ReCross: Efficient Embedding Reduction

• ReCross is an efficient embedding reduction scheme for deep learning recommendation models that leverages correlation-aware grouping, access-aware replication, and dynamic ADC switching on ReRAM-based in-memory computing substrates.
• It co-optimizes embedding access patterns with crossbar characteristics, achieving up to 3.97x speedup and 6.1x energy efficiency improvement compared to state-of-the-art IMC approaches.
• The design assumes stable access distributions and employs a static offline mapping strategy, which may require re-profiling if workload characteristics change substantially.

Searching arXiv for the specified ReCross paper and closely related recommender/IMC work to ground the article with current citations. arXiv_search.query({"^^^^^^^^2search_query2 OR ti:\2^^^^^^^^"ReCross: Efficient Embedding Reduction Scheme for In-Memory Computing using ReRAM-Based Crossbar\"","max_results":5,"sort_by":"submittedDate","sort_order":"descending"}) ReCross is an efficient embedding reduction scheme for deep learning recommendation models (DLRMs) on ReRAM-based in-memory computing (IMC) fabric. It targets the large and sparse embedding layers that dominate DLRM inference time and energy because of high memory access costs and irregular, power-law access patterns. The scheme co-optimizes embedding access statistics with ReRAM crossbar characteristics through correlation-aware grouping, access-aware replication, and a dynamic switch ADC that selects between MAC mode and read mode according to runtime conditions. In the reported evaluation, ReCross achieves a 3.97x reduction in execution time and a 6.^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^x improvement in energy efficiency compared to state-of-the-art IMC approaches (&&&^^^^2search_query2^^^^&&&).

^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^. Problem setting in DLRM inference

DLRMs, as described in the paper, consist of a bottom MLP for dense features, large embedding tables for sparse categorical features, and a top MLP that consumes concatenated dense and reduced embedding vectors (&&&^^^^2search_query2^^^^&&&). Each embedding table is a matrix whose rows are embedding vectors, and a request looks up multiple indices and aggregates their vectors, usually by summation. The embedding layer is therefore both a storage structure and a reduction operator.

Two properties make these layers dominant. First, embedding tables can be extremely large. The paper states that Meta reports up to 4 TB of embeddings, and that in the Amazon Review workloads used in ReCross, evaluated subsets include individual tables with up to approximately 962K entries (&&&^^^^2search_query2^^^^&&&). Second, embedding accesses are highly sparse, irregular, and skewed. Each query touches only a small number of rows; accesses follow a power-law distribution; and some embeddings frequently co-occur in the same query. Empirical studies cited in the paper show that embedding lookups alone contribute 5^^^^2search_query2^^^^–75% of DLRM inference runtime and dominate energy (&&&^^^^2search_query2^^^^&&&).

The paper frames ReRAM crossbars as a suitable substrate because they implement analog matrix-vector multiplication in situ. Conductances encode stored values, applied voltages select rows, and resulting bitline currents realize dot products. This reduces data movement and offers good energy per MAC. However, naively mapping embeddings to crossbars causes poor utilization: embeddings for a single query become scattered across many arrays, many activations use only a small subset of rows or columns, ADCs must convert each activation, and the skewed access distribution creates bottleneck arrays while others remain idle (&&&^^^^2search_query2^^^^&&&). ReCross is defined precisely as a response to those pathologies.

2. Architectural substrate and hardware model

ReCross is built on a ReRAM IMC substrate modeled with NeuroSim in 22 nm. The hardware configuration reported in the paper uses PRESERVED_PLACEHOLDER_^^^^2search_query2^^^^ crossbar arrays with 2 bits per ReRAM cell, organized into PRESERVED_PLACEHOLDER_^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^ logical tiles, with 4,5^^^^2search_query2search_query2^^^^ tiles in the modeled system. Peripheral circuitry includes wordline drivers, bitline sense amplifiers, 6-bit ADCs quantized from 8-bit using NeuroSim’s non-linear quantization, and a 5^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\22^^^^-bit global bus (&&&^^^^2search_query2^^^^&&&).

