Memory Precision Research Articles

Retrospective cue benefits in visual working memory are limited to a single location at a time.

Working memory (WM) performance can be improved by an informative cue presented during storage. This effect, termed a retrocue benefit, can be used to study limits on how human observers prioritize information stored in WM for behavioral output. There is disagreement about whether retrocue benefits extend to multiple WM locations. Here, we hypothesized that multiple retrocues may improve some aspects of memory performance (e.g., a reduction in random guessing) while worsening others (e.g., an increase in the probability of reporting a feature presented at a non-probed location). We tested this possibility in three experiments. Participants remembered arrays of four orientations or colors over a brief delay, and spatial retrocues instructed participants to prioritize zero, one, two, or all four remembered orientations for possible report. At the end of the trial, participants recalled the orientation that appeared at one location. The results of this study revealed that participants' recall errors were lower during cue-one relative to cue-two and cue-four trials, and this benefit was driven primarily by a reduction in random guessing during cue-one trials. We found no evidence suggesting that multiple spatial cues (i.e., during cue-two trials) induced a trade-off between memory precision, random guessing, and non-target reports compared to neutral trials (i.e., cue-zero or cue-four). Thus, cuing participants to prioritize information appearing at multiple unique spatial positions led to no improvement in memory performance compared to neutral or no-cue trials, providing additional support for the view that retrocue benefits on WM performance are limited to a single spatial location at a time.

Retrieval-induced forgetting of spatial position depends on access to multiple shared features within categories

Retrieval-induced forgetting (RIF) is typically observed in verbal memory tasks, although a few studies have observed RIF in visual spatial tasks. This leaves an open question as to whether RIF depends on semantic identity to link across semantic properties of objects, or whether RIF depends on access to the perceptual features of objects. To explore RIF of spatial positions, we report three experiments utilizing a continuous measure of the accessibility and precision for objects that were distinguished by their shape, color, and spatial region. After a study phase, half of the objects in a single-color category were selectively practiced for their spatial position, by requiring the object to be placed in the exact spatial position seen previously. Finally, all objects were probed for their spatial position at test. No RIF occurred for objects that shared only one color feature but were located within the same spatial region (in Experiment 1) or when objects shared the same color, but were located within different spatial regions (in Experiment 3). However, RIF did occur when objects shared the same spatial region and the same color (Experiment 2). Overall, the interim recall of the spatial positions of cue-objects impairs access to the position of other cue-objects within the same color category, but only when these groups had sufficient overlapping and competing features. The finding that RIF only occurs to the accessibility of spatial positions, not the precision of visual spatial memory, was interpreted as consistent with inhibitory theories of forgetting.

Enhancing Stock Market Predictability: A Comparative Analysis of RNN And LSTM Models for Retail Investors

The stock markets are important components of the global financial system and have a considerable impact on an economy's growth and stability. This research article uses algorithms, notably deep learning, to increase the prediction of stock values. The efficacy and precision of long short-term memory (LSTM) and recurrent neural networks (RNN) algorithms to estimate stock prices are compared in this study. The paper investigates the potential of deep learning algorithms in creating a more predictable and trustworthy environment for the stock market. The study utilizes historical market data obtained from the Alpha Vault API and evaluates the performance of the RNN and LSTM models in forecasting stock prices. The results indicate that LSTM exhibits superior precision and is better suited for stock price prediction, while RNN faces certain challenges. Overall, this research contributes to the understanding of the application of deep learning algorithms in stock market analysis, to make informed investment decisions, thereby reducing risks and maximizing returns.

Memory discrimination is promoted by the expression of the transcription repressor WT1 in the dentate gyrus.

The hippocampus is critical for the precise formation of contextual memories. Overlapping inputs coming from the entorhinal cortex are processed by the trisynaptic pathway to form distinct memories. Disruption in any step of the circuit flow can lead to a lack of memory precision, and to memory interference. We have identified the transcriptional repressor Wilm's Tumor 1 (WT1) as an important regulator of synaptic plasticity involved in memory discrimination in the hippocampus. In male mice, using viral and transgenic approaches, we showed that WT1 deletion in granule cells of the dentate gyrus (DG) disrupts memory discrimination. With electrophysiological methods, we then identified changes in granule cells' excitability and DG synaptic transmission indicating that WT1 knockdown in DG granule cells disrupts the inhibitory feedforward input from mossy fibers to CA3 by decreasing mIPSCs and shifting the normal excitatory/inhibitory (E/I) balance in the DG → CA3 circuit in favor of excitation. Finally, using a chemogenetic approach, we established a causal link between granule cell hyperexcitability and memory discrimination impairments. Our results suggest that WT1 enables a circuit-level computation that drives pattern discrimination behavior.

