# alternating_updates_for_efficient_transformers__2009f06b.pdf

Alternating Updates for Efficient Transformers

Cenk Baykal Google Research Dylan Cutler Google Research Nishanth Dikkala Google Research

Nikhil Ghosh UC Berkeley Rina Panigrahy Google Research Xin Wang Google Research

It has been well established that increasing scale in deep transformer networks leads to improved quality and performance. However, this increase in scale often comes with prohibitive increases in compute cost and inference latency. We introduce Alternating Updates (Alt Up), a simple-to-implement method to increase a model s capacity without the computational burden. Alt Up enables the widening of the learned representation, i.e., the token embedding, while only incurring a negligible increase in latency. Alt Up achieves this by working on a subblock of the widened representation at each layer and using a predict-and-correct mechanism to update the inactivated blocks. We present extensions of Alt Up, such as its applicability to the sequence dimension, and demonstrate how Alt Up can be synergistically combined with existing approaches, such as Sparse Mixture-of-Experts models, to obtain efficient models with even higher capacity. Our experiments on benchmark transformer models and language tasks demonstrate the consistent effectiveness of Alt Up on a diverse set of scenarios. Notably, on Super GLUE and SQu AD benchmarks, Alt Up enables up to 87% speedup relative to the dense baselines at the same accuracy.

1 Introduction

Contemporary machine learning models have been remarkably successful in many domains, ranging from natural language [6, 20] to computer vision [56, 40]. Many of these successes have come in part through sheer scale. A vast amount of empirical studies justify the conventional wisdom that bigger (models and data sets) is better [19, 24]. Accordingly, state-of-the-art Transformer [48] models often contain billions of parameters and are trained for weeks on enormously large data sets using thousands of AI accelerators. Their immense size leads to prohibitive compute and energy costs [36] and prevents their deployment to resource-constrained applications [31].

To alleviate these costs and enable scalability of modern Transformers, a recent line of works have proposed techniques to increase the capacity of models without drastically increasing the computational costs via conditional computation. A notable paradigm is sparsely-activated networks, such as Mixture-of-Experts (Mo E) models [11, 59, 35, 1, 28, 43, 45]. The main idea of Mo E is to effectively widen each network layer by accessing dynamically invoked parameters, i.e., experts, where each expert corresponds to a small subset of disjoint parameters that can be acted on by the input. During training and inference, a given input to the network is routed to a small subset of experts (parameters) to compute the output. As a result, the computation cost remains small relative to the total number of parameters. This scheme enables models with higher capacity with only a relatively small increase in computation.

Correspondence to baykalc@google.com. Work done as an intern at Google Research

37th Conference on Neural Information Processing Systems (Neur IPS 2023).

While prior approaches in conditional computation have predominantly focused on the processing power of transformers, there is a research gap in efficiently incorporating widened learned representations. Recent works have empirically and theoretically established that a wider token representation (i.e., a larger model dimension) helps in learning more complicated functions by enabling more information to be packed in the representation vectors [19, 24, 54]. This phenomenon is also evident in modern architectures of increasing capability. For instance, the representation dimension grows from 512 (small) to 768 (base) and 1024 (large, 3B, and 11B) in T5 models [37], and from 4096 (8B) to 8192 (64B) and 18432 (540B) in Pa LM models [6]. A widened representation dimension also significantly improves performance for dual encoder retrieval models [33, 34]. However, naively widening the learned representation requires accordingly increasing the model dimension (see Fig. 1), which quadratically increases the amount of computation in the feedforward computation. In light of the above, a natural question arises: can we leverage the benefit of wider representations without incurring the additional cost of wider transformer layers?

embedding layer (2x width)

transformer layer (2x width)

transformer layer (2x width)

(a) 2x Wider Model

embedding layer (2x width)

transformer layer

lightweight corrector

lightweight

transformer layer

lightweight corrector

lightweight

(b) 2x Wider Model with Alt Up

Figure 1: An illustration of widening the token representation without (left) and with Alternating Updates (right). This widening causes a near-quadratic increase in computation in a vanilla transformer due to the increased layer width. In contrast, Alternating Updates keeps the layer width constant and efficiently computes the output by operating on a sub-block of the representation at each layer.

In this paper, we address this research gap by introducing Alternating Updates (Alt Up), a technique to incorporate wider representations in a simple and efficient way. Alt Up operates by partitioning the widened representation vector into blocks, processing only a single block at each layer, and using an efficient prediction mechanism to infer the outputs of the other blocks (see Fig. 1). Processing a single block in each transformer layer enables Alt Up to simultaneously keep the model dimension, hence the computation cost, constant and take advantage of using an increased token dimension. Unlike prior approaches, e.g., Sparse Mixture of Experts, Alt Up is easy to implement, requires minimal hyperparameter tuning, and does not necessitate sharding. Moreover, since Alt Up focuses on increasing the representation dimension, it can be applied synergistically with orthogonal techniques like Mo E [60] to obtain complementary performance gains.

In particular, our contributions are:

1. We introduce Alternating Updates (Alt Up) to bridge the research gap in efficiency techniques by enabling wider representations with little additional computation cost. Alt Up is simpleto-implement, requires minimal hyperparameter tuning, and does not necessitate sharding.

2. We develop two notable extensions of Alt Up: (i) Recycled-Alt Up, a faster variant of Alt Up that requires virtually no additional learnable parameters and (ii) Sequence-Alt Up, an extension of the Alt Up idea to the sequence dimension.

