as “Frequency Enhanced Hybrid Attention Network for Sequential Recommendation,” is not a Deep Interest Network variant and does not introduce a method named FEDIN (Du et al., 2023). FEARec combines time-domain self-attention and frequency-domain attention based on autocorrelation within a hybrid attention stack, together with contrastive learning and frequency regularization (Du et al., 2023). By contrast, FEDIN is a CTR prediction model with a DIN-style target-attention lineage, a frequency-domain branch built on target-aware spectrum filtering of attention scores, and a Top-k Target Attention aggregator (Dai et al., 3 May 2026).

This distinction matters conceptually. FEARec addresses sequential recommendation through hybrid attention and frequency ramp sampling, motivated in part by the claim that standard self-attention behaves as a low-pass filter (Du et al., 2023). FEDIN, in contrast, is organized around the idea that the target item acts as a frequency selector and that positive versus negative targets are separable through spectral entropy patterns in target-attention spectra (Dai et al., 3 May 2026). The two methods therefore share a frequency-domain orientation but differ in problem framing, architecture, and the role assigned to target conditioning.

Taken together, FEDIN can be understood as a model that asks two complementary questions: which past behaviors are locally relevant and how did interest evolve, and whether the candidate item activates a coherent periodic pattern rather than high-entropy noise (Dai et al., 3 May 2026). Its contribution is therefore not reducible to the generic use of FFT in recommendation. The defining feature is target-aware spectral filtering motivated by an empirical difference in spectral entropy between positive and negative target-conditioned attention patterns (Dai et al., 3 May 2026).