Adaptive visual working memory: Expecting a delayed estimation task enhances visual working memory precision.

Two of the dominating tasks in the visual working memory (VWM) literature are the Delayed Estimation (DE) task and the Change Detection (CD) task. However, there are no studies that directly compared how participants' expectation to be tested in these tasks impacts memory formation. Here, three experiments interspersed DE and CD trials with identical displays until the reporting stage. During each session, the frequency of trials of each task was altered to manipulate expectations of which task would be required. Expectation of a DE task led to an increase in the number of fixations during encoding and to more precise estimation. By contrast, expectation of a CD trial did not modulate CD accuracy. These results suggest that the precision with which information is encoded into VWM differs between these two tasks. This has implications for current theoretical debates on VWM and underscores the importance of the typically overlooked effect of task type on memory performance. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Attentional priority is determined by predicted feature distributions.

Visual attention is often characterized as being guided by precise memories for target objects. However, real-world search targets have dynamic features that vary over time, meaning that observers must predict how the target could look based on how features are expected to change. Despite its importance, little is known about how target feature predictions influence feature-based attention, or how these predictions are represented in the target template. In Experiment 1 (N = 60 university students), we show observers readily track the statistics of target features over time and adapt attentional priority to predictions about the distribution of target features. In Experiments 2a and 2b (N = 480 university students), we show that these predictions are encoded into the target template as a distribution of likelihoods over possible target features, which are independent of memory precision for the cued item. These results provide a novel demonstration of how observers represent predicted feature distributions when target features are uncertain and show that these predictions are used to set attentional priority during visual search. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Object-based visual working memory: an object benefit for equidistant memory items presented within simple contours

Previous research has shown that more information can be stored in visual working memory (VWM) when multiple items belong to the same object. Here, in four experiments, we investigated the object effect on memory for spatially equidistant features by manipulating simple, task-irrelevant contours that combined these features. In Experiments 1, 3, and, 4, three grating orientations, and in Experiment 2, one color and two orientations, were presented simultaneously to be memorized. Mixture modeling was applied to estimate both the precision and the guess rates of recall errors. Overall results showed that two target features were remembered more accurately when both were part of the same object. Further analysis showed that the probability of recall increased in particular when both features were extracted from the same object. In Experiment 2, we found that the object effect was greater for features from orthogonal dimensions, but this came at the cost of lower memory precision. In Experiment 3, when we kept the locations of the features perfectly consistent over trials so that the participants could attend to these locations rather than the contour, we still found object benefits. Finally, in Experiment 4 when we manipulated the temporal order of the object and the memory features presentations, it was confirmed that the object benefit is unlikely to stem from the strategical usage of object information. These results suggested that the object benefit arises automatically, likely at an early perceptual level.

The Neural Mechanism Underlying Visual Working Memory Training and Its Limited Transfer Effect.

Visual working memory (VWM) training has been shown to improve performance in trained tasks with limited transfer to untrained tasks. The neural mechanism underlying this limited transfer remains unknown. In the present study, this issue was addressed by combining model-fitting methods with EEG recordings. Participants were trained on a color delay estimation task for 12 consecutive 1-hr sessions, and the transfer effect was evaluated with an orientation change detection task. The EEG responses during both tasks were collected in a pretraining test, a posttraining test conducted 1 day after training, and a follow-up test conducted 3 months after training. According to our model-fitting results, training significantly improved the capacity but not the precision of color working memory (WM), and this capacity improvement did not transfer to the orientation change detection task, spatial 2-back task, symmetry span task, or Raven reasoning test. The EEG results revealed that training resulted in a specific and sustained increase in parietal theta power suppression in the color WM task, which reflected individual color WM capacity. In contrast, the increase in parietal-temporal alpha power, which reflected individual orientation WM capacity, did not change with training. Together, these findings suggest that the simultaneous change of stimulus type and task structure would modulate the cognitive and neural substrates of WM tasks and introduce additional constraints for the transfer of WM training.