3. We present an extensive evaluation of Alt Up on T5 models on various benchmark language tasks. Our experimental results show that Alt Up and its variants uniformly lead to models with improved speed-accuracy trade-offs. Notably, on Super GLUE and SQu AD benchmarks, Alt Up enables up to 87% speedup relative to the dense baselines at the same accuracy.

2 Related Work

Prior work is rich with a diverse set of techniques to increase the efficiency of contemporary transformer models. Here, we cover the most relevant subset of state-of-the-art techniques and refer the interested reader to [47] for a more comprehensive survey.

Recent works have introduced extremely large, yet scalable models with the use of conditional routing of inputs to a learnable subset of parameters. These sparsely-activated models have achieved state-ofthe-art performance on various benchmarks [11] and exhibit favorable theoretical properties [4, 1]. Notably, the Sparse Mixture of Experts (SMo E) [45, 57, 22] family of models use a learned softmax probability distribution to conditionally direct the computation to experts, i.e., subsets of network parameters. By routing the computation to a small subset of parameters on an input-dependent basis, SMo E leads to higher capacity models with a relatively small and controllable increase in computation. Switch Transformers [12] show that routing to a single expert on an input-dependent basis reduces computation and outperforms prior SMo E approaches on language tasks. Deja Vu [32] centers around selecting subsets of the attention and MLP parameters to apply for each input (contextual sparsity). Our work is orthogonal to Deja Vu and synergistic with these approaches at large as it focuses on conditional computation.

Follow-up work on SMo E include those that improve the load balancing of experts [60, 29], use reinforcement learning to learn the routing function [7], and leverage smooth top-k expert selection [18] (see [11] for a survey). Other choices for the routing function include non-learnable ones such as Locality Sensitivity Hashing (LSH) [35] which generally maps similar inputs to the same expert, Hash Layers that use token-based hashing [43], and language-specific deterministic routing [10]. Residual Mixture of Experts [51] separates the expert weights into input-independent and input-dependent components.

Conditionally accessing external memory is another related approach to vastly increase model capacity at the cost of a relatively small increase in computation [15, 14]. For examples, Memorizing Transformers [53], Memformer [52], and Product key memory [27] leverage dynamic memory to encode and retrieve relevant information. Additional works include those that use an immensely large untrainable corpus, such as Wikipedia, REALM [17], or a 2 trillion token database, RETRO [2]. These prior works that focus on routing(expert)-based mechanisms often necessitate complicated, sharded implementations due to the sheer number of additional parameters that they introduce often on the order of billions. Our work, on the other hand, is simple-to-implement and requires virtually no hyperparameter tuning. Moreover, Alt Up can be synergistically combined with sparsely-activated models like Mo E to obtain complementary improvements in efficiency.

Additional relevant works in the realm of efficient transformers include Funnel transformers [8], Reformers [25], Performers [5], Big-Bird [58], and Long T5 [16], among others. These works notably present methods to reduce the quadratic cost of the attention mechanism of transformers. Another flavor of methods complementary to our work is that of adaptive computation, e.g., CALM [44], Dyna BERT [21] Cascade BERT [30] and Dee Cap [13], where different amounts of computational power is allotted on an example-specific basis via some type of early-exit strategy. Alt Up achieves its efficiency via the orthogonal direction of conditionally leveraging wider token representations, and hence can be easily combined with these efficiency techniques and others (e.g., quantization [55], Flash Attention [9]).

3 Alternating Updates

In this section, we introduce the method of Alternating Updates (Alt Up), an approach to enable increased token dimension with little additional computation cost.

3.1 Background

At a high level, a standard transformer with L layers generates a d-dimensional representation by applying a sequence of layers transformer layers L1, . . . , LL as follows. For a particular input token within a sequence of length N, the initial token representation x1 Rd is computed by an embedding table lookup. Subsequently, this d-dimensional representation is refined across the transformer layers by iteratively computing xi+1 = Li(xi) for each layer i [L]; here and throughout [N] denotes the set {1, . . . , N} for N N. Each transformer layer Li : Rdmodel Rdmodel has width dmodel (with dmodel = d in the standard setting) and contains an attention block and a Feed Forward (FFN) block. The width of the layer dmodel controls the dimensions of the matrices involved in the attention and FFN blocks. Consequently, the computation cost of attention and FFN scales with O(N 2dmodel) and O(Nd2 model), respectively. The output, x L+1 is the output token representation generated by the transformer. This computation is usually followed by a linear layer operation that maps from the d-dimensional representation x L+1 to |V|-dimensional logits (in O(|V|d) time), followed by a softmax non-linearity to generate the probabilities over the vocabulary V.

Increasing the representation dimension d is a way to enhance the capacity of the transformer model, as a wider representation enables the transformer to store richer information about the input and helps in learning more complicated functions [19, 24, 54]. Naively widening the token representation d requires widening each layer as well, since dmodel must match d in a standard transformer model. However, the computation time of each transformer layer grows roughly quadratically with dmodel, notably for relatively short input sequences. This means that, growing the token dimension from d to 2d, for example, leads to a model that is at least 2 times (and closer to 4 times for small N) slower than the original model with a d-dimensional representation.

3.2 Alternating Updates

The core idea of Alternating Updates is to widen the representation vector, but perform computation with a d-dimensional sub-block, and estimate the updated representation using a Predict-Compute Correct algorithm, as illustrated in Figure 1, right. More specifically, Alt Up expands the representation width from d to Kd, for integers K > 1, d > 0 (for example, K = 2 in Fig. 1), but uses layers of width dmodel = d (not dmodel = Kd) to transform the representation vector. By keeping the width of each transformer layer constant, Alt Up avoids incurring the quadratic increase in computation cost that would otherwise be present with a naive expansion of the representation.