The analog computation follows Ohm’s law and Kirchhoff’s current law. For a crossbar with conductance matrix $G$ and input voltages $V$, the current on column $j$ is

$I_j = \sum_i G_{ij} V_i .$

This one-shot current accumulation is used to realize embedding reduction. In the conceptual embedding-table view, rows correspond to embedding IDs and columns correspond to vector dimensions. Activating several selected rows causes each column current to be proportional to the sum of the corresponding embedding components, which is exactly the required reduction for DLRM inference (&&&^^^^2search_query2^^^^&&&).

The paper emphasizes that the baseline IMC substrate alone is insufficient. ReCross therefore adds three mechanisms: correlation-aware grouping and mapping of embeddings, access-aware crossbar allocation with replication, and a dynamic switch ADC circuit. The architecture is described as a two-phase system. The offline phase performs profiling, co-occurrence graph construction, grouping, and replication mapping; the online phase schedules lookups across crossbars and selects read or MAC conversion through a popcount-guided ADC controller (&&&^^^^2search_query2^^^^&&&).

3. Correlation-aware grouping and mapping

The first major mechanism is correlation-aware grouping. ReCross constructs a co-occurrence list from real DLRM inference traces and transforms it into a co-occurrence graph whose nodes are embeddings, whose edges indicate co-access, and whose edge weights encode co-occurrence frequency (&&&^^^^2search_query2^^^^&&&). Both access frequency and co-occurrence counts exhibit power-law behavior, so only a small fraction of embeddings account for a large fraction of graph structure and demand.

Grouping is formulated as a fixed-size partitioning problem under crossbar capacity constraints. The objective is to place frequently co-occurring embeddings in the same group so that a query can activate multiple relevant rows within one crossbar. The paper’s Algorithm ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^ grows groups greedily: it maintains a current group, a set of already assigned indices, and a candidate list of neighboring embeddings, then repeatedly selects the candidate with maximum co-occurrence weight relative to the seed embedding. Structural connectivity is preserved by merging candidate neighborhoods as the group expands (&&&^^^^2search_query2^^^^&&&).

This grouping policy is the central data-layout optimization in ReCross. By mapping co-occurring embeddings into the same crossbar, the design increases the probability that a query is served by fewer arrays, reduces the total number of crossbar activations, and correspondingly reduces ADC invocations. The paper reports that ReCross reduces crossbar activations by up to 8.79x relative to naïve mapping and by up to 5.27x relative to a frequency-only grouping approach (&&&^^^^2search_query2^^^^&&&). Those activation reductions are presented as the basis for both latency and energy gains.

A plausible implication is that grouping changes the effective granularity of in-memory reduction from per-embedding retrieval to per-co-occurrence cluster retrieval. The paper does not formalize that abstraction, but its measured activation reductions suggest that co-access structure, rather than standalone frequency alone, is the critical placement signal.

4. Access-aware replication and runtime scheduling

Grouping does not eliminate skew; after grouping, access frequency per group still follows a power law. ReCross therefore introduces access-aware replication to relieve hot spots. The paper identifies hot embeddings or groups using the same profiling data that were used for co-occurrence analysis, then computes the number of copies according to a logarithmic rule:

$${Num}_{copies} = \left\lfloor \frac{\log({freq})}{\log({freq}_{total})} \times \log({batch}_{size}) \right\rfloor .$$

Here, $\text{freq}$ is the frequency of an embedding or group, $\text{freq}_{total}$ is the normalization factor, and $\text{batch}_{size}$ bounds useful replication through available concurrency (&&&^^^^2search_query2^^^^&&&). The use of logarithms compresses the power-law dynamic range, avoiding the extreme over-replication that would result from scaling directly with raw frequency.