Daily fluctuations in children’s working memory accuracy and precision: Variability at multiple time scales and links to daily sleep behavior and fluid intelligence

Children often experience better and worse days when performing cognitive tasks. Whether such fluctuations are systematic and how they are linked to fluctuations at faster time scales within days is less clear. To fill these gaps, we probed N = 108 fifth graders on WM tasks twice daily in morning and afternoon sessions, and also assessed nightly sleep behavior, over a period of four weeks using ambulatory assessment. Children systematically fluctuated in their recall of visuospatial and numerical information in WM across multiple time scales. These fluctuations showed consistencies but also discrepancies among each other. Especially, fast variability of memory precision across moments was related to load and fluid intelligence. Daily WM accuracy was positively coupled to sleep quality, but only in a subset of children with larger daily WM fluctuations. We propose that short-term WM fluctuations and their couplings to other time-varying constructs could help to explain long-term cognitive development. • Children show systematic intra-individual working memory (WM) fluctuations. • WM load particularly affected the rapid item-to-item variability of recall precision. • Lower momentary recall variability was linked to higher levels in fluid intelligence. • Nightly sleep quality predicted higher daily WM accuracy, but only in a subset of children. • These dynamics emphasize a nuanced distinction of faster and slower WM variability.

Perceptual comparisons modulate memory biases induced by new visual inputs.

It is well-established that stimulus-specific information in visual working memory (VWM) can be systematically biased by new perceptual inputs. These memory biases are commonly attributed to interference that arises when perceptual inputs are physically similar to VWM contents. However, recent work has suggested that explicitly comparing the similarity between VWM contents and new perceptual inputs modulates the size of memory biases above and beyond stimulus-driven effects. Here, we sought to directly investigate this modulation hypothesis by comparing the size of memory biases following explicit comparisons to those induced when new perceptual inputs are ignored (Experiment 1) or maintained in VWM alongside target information (Experiment 2). We found that VWM reports showed larger attraction biases following explicit perceptual comparisons than when new perceptual inputs were ignored or maintained in VWM. An analysis of participants' perceptual comparisons revealed that memory biases were amplified after perceptual inputs were endorsed as similar-but not dissimilar-to one's VWM representation. These patterns were found to persist even after accounting for variability in the physical similarity between the target and perceptual stimuli across trials, as well as the baseline memory precision between the distinct task demands. Together, these findings illustrate a causal role of perceptual comparisons in modulating naturally-occurring memory biases.

Is Categorization in Visual Working Memory a Way to Reduce Mental Effort? A Pupillometry Study

Recent studies on visual working memory (VWM) have shown that visual information can be stored in VWM as continuous (e.g., a specific shade of red) as well as categorical representations (e.g., the general category red). It has been widely assumed, yet never directly tested, that continuous representations require more VWM mental effort than categorical representations; given limited VWM capacity, this would mean that fewer continuous, as compared to categorical, representations can be maintained simultaneously. We tested this assumption by measuring pupil size, as a proxy for mental effort, in a delayed estimation task. Participants memorized one to four ambiguous (boundaries between adjacent color categories) or prototypical colors to encourage continuous or categorical representations, respectively; after a delay, a probe indicated the location of the to‐be‐reported color. We found that, for memory load 1, pupil size was larger while maintaining ambiguous as compared to prototypical colors, but without any difference in memory precision; this suggests that participants relied on an effortful continuous representation to maintain a single ambiguous color, thus resulting in pupil dilation while preserving precision. Strikingly, this effect gradually inverted, such that for memory load 4, pupil size was smaller while maintaining ambiguous and prototypical colors, but memory precision was now substantially reduced for ambiguous colors; this suggests that with increased memory load participants increasingly relied on categorical representations for ambiguous colors (which are by definition a poor fit to any category). Taken together, our results suggest that continuous representations are more effortful than categorical representations and that very few continuous representations (perhaps only one) can be maintained simultaneously.

Memory resources recover gradually over time: The effects of word frequency, presentation rate, and list composition on binding errors and mnemonic precision in source memory.