Alg. 1 depicts the details of the per-layer computation involved in a transformer with Alt Up with a Kddimensional representation vector. The input to the Alt Up layer is assumed to be the concatenation of d-dimensional contiguous subblocks xold = concat(x1 old, x2 old, ..., x K old) Rd K. Inspired by predictor-corrector methods used to solve ordinary differential equations [3], Alt Up first generates a prediction ˆxi for each of the subblocks i [K] (Line 1). This prediction takes the form of a mixture of subblocks ˆxi = PK j=1 pi,jxj old, where pi,j R for i, j [K] are learnable scalars. Subsequently, one of the K sub-blocks is chosen and the computation with the unexpanded transformer layer of width dmodel = d is performed on this sub-block (Line 2). Finally, the result of this computation is used in the correction step to generate the updated representation for each sub-block (Line 3).

Computation time We see from Alg. 1 that Alt Up introduces negligible amount of additional computation per layer, as the prediction and correction steps involve only vector addition and scalarvector multiplications (O(d) operations). Thus, relative to the computation cost of a transformer layer with width d (which we incur on Line 2 in Alt Up), the cost of Alt Up is only an additional O(d K2) per token, where d is the original model dimension and K is the factor of increase in the representation dimension (typically K = 2 or K = 4, see Sec. 5). This additional O(d K2) cost per token is a factor of d smaller than the O(d2K2) per token cost of the FFN block alone in a K-times wider transformer layer. In fact, an Alt Up layer does not lead to an increased computation time relative to a d-width transformer layer asymptotically, since the O(d K2) additional cost per token per layer is dominated by the cost of the FFN block as K d in practice. At a higher level, Alt Up requires using an embedding table with width Kd and invoking the final linear operation with Kd-dimensional vectors. The initial embedding lookup using a wider table and the linear + softmax operation with Kd (instead of d) dimensional vectors may lead to a perceptible increase in computation time. However, since we only incur this additional cost in the beginning and the end, these factors are often inconsequential,

Algorithm 1 Alternating Updates (Alt Up) Layer

Input: xold = concat(x1 old, x2 old, ..., x K old) Rd K: d K-dimensional input representation vector to the layer, where xj old Rd, j = 1, 2, ..., K are contiguous sub-blocks of xold. Output: xnew Rd K: The layer s d K-dimensional output representation. 1: Predict: for each i [K], predict the updated representation with a trainable linear map:

j=1 pi,jxj old,

where pi,j R, i, j [K] are trainable scalars. 2: Compute: select a sub-block j [K] and update this block with L:

3: Correct: for each i [K], correct the prediction with the computation result:

xi new = ˆxi + gi( xj ˆxj ),

where gi R, i [K] are trainable scalars.

and increasingly so for deeper transformers. Nevertheless, we present an extension to Alt Up in Sec. 4 that avoids this slowdown altogether for specialized applications.

Parameter count Alt Up introduces K2+K additional learnable parameters per layer, where K2 is due to pi,j, i, j [K] and K is a result of gi, i [K]. Since K d, this is an imperceptible amount of additional parameters per layer in practice. Zooming out, Alt Up with an expansion factor of K requires a Kd-width embedding table, and consequently requires (K 1)|V|d additional parameters, where |V| is the vocabulary size. In Sec. 4, we present a variant that requires no additional embedding parameters to be added to the model.

Memory footprint Due to the increase in the representation dimension, Alt Up incurs a slightly higher activation memory footprint compared to the baseline model during training. In particular, a transformer model with L layers, model dimension h, batch size b, sequence length s, and number of attention heads a has an activation memory footprint of sbh L(34+5as/h) [26]. Adding Alt Up (with K = 2) to this model leads to an additional activation memory of (sbh + 2sbh)L = 3sbh L, which is less than 10% of the vanilla transformer s. Moreover, a significant portion of memory is used by the weight parameters which only increase marginally with Alt Up. Model parallelism and techniques such as gradient checkpointing, sequence parallelism, or selective activation recomputation can mitigate the memory impact of a wider activation vector even further. During inference, the memory footprint of activations is dominated by the Key-Value cache, which is unaffected by the additional activations introduced by Alt Up.

Selection of sub-blocks The selection of the sub-block j for the computation step in Algorithm 1 can be any user-specified technique. We consider two simple, deterministic selection methods in this paper and leave more sophisticated methods for future work: (i) same: choose the same sub-block for all the layers in a neural network and (ii) alternating (default method): for a sequence of layers, alternating through the sub-blocks, that is, if the sub-blocks are indexed with zero-based index, then sub-block ℓmod K is selected for the computation step for layer ℓ [L]. This alternating selection is the default for Algorithm 1 (hence the name Alternating Updates). We compare the two selection methods empirically in the supplementary material and find that using alternating blocks performs better empirically.

4 Alt Up Extensions

In this section, we present extensions of the core Alt Up idea introduced in the previous section.

4.1 Recycled-Alt Up: Faster Alt Up via embedding recycling

Embed lookup (d-dim)

Recycle by concatenating embed

Embed lookup Embed lookup 2d embedding

N transformer layers with Alt Up (2x)

Output representation (2d-dimensional)

d-dim subvector d-dim subvector subdivide into d-dim chunks

d-dim repr. add chunks to downproject to d-dimensional repr.

final softmax final softmax computation with respect to d-dim repr.

Figure 2: Recycled-Alt Up with K = 2.