Replicas are placed on different crossbars while respecting capacity constraints and target duplication ratios. The paper evaluates ^^^^2search_query2^^^^%, 5%, ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2search_query2^^^^%, and 2^^^^2search_query2^^^^% extra crossbar area. More replication improves parallelism and reduces queueing delay at hot crossbars, but it also increases memory footprint and programming overhead. The reported sensitivity study shows monotonic improvements in speedup and energy efficiency as duplication ratio increases, with gains saturating because concurrency is bounded by workload structure (&&&^^^^2search_query2^^^^&&&).

The software-hardware co-design is static rather than adaptive. In the offline phase, ReCross profiles access traces, constructs the co-occurrence graph, applies grouping, computes replication counts, and preloads the embedding table into ReRAM according to the final mapping. In the online phase, each query resolves embedding IDs to crossbar locations, selects among replicas to avoid loaded instances, builds activation masks, and schedules operations across crossbars (&&&^^^^2search_query2^^^^&&&). The paper states that the mapping is static for a given model and data distribution and does not propose online remapping.

This suggests that ReCross assumes relative stability in recommender traffic. The paper makes that assumption explicit and notes that substantial distribution shift would require re-profiling and re-programming (&&&^^^^2search_query2^^^^&&&).

5. Dynamic switch ADC and in-memory reduction semantics

The third major mechanism is the dynamic switch ADC. The paper identifies the ADC as a power- and area-dominant component in crossbar-based accelerators, noting that Flash ADC cost scales with resolution and that a 6-bit Flash ADC requires 63 comparators per column (&&&^^^^2search_query2^^^^&&&). That overhead is disproportionate when an activation serves only a single embedding rather than a true multi-row reduction.

ReCross therefore equips the ADC with two modes. In MAC mode, the full 6-bit conversion is used for multi-embedding activations. In read mode, the hardware performs low-resolution conversion, effectively using 3 bits for single-embedding accesses. A popcount circuit examines the row-activation mask: if exactly one row is active, the ADC enters read mode; if more than one row is active, it enters MAC mode. A MAC-enabled control signal gates comparator banks so that unnecessary comparators remain disabled in read mode (&&&^^^^2search_query2^^^^&&&).

This control path is integrated directly into runtime operation. For each activation, the scheduler already knows which rows are active; the popcount therefore requires no software-visible annotation. The paper states that the switching is transparent to software and that read mode yields up to ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2search_query2search_query2^^^^% reduction in energy per ADC activation for MAC operations when single embedding is required, because the incremental MAC-ADC cost is avoided (&&&^^^^2search_query2^^^^&&&).

The need for this optimization is empirically supported. After grouping, the paper reports that 25.9% of crossbar activations in the software dataset and 53.5% in the automotive dataset still involve only a single embedding (&&&^^^^2search_query2^^^^&&&). ReCross exploits those single-row cases rather than forcing them through full-resolution conversion.

At the level of execution semantics, a query proceeds through index gathering, per-crossbar row-mask construction, analog activation, dynamic ADC conversion, and digital aggregation of any partial sums that remain distributed across crossbars. Grouping reduces the number of partial aggregations, replication reduces crossbar contention, and dynamic ADC switching reduces energy per activation (&&&^^^^2search_query2^^^^&&&).

6. Evaluation methodology and reported results

The evaluation uses NeuroSim-based circuit-level latency and energy estimation on the 22 nm hardware model, with popcount latency and energy taken from cited prior work. Workloads are drawn from five Amazon Review categories: Software, Office_Products, Electronics, Automotive, and Sports, with embedding counts ranging from 26,8^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^5 to 962,876 (&&&^^^^2search_query2^^^^&&&). Average query length is reported as roughly 4^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^ to 96 embeddings per query.

The baselines are a naïve mapping that preserves original itemID order and performs plain MAC-based IMC, and nMARs, described as a state-of-the-art IMC-based recommendation architecture that does not use co-occurrence-aware grouping, replication, or dynamic ADC switching (&&&^^^^2search_query2^^^^&&&). For activation-count comparison, the paper also includes a frequency-based grouping approach.