Normative word frequency has played a key role in the study of human memory, but there is little agreement as to the mechanism responsible for its effects. To determine whether word frequency affects binding probability or memory precision, we used a continuous reproduction task to examine working memory for spatial positions of words. In three experiments, after studying a list of five words, participants had to report the spatial location of one of them on a circle. Across experiments we varied word frequency, presentation rate, and the proportion of low-frequency words on each trial. A mixture model dissociated memory precision, binding failure, and guessing rate parameters from the continuous distribution of errors. On trials that contained only low- or only high-frequency words, low-frequency words led to a greater degree of error in recalling the associated location. This was due to a higher word-location binding failure and not due to differences in memory precision or guessing rates. Slowing down the presentation rate eliminated the word frequency effect by reducing binding failures for low-frequency words. Mixing frequencies in a single trial hurt high-frequency and helped low-frequency words. These findings support the idea that word frequency can lead to both positive and negative mnemonic effects depending on a trade-off between an HF encoding advantage and a LF retrieval cue advantage. We suggest that (1) low-frequency words require more resources for binding, (2) that these resources recover gradually over time, and that (3) binding fails when these resources are insufficient. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Forgetting in visual working memory: Internal noise explains decay of feature representations.

The precision of visual working memory (VWM) representations decreases as time passes. It is often assumed that VWM decay is random and caused by internal noise accumulation. However, forgetting in VWM could occur systematically, such that some features deteriorate more rapidly than others. There exist only a few studies testing these two models of forgetting, with conflicting results. Here, decay of features in VWM was thoroughly tested using signal detection theory methods: psychophysical classification images, internal noise estimation, and receiver operant characteristic (ROC). A modified same–different memory task was employed with two retention times (500 and 4000 ms). Experiment 1 investigated VWM decay using a compound grating memory task, and Experiment 2 tested shape memory using radial frequency patterns. Memory performance dropped some 15% with increasing retention time in both experiments. Interestingly, classification images showed virtually indistinguishable weighting of stimulus features at both retention times, suggesting that VWM decay is not feature specific. Instead, we found a 77% increase in stimulus-independent internal noise at the longer retention time. Finally, the slope of the ROC curve plotted as z-scores was shallower at the longer retention time, indicating that the amount of stimulus-independent internal noise increased. Together these findings provide strong support for the idea that VWM decay does not result from a systematic loss of some stimulus features but instead is caused by uniformly increasing random internal noise.

0110 Nap-Related Change in Memory Precision may be Related to Slow-Wave Sleep in Early Childhood

Abstract Introduction In early childhood (3-5 years), naps comprise part of children’s 24-hr sleep. Naps support some types of learning (declarative, emotional), enhancing children’s ability to correctly identify previously seen items. During this time, children’s ability to form precise memories also improves, likely due to ongoing hippocampal development and maturation of processes allowing for pattern separation. Whether naps support the ability to form precise memory representations, allowing children to discriminate between previously seen vs. similar but novel items, is unclear. Here, we used a mnemonic similarity task to examine whether daytime naps support children’s recall of specific images more so than a period of wake. Further, we tested whether this nap-related improvement persists across overnight sleep. We hypothesized that task improvement would be associated with slow-wave sleep (SWS), as this stage has been shown to support episodic memory in preschool-aged children. Methods Participants (N=7, 4 females, Mage=56.1 mos) encoded items in the morning, verbally categorizing each image as something they would find “inside” or “outside”. They recalled items at three time points: immediately following encoding, after their nap/wake period, and the following morning after overnight sleep. Recall involved being shown a single image and responding whether it had been previously seen or not. Recall items included targets, foils, and lures. PSG was recorded during the nap and overnight sleep bouts. Results When controlling for age, children forgot fewer target items following a nap than a comparable period of wake (p=.05). Following a nap and overnight sleep, children also exhibited marginally less forgetting of target items than following a period of wake and overnight sleep (p=.102). Lure discrimination index (LDI; false alarm lures minus false alarm foils) did not differ between nap and wake conditions. Change in target recall following the nap was associated with SWS% during the nap (r=.96, p=.01), but not nap duration (p=.27). Conclusion Napping supported children’s ability to recall target items, but not to correctly reject lures, suggesting naps’ benefit towards more generalized memory. Nap SWS% was associated with less forgetting of target items, supporting its role in hippocampal-dependent memory consolidation. Analyses of overnight sleep data and inclusion of more participants may help better elucidate the relationship between preschool children’s sleep and memory development. Support (If Any) NSF BCS 1749280 NIH R21 HD094758 NIH R01 HL111695