The Alt Up formulation presented in Sec. 3 adds an insignificant amount of per-layer computation, however, it does require using a K-times wider embedding table. In certain scenarios where the vocabulary V is very large, this may lead to a non-trivial amount of added computation for the initial embedding lookup and the final linear + softmax operation. A colossal vocabulary may also lead to an undesirable amount of added embedding parameters. Recycled-Alt Up is an extension of Alt Up that avoids these computational and parameter costs by keeping the embedding table s width d-dimensional.

Figure 2 depicts an example application of Recycled Alt Up with K = 2. The general idea is to recycle the initial d-dimensional lookup by replicating the d-dimensional lookup K times. Hence, Recycled-Alt Up virtually adds no additional parameters relative to the baseline width d model. Subsequently, the regular Alt Up layers (Alg. 1) are applied until the last linear + softmax operation. To avoid the computational cost of this final operation, Recycled Alt Up downprojects the Kd-dimensional representation vector x L+1 Rd K to a d-dimensional representation by simply elementwise-adding the d-dimensional contiguous subblocks in O(Kd) time. Applying the linear + softmax operation on this down-projected vector implies that the computation cost of this operation is now O(|V|d) rather than O(K|V|d), effectively reducing the amount of computation by O((K 1)|V|d). Our results in Sec. 5 show that Recycle-Alt Up s improved speed and reduced parameter count may make it more appealing for certain applications.

4.2 Sequence-Alt Up: Extension of Alt Up to the sequence dimension

Here, we introduce Sequence-Alt Up, a natural extension of Alternating Updates to reduce the apparent sequence length. This extension is motivated by the computation cost associated with the cost of the attention mechanism for long input sequence lengths. Our approach is similar in its goal to that of prior techniques focused on designing efficient attention mechanisms to reduce the quadratic dependency of attention cost on the sequence length: Funnel transformers [8], Reformers [25], Performers [5], Big-Bird [58], and Long T5 [16].

Similar to the Funnel transformer [8], Sequence-Alt Up uses a simple striding operation to reduce the sequence length. Only sampled tokens are processed by the transformer layer while the rest of the tokens require little computation, leading to a computation cost reduction by a factor of k, where k is the stride parameter. In this way, Sequence-Alt Up is similar to Alt Up in that it applies the predict-compute-correct algorithm (Algorithm 1) to the sequence dimension, but it is different from Alt Up in that it does not increase the sequence dimension.

Figure 3 depicts the baseline stride-and-skip technique (left) and the proposed Sequence-Alt Up method (right). Given an input sequence of vectors (x0, x1, ..., x T 1) to a transformer layer L, we propose the following extension of Algorithm 1 to reduce the effective sequence length by a factor of k. First, we apply a lightweight predictor on the full sequence to obtain a predicted output ˆy = (ˆy0, ..., ˆy T 1). Next, we subsample the input with a fixed stride k and apply L on the subsampled input and get computed output y = ( y0, yk, y2k, ..., y (T 1)/k k) = L(x0, xk, ..., x (T 1)/k k). Finally, we use a lightweight corrector to combine ˆy and y to form the final output sequence. This design allows unsampled token vectors to obtain contextual information, even though they are not processed by the transformer layer directly analogous to the inactivated sub-blocks in original Alt Up. In contrast, a simple stride-and-skip approach (Figure 3, left) lacks the ability to bring contextual information to the skipped tokens. We present the full algorithm pseudocode and implementation details of Sequence-Alt Up in the supplementary material.

(a) Stride-and-skip (b) Sequence-Alt Up

Figure 3: An illustration of Sequence-Alt Up (right) and the baseline Stride-and-skip method (left). Sequence-Alt Up has virtually the same computation cost as Stride-and-skip, but enables contextual information passing to the skipped tokens.

In this section, we apply Alt Up and its variants to benchmark language models and tasks. We proceed by outlining the experimental setting below. In Secs. 5.1 and 5.2 we present the performance of Alt Up on standard benchmarks with varying configurations and model sizes; in Secs. 5.3 and 5.4 we evaluate the performance of Alt Up extensions and demonstrate their effectiveness. We present the full details of our evaluations and additional experimental results in the supplementary; namely, the supplementary contains additional evaluations that demonstrate the synergistic combination of Alt Up with other conditional compute techniques, additional finetune results, and complementary ablation studies. Overall, our results consistently show that Alt Up and its variants enable sizeable performance gains, e.g., up to 87% faster models, across all evaluations on standard benchmarks.

Setting We performed all of our experiments using T5-model architectures [37] of varying sizes (small, base, large, and 3B) which we pretrained on the C4 dataset for 500, 000 steps with a batch size of 256. The pretrained models were then finetuned on either the GLUE [50], Super GLUE (SG) [49], SQu AD [39] or Trivia-QA (closed-book) [23, 42] benchmark tasks for a further 50, 000 steps with a batch-size of 256. The pretraining task is to predict corrupted text spans, and the finetuning tasks are re-cast into text generation tasks. We report both pretraining and finetuning metrics: for pretraining, we report span prediction accuracy on a hold-out validation set, and for finetuning, we follow the same recipe as the T5 models, see [37] for more details. The supplementary contains the full details of our evaluations and hyperparameters.

5.1 Alternating updates on benchmarks

First, we investigate whether incorporating Alt Up on a baseline model leads to an unambiguously better model when we consider the predictive performance and actual observed latency (not theoretical FLOPS). To this end, we compare the dense T5-Base/Large/XL models to models augmented with Alt Up with K = 2 on GLUE, Super GLUE, SQu AD, and Trivia QA (closed-book) finetuning tasks. Figure 4 plots the performance and normalized speed of the evaluated models.