Across the five workloads, ReCross reports speedups over the naïve baseline of 2.58x, 6.7^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^x, 5.87x, 6.85x, and 5.45x, and speedups over nMARs of 2.6^^^^2search_query2^^^^x, 2.82x, 4.6^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^x, 5.48x, and 4.33x. The average improvement over nMARs is stated as approximately 3.97x (&&&^^^^2search_query2^^^^&&&). For energy efficiency, the reported factors relative to the naïve baseline are 3.6^^^^2search_query2^^^^x, ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\22^^^^.33x, 8.44x, ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\22^^^^.55x, and 9.^^^^2search_query2^^^^6x, while the reported factors relative to nMARs are ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^.39x, ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^.64x, 2.43x, 3.65x, and 2.62x (&&&^^^^2search_query2^^^^&&&).

The paper also compares against conventional CPU and CPU+GPU execution and reports average energy-efficiency improvements of 363x versus CPU-only and ^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^44.^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^5x versus CPU-GPU (&&&^^^^2search_query2^^^^&&&). Within the paper, the stated energy-efficiency summary is not fully uniform: the abstract gives 8.4x versus naïve and 6.^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^x versus nMARs, while the conclusion states 2.35x versus nMARs. The data block explicitly notes this as a minor textual inconsistency and also notes that the figures clearly show substantial gain (&&&^^^^2search_query2^^^^&&&).

The ablation narrative attributes the gains to three sources. Grouping reduces activations by up to 8.79x relative to naïve mapping; replication increases parallelism but saturates at higher duplication ratios; and the dynamic switch ADC exploits the 25.9–53.5% fraction of single-embedding activations (&&&^^^^2search_query2^^^^&&&). The reported evidence is therefore cumulative rather than monolithic: ReCross is presented as a composition of placement, allocation, and circuit-level control policies.

7. Scope, limitations, and disambiguation of the name

ReCross is explicitly an inference-time embedding reduction scheme rather than a training algorithm. Its effectiveness depends on stable access distributions, large embedding tables, skewed and co-occurring access patterns, and batch inference that exposes parallelism (&&&^^^^2search_query2^^^^&&&). The paper does not describe online remapping or adaptive reprogramming, and it does not deeply discuss accuracy loss from quantization or analog variability. Replication incurs area overhead, and the dynamic switch ADC adds a popcount circuit and gating logic, although the paper characterizes those modifications as lightweight and practical (&&&^^^^2search_query2^^^^&&&).

Within the paper’s own positioning, ReCross differs from software-only embedding optimizations, near-memory processing architectures, and earlier IMC recommender accelerators by combining graph-based co-occurrence grouping, logarithmic access-aware replication, and circuit-level ADC mode switching in one design (&&&^^^^2search_query2^^^^&&&). This is the scheme’s principal conceptual identity: it does not merely place embeddings on crossbars, but aligns workload structure with crossbar utilization and ADC cost.

The name “ReCross” is not unique across arXiv. In a separate NLP context, “ReCross” denotes a retrieval-augmentation method for unsupervised cross-task generalization in multi-task LLMs; that method retrieves upstream data using a few unlabeled target examples and fine-tunes the model for better generalization (&&&3^^^^2id:(Lai et al., 12 Sep 2025) OR ti:\2^^^^&&&). In an unrelated chemical-dynamics context, the supplied literature uses “ReCross” as shorthand for recrossing behavior on a post-transition-state bifurcating potential energy surface, where the location of a valley-ridge inflection point controls the fraction of trajectories that recross the high-energy saddle region without entering product wells (García-Garrido et al., 2021). In current hardware-recommender usage, however, ReCross most specifically refers to the ReRAM-based embedding reduction scheme introduced in 2^^^^2search_query22^^^^5 (&&&^^^^2search_query2^^^^&&&).