Long-term memory interference is resolved via repulsion and precision along diagnostic memory dimensions

When memories share similar features, this can lead to interference, and ultimately forgetting. With experience, however, interference can be resolved. This raises the important question of how memories change, with experience, to minimize interference. Intuitively, interference might be minimized by increasing the precision and accuracy of memories. However, recent evidence suggests a potentially adaptive role for memory distortions. Namely, similarity can trigger exaggerations of subtle differences between memories (repulsion). Here, we tested whether repulsion specifically occurs on feature dimensions along which memories compete and whether repulsion is predictive of reduced memory interference. To test these ideas, we developed synthetic faces in a two-dimensional face space (affect and gender). This allowed us to precisely manipulate similarity between faces and the feature dimension along which faces differed. In three experiments, participants learned to associate faces with unique cue words. Associative memory tests confirmed that when faces were similar (face pairmates), this produced interference. Using a continuous face reconstruction task, we found two changes in face memory that preferentially occurred along the feature dimension that was “diagnostic” of the difference between face pairmates: (1) there was a bias to remember pairmates with exaggerated differences (repulsion) and (2) there was an increase in the precision of feature memory. Critically, repulsion and precision were each associated with reduced associative memory interference, but these were statistically dissociable contributions. Collectively, our findings reveal that similarity between memories triggers dissociable, experience-dependent changes that serve an adaptive role in reducing interference.

Motivation improves working memory by two processes: Prioritisation and retrieval thresholds

Motivation can improve performance when the potential rewards outweigh the cost of effort expended. In working memory (WM), people can prioritise rewarded items at the expense of unrewarded items, suggesting a fixed memory capacity. But can capacity itself change with motivation? Across four experiments (N = 30–34) we demonstrate motivational improvements in WM even when all items were rewarded. However, this was not due to better memory precision, but rather better selection of the probed item within memory. Motivational improvements operated independently of encoding, maintenance, or attention shifts between items in memory. Moreover, motivation slowed responses. This contrasted with the benefits of rewarding items unequally, which allowed prioritisation of one item over another. We conclude that motivation can improve memory recall, not via precision or capacity, but via speed-accuracy trade-offs when selecting the item to retrieve.

Reward and loss incentives improve spatial working memory by shaping trial-by-trial posterior frontoparietal signals

Integrating motivational signals with cognition is critical for goal-directed activities. The mechanisms that link neural changes with motivated working memory continue to be understood. Here, we tested how externally cued and non-cued (internally represented) reward and loss impact spatial working memory precision and neural circuits in human subjects using fMRI. We translated the classic delayed-response spatial working memory paradigm from non-human primate studies to take advantage of a continuous numeric measure of working memory precision, and the wealth of translational neuroscience yielded by these studies. Our results demonstrated that both cued and non-cued reward and loss improved spatial working memory precision. Visual association regions of the posterior prefrontal and parietal cortices, specifically the precentral sulcus (PCS) and intraparietal sulcus (IPS), had increased BOLD signal during incentivized spatial working memory. A subset of these regions had trial-by-trial increases in BOLD signal that were associated with better working memory precision, suggesting that these regions may be critical for linking neural signals with motivated working memory. In contrast, regions straddling executive networks, including areas in the dorsolateral prefrontal cortex, anterior parietal cortex and cerebellum displayed decreased BOLD signal during incentivized working memory. While reward and loss similarly impacted working memory processes, they dissociated during feedback when money won or avoided in loss was given based on working memory performance. During feedback, the trial-by-trial amount and valence of reward/loss received was dissociated amongst regions such as the ventral striatum, habenula and periaqueductal gray. Overall, this work suggests motivated spatial working memory is supported by complex sensory processes, and that the IPS and PCS in the posterior frontoparietal cortices may be key regions for integrating motivational signals with spatial working memory precision.