As the figure depicts, models augmented with Alt Up are uniformly faster than the extrapolated dense models at the same accuracy. For example, we observe that a T5 large model augmented with Alt Up leads to a 27%, 39%, 87%, and 29% speedup on GLUE, Super GLUE, SQu AD, and Trivia-QA benchmarks, respectively. Moreover, we see that Alt Up s relative performance improves as we apply it to larger models (compare relative speedup of T5 Base + Alt Up to that of T5 Large + Alt Up). This demonstrates the scalability of Alt Up to and its improved performance on even larger models. Overall, Alt Up consistently leads to models with better predictive performance than the corresponding baseline models with the same speed on all model sizes and benchmarks.

(b) Super GLUE

B + Alt Up2x

L + Alt Up2x

XL 87% rel. speedup

34% rel. speedup

(d) Trivia-QA

Figure 4: Evaluations of Alt Up on T5 models of various sizes and popular benchmarks. Alt Up consistently leads to sizeable speedups relative to baselines at the same accuracy. Latency is measured on TPUv3 with 8 cores. Relative speedup is defined as latency delta divided by Alt Up latency.

5.2 Alt Up with varying representation size

In the previous subsection, we had used a value of K = 2 for the runs with Alt Up. As discussed in Sec. 3, K controls the width of the representation vector, and is the only hyperparameter required by Alt Up. Can we obtain even more performant models by using a larger expansion factor K? Here, we compare the performance of Alt Up with K = 2 to Alt Up with a larger expansion factor K = 4.

Table 1: Performance of Alt Up with varying representation dimension scaling parameter K on T5.

Model Pretrain Accuracy GLUE SG SQu AD (EM/F1) Trivia QA (EM/F1)

S 61.21 75.83 59.52 76.44/84.97 19.03/22.83 S + Alt Up (K=2) 61.86 76.82 59.60 77.51/85.79 19.27/22.95 S + Alt Up (K=4) 62.00 76.40 59.54 76.38/84.86 19.07/22.84 B 66.42 84.25 73.56 83.78/91.19 23.1/27.56 B + Alt Up (K=2) 66.96 85.32 75.80 85.24/92.36 24.35/28.78 B + Alt Up (K=4) 67.18 84.95 78.91 84.82/92.07 24.41/28.90 L 69.13 87.23 81.21 86.77/93.56 26.15/30.76 L + Alt Up (K=2) 69.32 88.20 82.75 87.81/94.29 27.10/32.04 L + Alt Up (K=4) 69.55 88.42 82.94 87.59/94.02 27.36/32.42

Table 1 summarizes the results with Alt Up instantiated on T5 small, base, and large sized models with hyperparameter K = 2 and K = 4. We observe that a larger value of K = 4 leads to strict improvements in pretrain accuracy over Alt Up with K = 2 for all models (Table 1, column 2). This is perhaps intuitive, as a wider representation vector enables more information to be learned during the pretraining stage. Interestingly, however, a larger K does not always lead to better finetune performance, especially for smaller models. For example, despite having a worse pretrain accuracy, Alt Up with K = 2 is better than Alt Up with K = 4 on all finetune tasks GLUE, Super GLUE, and SQu AD. We see a similar phenomenon occur for the Base model, but here K = 4 is better on GLUE;

and on Large, the trend reverses: K = 4 is better on every metric except for SQu AD. Our results indicate that a larger value of K has potential to increase the performance of models on pretrain and fine-tune metrics when Alt Up is applied to larger models. We note that there is an inherent trade-off between a larger factor K and trainability, however, as a larger value of K leads to less frequent activation of each sub-block which may impair performance. We envision that practitioners can pick a value of K other than the default K = 2 to optimize performance on an application-specific basis.

5.3 Recycled-Alt Up

Next, we consider the performance of the lightweight extension of Alt Up, Recycled-Alt Up, introduced in Sec. 4. We apply Recycled-Alt Up with K = 2 to T5 base, large, and XL models and compare its pretrain accuracy and speed to those of baselines. We record both the training speed and inference speed of the resulting models. Since Recycled-Alt Up does not require an expansion in the embedding table dimension (see Sec. 4), we remark that the models augmented with it have virtually the same number of trainable parameters as the baseline models.

Figure 5: Recycled-Alt Up on T5-B/L/XL compared to baselines. Recycled-Alt Up leads to strict improvements in pretrain performance without incurring any perceptible slowdown.

The results of our experiments are shown in Fig. 5. The figures for both the training and inference speed show that models with Recycled-Alt Up clearly improve over baselines in pretrain accuracy, without any perceptible slowdown. While Recycled-Alt Up s predictive strength generally falls below that of standard Alt Up (cf., pretrain values for Alt Up in Table 1), its improved speed and reduced parameter count may make it more suitable for certain applications see Recycled-Alt Up Fine-tune evaluations in the Appendix (Sec. G). We present additional fine-tuning results with Recycled-Alt Up in the supplementary material; overall, our results demonstrate that Recycled-Alt Up is similarly effective on fine-tuning tasks.

5.4 Sequence-Alt Up

Here, we evaluate Sequence-Alt Up (from Sec. 4) to reduce the apparent sequence length for the T5 base model. In particular, we apply average pooling, stride-and-skip, and Sequence-Alt Up to the encoder layers to reduce the apparent input sequence length. We apply stride-and-skip and Sequence-Alt Up to layers 2, . . . , L 1 of the encoder, rather than all the layers, with stride length 4 as we found that this configuration results in a better accuracy/speed trade-off for both techniques. For average pooling, the sequence length is immutably reduced from the start according to the method.

Table 2: Performance and pretrain speed of different methods for sequence length reduction on T5.

Model Pretrain Accuracy Finetune GLUE Finetune SG Speed

S 61.21 59.52 76.44/84.97 166.1 B (Baseline) 66.42 73.56 83.78/91.19 52.4 Average pooling 63.89 57.85 71.37/81.87 91.9 Stride-and-Skip 65.02 65.98 79.72/87.64 79.4 Sequence-Alt Up 65.39 66.94 81.67/89.37 74.9

Table 2 presents the comparisons on pretrain and finetune metrics (GLUE and Super GLUE) and pretrain speed (measured by the number of sequences per second per core). The table additionally lists the relevant metrics for T5 Base (which is the baseline model) and T5 Small as reference points in the table. We observe that average pooling gives a large speed-up, but suffers from severe quality degradation, especially on the finetune metrics where it performs even worse than T5 small. Stride-and-skip and Sequence-Alt Up, on the other hand, offer an improved quality and speed trade-off relative to T5 Base. In particular, Sequence-Alt Up is only slightly slower than stride-and-skip (yet, still 40% faster than the baseline), but is much closer to the baseline model s quality.

6 Conclusion

We propose the method of Alternating Updates (Alt Up) to increase the capacity of modern transformer models without incurring a significant increase in latency. Our approach bridges the research gap in efficient transformers by enabling the use of wider token representations without widening the transformer layers. Alt Up utilizes lightweight prediction and correction steps to update a wider representation vector without increasing the transformer layer s computation cost. As a result, we achieve strong performance improvements on language modeling and language understanding benchmarks. We present extensions of Alt Up that enable additional gains in efficiency. Given its orthogonal scope, Alt Up can be synergistically applied with existing techniques like Mo E. On popular language understanding and QA benchmarks, Alt Up enables up to 87% speedup relative to the dense baselines at the same accuracy.

Limitations and future work A current limitation of the technique we propose is the lack of a deep theoretical understanding of its properties due to the complicated nature of rigorously analyzing transformer models. An interesting open question is whether it would be possible to analyze Alt Up by relating its performance to a block compressed layer, and transitively relating that to a wide layer without block compression. A deeper understanding of Alt Up may also shed light on the optimal hyperparameter K on an application-specific basis. In future work, we plan to conduct a theoretical investigation of alternating updates to develop a deeper understanding of its effectiveness across differing applications. We also plan to experiment with the use of a very large expansion factor K.

Broader Impact Training and deploying modern neural network models consumes colossal amounts of resources. This leads to detrimental effects on the environment and hampers the widespread applicability and democratization of AI. We envision that Alt Up can serve as a valuable component of efficient architectures of the future and help alleviate these negative impacts.

Acknowledgments

We would like to thank Ravi Kumar, Erik Vee, and Nikhil Vyas for constructive discussions and their feedback.

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Supplementary Material for Alternating Updates for Efficient Transformers

In this supplementary, we present the full details and hyperparameters of our evaluations, provide details of our algorithmic contributions, and present complementary empirical results that support the effectiveness the presented work.

A Experimental Setup

We experiment with various T5 baseline model sizes: small (S), base (B), large (L), and XL. The base (B), large (L), and XL models follow the same model configurations as in the T5 paper, while the small model is shallower than the T5 paper [37] to cover a larger range of model sizes (4 encoder/decoder layers instead of 8 encoder/decoder layers). In particular, we use the T5 version 1.1 models with gated GELU feedforward network and pre layer norm. The models are implemented on top of the T5X [41] codebase. During pretraining, we use 256 batch size, Adafactor optimizer [46] with base learning rate 1.0 and reciprocal square-root decay with 10000 warmup steps, and zero dropout. During finetuning, we use 256 batch size, Adafactor optimizer with constant learning rate of 0.001 and 0.1 dropout. Unless explicitly stated, we pretrain for 500k steps and finetune for 50k steps. Our experiments were implemented in Python and run on TPUv3 with 8 cores.

B Parameter Counts and Speed

Here, we present the number of additional parameters needed by adding Alt Up, its speed, and its pretrain accuracy on T5 models of varying sizes. In the following tables, the embedding parameters include input embedding table parameters (shared between encoder and decoder) and output embedding table. Non-embedding parameters include all the transformer blocks. Train speed is measured by number of examples per second per core. Table 3 documents the parameter count and training speed comparison. Note that Alternating Updates increases the number of embedding parameters while leaving the non-embedding parameters roughly the same. Since the narrow transformer layer computation is not changed by alternating updates and since the predict and correct steps are lightweight (see Sec. 3), we incur a relatively small increase in the computation cost compared to a dense 2x width model.

Model # emb params # non-emb params train speed

S 3.29E+07 3.78E+07 166.1 S + Alt Up 6.58E+07 3.99E+07 119.4 B 4.93E+07 1.98E+08 52.4 B + Alt Up 9.87E+07 2.12E+08 42.3 L 6.58E+07 7.17E+08 17.1 L + Alt Up 1.32E+08 7.68E+08 14.4

Table 3: Model size and train speed comparisons on T5X models with Alt Up instantiated with K = 2.

Table 4 documents the parameter count, training speed and pretrain accuracy comparison when the representation dimension is scaled up with Alt Up or dense scaling. Note that Alternating Updates increases the number of embedding parameters while leaving the non-embedding parameters roughly the same, providing an efficient way to scale up the representation dimension relative to a K-times wider model.