Determinants of quality, specificity, and stability of emotional episodic memories in a fine-dining context

For theoretical and practical reasons, it is of great interest to understand how accurate and persistent episodic memories of enjoyable experiences are formed and maintained, for example, in the context of gastronomy and other instances of experience design. Here, we investigated factors that might affect the quality (a measure of coherence) of immediate and long-term emotional episodic memories of individual dishes of a long and complex dinner in a fine-dining restaurant. We also assessed long-term recognition memory for pictures of the dishes. Intra-class correlations revealed good immediate emotional episodic memory, which remained stable over three months. Contributing factors to these kinds of memory were assessed with path modelling. The quality of emotional episodic memory was enhanced by the hedonic intensity of the most valued dishes during the meal and was impaired with the hedonic intensity of the least valued dishes. Enjoying the final dish positively affects emotional memory after the experience. Interestingly, when diners reported to have been distracted from the meal, presumably by communicating with their meal companions about the food, it had a positive effect on the long-term emotional episodic memory. Personality traits of the diners had no substantial impact on either type of memory. Alcohol intake during the meal modestly affected recognition memory but – interestingly – had no statistically significant effect on emotional episodic memory. Altogether, this study provides novel information about the main determinants of the precision and temporal stability of emotional episodic memory and nonemotional recognition memory for a meal. These findings contribute to the psychological foundations of designing memorable experiences in gastronomy and other areas. Implications for gastronomyKnowing what factors may determine whether a gastronomic experience would be memorable to diners is the holy grail of any chef. The design of a gastronomic experience should provide intense emotional moments to the diners aiming to increase the quality of emotional memory of those moments. Different factors contribute to this stability, for instance, how the diner interacts with the food and the food itself. In this regard, serving in a dining course very tasty and less delicious dishes thereafter can enhance the memorability of the former, but not so much of the latter, as it may be disturbing for the diner. Critically, enjoying the final dish positively affects emotional memory after the experience. In addition, most gastronomic events are shared with companions. Far from being a distracting element, social relationships in a table seem to increase the memorability of the experience, as communication deeply elaborates and reinforces memory traces. In the reinforcement of emotional memories for foods, alcohol has a negligible effect. Although our findings have been obtained in a fine-dining context, the implications of our current findings might be generalizable to other, more standard contexts. The critical point is to focus on having positive specific episodes rather than having a positive global valuation. All these outcomes would converge to increase the probability of repeating the gastronomic experience, regardless of whether it is a high-level restaurant or a standard one.

Episodic Memory Precision and Reality Monitoring Following Stimulation of Angular Gyrus.

The qualities of remembered experiences are often used to inform "reality monitoring" judgments, our ability to distinguish real and imagined events. Previous experiments have tended to investigate only whether reality monitoring decisions are accurate or not, providing little insight into the extent to which reality monitoring may be affected by qualities of the underlying mnemonic representations. We used a continuous-response memory precision task to measure the quality of remembered experiences that underlie two different types of reality monitoring decisions: self/experimenter decisions that distinguish actions performed by participants and the experimenter and imagined/perceived decisions that distinguish imagined and perceived experiences. The data revealed memory precision to be associated with higher accuracy in both self/experimenter and imagined/perceived reality monitoring decisions, with lower precision linked with a tendency to misattribute self-generated experiences to external sources. We then sought to investigate the possible neurocognitive basis of these observed associations by applying brain stimulation to a region that has been implicated in precise recollection of personal events, the left angular gyrus. Stimulation of angular gyrus selectively reduced the association between memory precision and self-referential reality monitoring decisions, relative to control site stimulation. The angular gyrus may, therefore, be important for the mnemonic processes involved in representing remembered experiences that give rise to a sense of self-agency, a key component of "autonoetic consciousness" that characterizes episodic memory.

Does motor noise contaminate estimates of the precision of visual working memory?

ABSTRACT The continuous-report task, in which subjects report the colour of a visual working memory representation by clicking on a colour wheel, has become the gold standard for measuring the precision of representations stored in visual working memory. This task requires fine motor control, typically with a mouse, but the precision of responses have been interpreted as being entirely due to the precision of the memory representations. Here we tested the possibility that motor noise contaminates our estimates in the continuous-report task by simply asking subjects to complete the task using either their dominant or non-dominant hand on different blocks of trials. We found that subjects took longer with their non-dominant hand, but this did not affect the precision of their responses. Our findings suggest that this commonly used task to study visual memory may be relatively immune from contamination by motor noise at the output stage.