Table 5 contains pretrain performances for T5 XL sized models. We note the Alt Up technique continue to offer quality boost at the billion parameters scale (note that T5XL has roughly 3B parameters), suggesting that Alt Up is a robust technique for increasing model capacity for modern large language models.

C Combination with Mo E

Here, we investigate whether Alt Up can be combined with orthogonal techniques, namely Mo E, to obtain additive performance gains in pretrain accuracy for T5 small, base, and large models. In

Model # emb params # non-emb params Train speed Pretrain accuracy

T5 Base 4.93E+07 1.98E+08 52.4 65.29 T5 Base + Alt Up2x 9.87E+07 2.12E+08 42.3 65.78 T5 Base + Dense2X 9.87E+07 3.97E+08 32.9 66.45 T5 Base + Alt Up4x 1.97E+08 2.41E+08 28.1 66.00 T5 Base + Dense4X 1.97E+08 7.93E+08 12.6 67.01

Table 4: Alt Up compared with dense scaling evaluated at 250k pretrain steps.

Model # emb params # non-emb params Train speed Pretrain accuracy

T5 XL 1.32E+08 2.72E+09 3.6 70.01 T5 XL + Alt Up2x 2.63E+08 2.92E+09 3.0 70.61

Table 5: Pretrain performances for T5 XL sized models. Pretrain accuracy is measured at 400k steps. Alt Up continues to offer a performance boost even on the scale of models with billions of parameters.

particular, we consider the partial experts setting similar to [38, 35], where at each layer, in addition to the layer s module, we route the input to a smaller expert module and combine the outputs of the main and auxiliary modules as the input to the subsequent layer (see Fig. 6).

(a) Mixture of Experts

(b) Mixture of Partial Experts

Figure 6: The partial experts setting in the context of the evaluations in Sec. C. The standard Mo E model (left) routes the inputs to one or more of n experts based on a routing function. Mixture of Partial Experts (right) always routes the input to the main expert and additionally routes the input to one or more partial experts; the output is a function of the main expert s and partial experts outputs.

The Mo E layer routes an input token x to k of n experts where each expert is itself a parametrized subnetwork (e.g., a fully-connected layer). Following [11], we let {Ei( )}i [n] and Ei(x) denote the set of experts and the output of lookup the input token x to expert i, respectively. For an input token x, a learnable weight matrix W is applied to obtain the logits h(x) = Wx. The lookup probabilities are computed by taking the softmax of h(x)

pi(x) = exp(hi(x)) P

j [n] exp(hj(x)) i [n].

The token x is routed to the expert(s) T [n] with the top-k probabilities p(x). Since this operation is not differentiable, the output y is computed as a probability weighted combination of the experts outputs to enable gradients to propagate back to the router parameters [45], i.e.,

i T pi(x)Ei(x).

For Mo E, we used the simplified implementation of the top-1 softmax routing of [12]. We use 128 experts each per encoder and decoder layer, with each expert representing a 2 layer fully-connected neural network with hidden dimension 16. For sake of the synergistic demonstration even with the core Mo E implementation, we did not incorporate a sophisticated mechanism for load balancing such as load balancing loss [12] or router z loss [60]. We use multiplicative jitter noise sampled from a uniform distribution over [1 ε, 1 + ε]din with ε = 0.01. The router matrix W was initialized by drawing from a zero mean Normal distribution with standard deviation 2 10 2.

Method T5 Small T5 Base T5 Large

Baseline 59.10 63.35 65.58 Mo E [60] 59.42 63.62 65.71 Alt Up (K=2) 59.67 63.97 65.73 Alt Up (K=2) + Mo E 59.91 64.13 65.95

Table 6: Pretrain accuracy at 100k steps of T5 models augmented with Alternating Updates (see Sec. 3) and Mo E. Mo E synergistically combines with Alternating Updates and enables further increases in model capacity.

Table 6 synthesizes the pretraining performance on the C4 dataset at 100k training steps of Alt Up and compared techniques on T5 Small, Base, and Large models. Perhaps most notably, we show that combining Alt Up and Mo E leads to even further sizable improvements in the pretrain performance (last row of Table 6). For example, the combination of Mo E and Alt Up improves over the baseline by 0.81, over Alt Up alone by 0.24, and over Mo E alone by 0.49. For all model sizes, the combination of Alt Up and Mo E is synergistic and leads to significant improvements compared to not only the baseline, but also to each approach in isolation.

D Alternating updates with varying block selection

In this section, we present empirical results on the alternating updates technique and comparison with other techniques that widen token representation vectors. We increase the token representation dimension by a factor of 2 (corresponding to K = 2 in Algorithm 1) unless otherwise specified. The model capacity increase comes from a wider embedding table at the bottom layer of the model while the transformer layers remain the same, which results in minimal additional computation cost.

Model Pretrain Accuracy Finetune GLUE Finetune SG Finetune SQu AD (EM/F1)

S (baseline) 61.21 75.83 59.52 76.44/84.97 S + Sum 61.67 77.54 59.63 75.06/83.82 S + Same Up 61.91 77.75 60.81 76.85/85.51 S + Alt Up 61.86 76.82 59.60 77.51/85.79 B (baseline) 66.42 84.25 73.56 83.78/91.19 B + Sum 66.82 84.85 75.2 84.36/91.36 B + Same Up 66.82 84.06 74.15 84.41/91.76 B + Alt Up 66.96 85.32 75.80 85.24/92.36 L (baseline) 69.13 87.23 81.21 86.77/93.56 L + Sum 69.09 86.18 78.93 86.19/93.08 L + Same Up 69.45 87.95 82.72 87.65/94.13 L + Alt Up 69.32 88.20 82.75 87.58/94.27

Table 7: Comparison of Algorithm 1 with various sub-block selection methods on T5-S/B/L.

In Table 7, we compare the summation method (Sum) in which additional embedding vectors are added to the token representation vector, Algorithm 1 with same block selection (Same Up), and Algorithm 1 with alternating block selection (Alt Up), all on top of the T5 version 1.1 small (S), base (B), and large (L) models. We observe the Prediction-Compute-Correct scheme as described in Sec. 3 with same and alternating block selection methods outperforms the summation method. For the small models, same block selection method performs better in most tasks, while for the base and

large models, alternating block selection method performs better in most tasks. We note all three methods bring improvements in both pretraining and finetuning, and Alt Up is generally the most effective one. While pretraining accuracies for all three methods are mostly similar, differences in finetuning metrics are large, and Alt Up generally achieves roughly twice the gains of the other two variants. Moreover, we observe that the gains of Alt Up in pretraining accuracies show diminishing returns when model sizes grows, but the gains in finetuning metrics do not.

E Additional Evaluations

In addition to the T5-based evaluations presented in the main body of the paper, we conducted a preliminary study on a lightweight BERT model. The model has 12 layers, 256 model dimension, and 4 attention heads. On a masked language pretraining task (with BERT pretraining data), lightweight BERT achieves 54.7 MLM accuracy while lightweight-BERT + Alt Up (K = 2) achieves 56.2 MLM accuracy.

In Fig. 4, we observed that Super GLUE is particularly exceptional in terms of the diminishing returns with respect to the model capacity. For example, in any of the other plots (GLUE, SQu AD, Trivia QA), we see that the dense baselines fall well below the lines formed by Alt Up s data points. In order to obtain a more direct comparison on Super GLUE, we compared L + Alt Up with a size-matched dense baseline T5L+4, which adds 4 encoder layers and 4 decoder layers to the T5L model. Note this model has the same number of parameters as L + Alt Up, but uses more computation and is roughly 10% slower than L + Alt Up. On Super GLUE, T5L+4 achieves an average score of 82.57, versus 82.75 for L + Alt Up. Therefore, Alt Up is not only faster, but more performant when compared to a dense baseline. Note that this is specific to Super GLUE, and we see larger speedups up to 87% on other datasets.

F Sequence-Alt Up Details

Here, we provide the full pseudocode of Sequence-Alt Up from Sec. 4 (see Alg. 2).

Algorithm 2 Alt Up extension to sequence dimension

Input: A sequence of vectors x = (x0, x2, ..., x T 1), where xi Rd. Transformer layer L and stride parameter k. Output: A sequence of vectors y = (y0, y2, ..., y T 1). 1: Prediction: predict the output sequence with a trainable linear map:

ˆyi = a1xi + a2x i/k k

for i = 0, 1, ..., T 1, where a1, a2 R are trainable scalars; 2: Computation: subsample the input sequence with stride k and apply the transformer layer on the subsampled sequence:

( y0, yk, ..., y (T 1)/k k) = L(x0, xk, ..., x (T 1)/k k);

3: Correction: correct the prediction with the computation result:

yi = ˆyi + b( y i/k k ˆy i/k k)

for i = 0, 1, ..., T 1, where b R is a trainable scalar.

G Recycled-Alt Up Fine-tune Evaluations

We conclude the supplementary material by presenting evaluations with Recycled-Alt Up as described in Sec. 4. Table 8 presents the results of our pretrain and fine-tune evaluations on T5 Small, Base, and Large. The pretrain accuracy is the one reported at 500k steps, and we fine-tune for an additional 50k steps for the fine-tune evaluations.

Consistent with our results presented in the main body of our paper, we observe that Alt Up and Recycled-Alt Up both provide clear and consistent gains over the baseline on virtually all pretrain

Model Pretrain Acc. GLUE SG SQu AD (EM/F1) Trivia QA (EM/F1)

S 61.21 75.83 59.52 76.44/84.97 19.03/22.83 S + Recycled-Alt Up 61.33 77.24 59.12 77.76/85.64 19.06/22.77 S + Alt Up 61.86 76.82 59.60 77.51/85.79 19.27/22.95 B 66.42 84.25 73.56 83.78/91.19 23.1/27.56 B + Recycled-Alt Up 66.63 85.60 74.83 84.81/91.93 22.72/27.15 B + Alt Up 66.96 85.32 75.80 85.24/92.36 24.35/28.78 L 69.13 87.23 81.21 86.77/93.56 26.15/30.76 L + Recycled-Alt Up 69.30 87.91 82.53 87.37/93.88 27.51/32.38 L + Alt Up 69.32 88.20 82.75 87.81 / 94.29 27.10/32.04

Table 8: The performance of baseline, Recycled-Alt Up, and Alt Up on pretrain and fine-tune evaluation metrics. Recycled-Alt Up and Alt Up were instantiated with K = 2 for all evaluations.

and fine-tune metrics. As conjectured in Sec. 4 Recycled-Alt Up generally does not provide the full benefits of Alt Up in terms of pretrain and fine-tune accuracies, however, this gap seems to shrink for larger models. Moreover, Recycled-Alt Up has the appeal that it practically adds no additional parameters to the model and, as a result, has roughly the same speed as the baseline model (see Fig. 5). Given the lightweight and latency-matching nature of Recycled-Alt Up, these improvements directly translate to clear gains over the dense baselines. We envision that Recycled-Alt Up s improved speed and reduced parameter count may make it more appealing for certain applications.